AAE 421

Jordan Simonson

Jordan Simonson AAE 421 Homework 1 Redo1 Redo AAE 421 Homework

BS and “truth”

Formatted: Font: 36 pt

Functions Formatted: Right Formatted: Left

Managerial Economics is Life “Managerial Economics is Life!” Life can be summed up in many ways: time, worth, family. Many expressions can explain life, but it is very rare to come across something that “is” life. This statement is essentially stating: managerial economics=life. It is an equation to live by, in a true economic sense. Managerial economics is the “cost” of life, “the use of economic analysis to make business decisions involving the best use of an organization’s scarce resources.” In the sense of myself as a business, I make business decisions daily, deciding what is the best use of my time in order to increase profitability. Life is my “revenue.” I gain fulfillment/income, not only from working at a job, but also from my family, hobbies and other important life values. I will continue to produce my output, which is homework, until my marginal managerial economic cost is equal to my marginal revenue of life, MR=MC. The Alpha Wow, there is a lot packed into that one equation, MR=MC. Does that really capture what we were set out to do as freshmen at the University of

Formatted: Font: Bold

Formatted: Indent: First line: 0.5"

Jordan Simonson AAE 421 Homework 1 Redo Wisconsin-Madison. We were given the task to “gain knowledge, take responsibility, establish relationships, learn university values, etc.” We were charged with getting to know who we are, knowing our personal strengths and values. These two main goals for our educational endeavors, gaining more knowledge and a sense of knowing yourself, are reflected in this MEIL philosophy. Everything that I was supposed to learn, about myself and general knowledge, is a part of managerial economics and life. For example, I was to gain skills in thinking critically, analytically and integratively, which has led to several costs in time and opportunity cost. I could be out in the world making money, but am instead in college going into debt. At the same time by being able to think critically, analytically and integratively, I get more enjoyment out of life and its problems. here in college, I will be able to transfer those skills to the working world and get a better job, spreading the fixed costs. This will allow me to make back the money I have lost in opportunity cost and time while in college.

I College has also allowed me tocan think through problems critically and come up with better answers to those problems. Making myself more efficient and increasing my time with my family and friends.

Figure 1 Insourcing, Outsourcing and

Formatted: Font: (Default) Times New Roman, 12 pt Formatted: Right

Opensourcing

Formatted: Font: (Default) Times New Roman, 12 pt, Bold Formatted: Font: Bold

With this notion of “knowing yourself,” I can understand what my limitations are. I am learning how to

Formatted: Font: Bold

Figure 2

Formatted: Indent: First line: 0.5" Formatted: Font: (Default) Times New Roman, 12 pt Formatted: Right

Jordan Simonson AAE 421 Homework 1 Redo minimize my transaction cost and operating costs. I am finding my personal balance between insourcing, outsourcing and opensourcing. Insourcing is using a resource from inside your company, while outsourcing is using a resource from outside of your company. Opensourcing is an extended version of outsourcing where you use collaboration among outside members to work together to find an answer. Figure 1 is a pictoral interpretation of insourcing, outsourcing and opensourcing. My sources of outsourcing, (i.e. professors, students, etc) and opensourcing (i.e. working in groups, class discussion, etc.) are how I learn and increase my efficiency to produce my product, of homework. Professors give me information and it is enriched by information from students and mentors that lead me to be more efficient at producing homework, increasing my “bandwidth.” I insource as well, using intuition and what I have learned in the past to also increase “bandwidth” while producing homework. This can include knowing how Figure 2 to write an essay, use a computer and

Formatted: Font: (Default) Times New Roman, 12 pt Formatted: Right

knowing what style of note-taking works best for me. Figure 2 gives a good demonstration of optimizing insourcing, outsourcing and opensourcing to reduce costs, something I do well. After all, you as a professor and me as a student are in a four market system.

Formatted: Font: (Default) Times New Roman, 12 pt

Jordan Simonson AAE 421 Homework 1 Redo Formatted: Font: Bold

The Four Markets 4 Markets Student Professor

Buy

Sell

BS & “t”

Homework

Homework

Value-Added Truth

You are buying homework, which I am trying to sell to you right now.

How much of your value-added “truth” I give you in this homework is how well I get paid for this process, how good of a letter grade I can get. If I increase the amount of “truth” I can also increase the amount of demand for my product, thus increasing the price for my product. The demand for my product is high as long as I am selling a quality product. On the other side, you are trying to sell me an

Formatted: Font: (Default) Times New Roman, 12 pt

attitude, a value-added “truth.” I am buying BS and “truth,” also commonly called information received from a “crazy” professor. There is a lot of value-added “truth” in what you are saying, but I have to wade through all of the BS you are saying as well. I have a variable cost for the homework I am selling in the amount of time it takes me to complete the homework and. My fixed costs are the cost of time to get BS and “truth” from you. The and the cost of my undergraduate instructional, books, tuition, rent and food are all my fixed costs.

Your variable cost, which I should know because I know who I am selling and buying from, is the amount of time it takes you to grade my homework, and come up with a lesson plan and . Your fixed cost is the amount of time it takes you to deliver your “attitude” or your value-added “truth.”

Formatted: Indent: First line: 0"

Jordan Simonson AAE 421 Homework 1 Redo My Total Cost Figure 3 The total cost of my instruction is

Formatted: Font: Bold Formatted: Font: (Default) Times New Roman, 12 pt, Bold Formatted: Right

$4,296.00, which adjusted for this class

Formatted: Font: (Default) Times New Roman, 12 pt

would be $1,074.00. I am paying you a

Formatted: Font: (Default) Times New Roman, 12 pt, Bold

fixed cost of over $1,000 and an average variable cost. I must be covering my average variable cost because I must cover mby average variable cost in order to still be in business. I am doing this by using financial aid, loans, grants and scholarships to pay for my college tuition initially. Over time, I will pay back my loans, covering my fixed costs with the future money I will make at my job.

My Four Inputs

Formatted: Font: Bold Formatted: Indent: First line: 0"

As mentioned before my variable costs are my time spent on creating this homework. I have four key inputs which affect the total variable cost of creating this homework: labor, capital, managerial and entrepreneurial abilities/skills. My labor costs are the amount of time I am giving up to complete this homework. It is my opportunity cost, the cost of me being able to sleep right now, work on other homework or actually gain a wage by working. The cost of my physical capital is the depreciation cost for using my computer. My human capital cost is the value of my sanity after completing this homework, which. What are the residual effects of doing this homework. My managerial input requires me to use my time wisely and effectively. It is a systematic process of getting this homework done,

Jordan Simonson AAE 421 Homework 1 Redo which will get better as I discover where to use my time in creating future homework assignments. My entrepreneurial skills/abilities come out in deciding where this homework assignment should go. What risks to take with my jokes, what I should and shouldn’t include and my intuition of what you want put in this assignment. If I do not manage my input wisely, I could spend wasted time on this assignment and reduce efficiency, essentially losing me time and money. By increasing my Marginal Product of Labor (MPL) I can move to maximizeizing the amount of “truth/hour” I can produce.

AAE 421 Firm Objectives as It Applies to My Omega

Formatted: Indent: First line: 0" Formatted: Font: Bold

My AAE 421 firm objectives are representative of these assumptions. My main objective is to increase my MPL. Be able to generate more “truth”/hour. I will do this by learning new tasks along the way, such as how to better use excel and what you want for your homework. This will help me increase long-term profits by increasing efficiency and using “problem solving skills” when using excel and learning about my future manager work styles and be able to work with them. To reduce my internal costs, I would prefer to outsource/opensource most of my inputs by going to classes and participate in lab. I have already paid for this class so I should go to class to reduce the amount of internal costs that I incur, thus spreading my fixed costs minimizing my total cost. To maximize short-term profits I would also like to maximize my efficiency which will help me either increase my grade or keep it constant as I reduce the amount of time needed to complete homework and studying. These objectives will feed into my overarching objective of long-term profitability by getting a job in the marketing field.

Formatted: Font: Bold

Jordan Simonson AAE 421 Homework 1 Redo By being able to use excel and have a greater knowledge of AAE, I will be able to bring a sense of economics to the world of marketing, something many people in marketing do not have. This will make me more marketable to future companies as I can give them a greater economic sense. Being able to do these things will allow me to more effectively pay off my debt and begin saving for the future. As I enter the Omega of my collegiate career, I know I will be fluent in the goals set forth from my capstone experience. Developing problem solving skills (insourcing), teamwork (opensourcing), and finding information (outsourcing), all things important to my end goals and career paths.

Jordan Simonson Simonson AAE 421Jordan Homework 2 2/13/20122-3 AAE 421 Homework 2/13/2012

“BS� and Truth

Functions While choosing which cost function is optimal for yourself, there are several things to keep in mind including the breakeven and shutdown points.

Knowing these objectives can point you to a more efficient business model by allowing you to assess where you should go with your business, or in the case of a person, human capital.

While going through the steps to take while assessing various cost functions, we will use these three cost functions as examples: Cubic: TC=1500+300Q- 25Q2+1.5Q3 Quadratic: TC=1500+300Q+25Q2 Linear: TC=1500+300Q When faced with various cost functions, you should first find the average variable cost (AVC) in the short run for the shutdown, average cost (AC) in the long run for the breakeven point and (MC) marginal cost curves to find the maximum profit for each cost function. The average variable cost curve shows what is the variable cost with respect to a specific quantity produced (AVC=VC/Q). The average cost is the total cost, fixed and variable, for each respective quantity produced (AC=TC/Q). The MC is a measure of the change in total cost when the quantity produced increases by one unit (MC=dTC/dQ).

Below are the respective AVC, AC and MC curves for each of our cost functions.

AVC= AC= MC=

Cubic 300-25Q+1.5Q2 1500/Q+300-25Q+1.5Q2 300-50Q+4.5Q2

Quadratic 300+25Q 1500/Q+300+25Q 300+50Q

Linear 300 1500/Q+300 300

Jordan Simonson AAE 421 Homework 2 2/13/2012 You then need to find the shutdown point for each cost

Cubic Cost Functions

2000

AC=Average Cost

function, which is where output 1500

AVC=Average Variable Cost

Cost

(Q) reaches the minimum average

1000

variable cost or where MC=AVC.

500

If your revenues are less than the

0

minimum average variable cost,

0

5

you or your company should

10 (Q) 15 Output Output (Q)

20

Cost

either be more efficient or should

Shutdown (Q) = MIN AVC:

8.33

$196

shutdown. You should also find

Breakeven (Q) = MIN AC:

11.88

$341

the breakeven point, which is the minimum averagervariable cost.

If your revenues are at the

AC=Average Cost AVC=Average Variable Cost MC=Marginal Cost

1500

Cost

breakeven point, you are not

Quadratic Cost Functions

2000

making any profits, but are also not losing money. Both of these

1000 500 0 0

5

Output (Q)

10

points are important values to know in

15

20

Q

Cost

regard to your cost functions. Below

Shutdown (Q) = MIN AVC:

0.00

$300

are graphs representing your AVC, AC

Breakeven (Q) = MIN AC:

7.75

$687

and MC and tables illustrating the shutdown and breakeven points for each respective cost functions.

Jordan Simonson AAE 421 Homework 2 2/13/2012 To analyze this 2000

compare the cubic, quadratic

1500

and linear functions against

Linear Cost Functions AC=Average Cost AVC=Average Variable Cost MC=Marginal Cost

Cost

information, we must now

1000

each other for Total Cost,

500

AVC, AC and MC. Our total cost graph

0 0

5

Output (Q)

10

15

tells us that the quadratic

20

Q

Cost

curve increases at a faster rate for

Shutdown (Q) = MIN AVC:

1.00

$300

every additional output. It is not wise

Breakeven (Q) = MIN AC:

∞

$300

for this situation, to keep increasing your output if you had this quadratic function. The linear cost curve is a standard linear function, increasing by the same rate for every increase in output. The cubic function has the lowest total cost until it crosses with the linear function

16 and 18 outputs.

12000

Linear

You should use the

Quadratic

10000 Cost

somewhere between

Total Cost

14000

Cubic

8000

cubic function if Q* is

6000

less than 16. You

4000

should never use the

2000

quadratic function.

0 0

5

10 Output (Q)

15

20

When

comparing the average cost curves for these functions, it shows that all of the functions drastically decrease in average cost initially. The linear function is

Jordan Simonson AAE 421 Homework 2 2/13/2012

Average Cost Curve

2000

Linear Quadratic

decreasing rate as

Cubic

more outputs are

Cost

1500

decreasing at a

1000

created.

The cubic

and quadratic

500

functions eventually

0 0

5

10 Output (Q)

15

20

begin to increase at an

increasing rate. The average cost of the cubic function begins increasing after output is 12. The quadratic begins increasing after an output equal to 8. The average cost curve again has the lowest cost until the output level of about 16. If you are minimizing costs at Q*, you should never use the quadratic cost function.

The average variable cost curves continue the same pattern, where the cubic function has the lowest cost until the 16th output. The quadratic cost curve is a positively sloping linear average variable cost curve. One thing that is different about the linear average

800

constant as you

Linear

700

variable cost curve is

Cubic

Quadratic

600 500 Cost

that it remains

Average Variable Cost Curves

400 300 200

increase output. In other words, there is

100 0 0

no change in the

5

10 Output (Q)

15

average variable costs as you increase your outputs. Maximum profits are achieved if you minimize MC at Q*.

20

Jordan Simonson AAE 421 Homework 2 2/13/2012 The marginal cost curves show the cubic function decreasing until output reaches about 6. It then increases at an increasing rate. The quadratic function is increasing at a linear pace. The linear function remains constant as additional units of Q are added.

Marginal Cost Curves

1200 1000

that you should use the

Linear Quadratic Cubic

800 Cost

The MC curve shows

600

cubic function for Q* less than 12 if P* is

400

greater $196.

200 0 0

5

10 Output (Q)

15

20

Otherwise you should use the linear function.

Never use the quadratic function.

800.00 700.00 600.00

Comparison of Breakeven and Shutdown Costs Linear Quadratic Cubic

Costs

500.00 400.00 300.00 200.00 100.00 0.00 Shutdown

Breakeven

The shutdown cost for the cubic function is the lowest among the three functions.

The cubic function is the more desirable function in relation to the

Jordan Simonson AAE 421 Homework 2 2/13/2012 shutdown point because this means your AVC are minimized at the shutdown level for the cubicthe P* is the lowest. As far as a breakeven point, the linear function is more desirable because it will allow you to make a profit sooner as the AC can be the lowest with the linear function.

As my own personal firm, if I were to choose a cost function, it would depend solely on the definition of my output. If my output was larger than 16, I would use a linear function and if my output was less than 16, I would use the cubic function. For example, if my output was how many words I could write in one hour, I would want my cost function to be linear. This is because as I increase the number of words I write, my total cost would be less than all other cost functions because I can writer more than 16 words in an hour. If it were how many words can I write in half of a minute, I would want to use the cubic function because I cannot write more than 16 words in half of a minute. So, in the end it really depends on the definition of Q to determine my preferred cost function.

Formatted: Font: (Default) Times New Roman, 12 pt

Jordan Simonson AAE 421 Homework 2 2/13/2012

Cubic Cost Functions

2000 1800

AC=Average Cost

1600

AVC=Average Variable Cost

1400

MC=Marginal Cost

Cost

1200 1000 800 600 400 200 0 0

Output

5

TC=Total Cost

10

Output (Q) AC=Average Cost

15

20

AVC=Average Variable Cost

MC=Marginal Cost

300

300

0

1,500

1

1,777

1,777

277

255

2

2,012

1,006

256

218

3

2,216

739

239

191

4 5

2,396 2,563

599 513

224 213

172 163

6

2,724

454

204

162

7

2,890

413

199

171

8

3,068

384

196

188

9

3,269

363

197

215

10

3,500

350

200

250

11

3,772

343

207

295

12

4,092

341

216

348

13

4,471

344

229

411

14

4,916

351

244

482

15

5,438

363

263

563

16

6,044

378

284

652

Jordan Simonson AAE 421 Homework 2 2/13/2012

Linear Cost Functions

2000

AC=Average Cost AVC=Average Variable Cost MC=Marginal Cost

1800 1600 1400 Cost

1200 1000 800 600 400 200 0 0

5

10

15

20

Output (Q)

TC=Total AC=Average AVC=Average MC=Marginal Output Cost Cost Variable Cost Cost 0 1,500 300 300 1 1,800 1,800 300 300 2 2,100 1,050 300 300 3 2,400 800 300 300 4 2,700 675 300 300 5 3,000 600 300 300 6 3,300 550 300 300 7 3,600 514 300 300 8 3,900 488 300 300 9 4,200 467 300 300 10 4,500 450 300 300 11 4,800 436 300 300 12 5,100 425 300 300 13 5,400 415 300 300 14 5,700 407 300 300 15 6,000 400 300 300 16 6,300 394 300 300

Jordan Simonson AAE 421 Homework 2 2/13/2012

Total Cost

14000

Linear

12000

Quadratic

10000 Cost

Q 0 1 2 3 4 5 6 7

Cubic

8000 6000 4000 2000 0

5

10 Output (Q)

Q L Qu C 0 1 1,800 1,825 1,777 2 1,050 1,100 1,006 3 800 875 739 4 675 775 599 5 600 725 513 6 550 700 454 7 514 689 413 8 488 688 384 9 467 692 363 10 450 700 350 11 436 711 343 12 425 725 341 13 415 740 344 14 407 757 351 15 400 775 363 16 394 794 378

15

20

8 9 10 11 12 13 14 15 16

C 1,500 1,777 2,012 2,216 2,396 2,563 2,724 2,890

3,900 5,500 3,068 4,200 6,225 3,269 4,500 7,000 3,500 4,800 7,825 3,772 5,100 8,700 4,092 5,400 9,625 4,471 5,700 10,600 4,916 6,000 11,625 5,438 6,300 12,700 6,044

Average Cost Curve

2000

Linear Quadratic

1500

Cubic Cost

0

L Qu 1,500 1,500 1,800 1,825 2,100 2,200 2,400 2,625 2,700 3,100 3,000 3,625 3,300 4,200 3,600 4,825

1000 500 0 0

5

10 Output (Q)

15

20

Jordan Simonson AAE 421 Homework 2 2/13/2012

Average Variable Cost Curves

800

Linear

700

Cubic

600

Quadratic

Cost

500 400 300 200 100 0

Q 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

5

L Qu C 300 300 300 300 350 255 300 400 218 300 450 191 300 500 172 300 550 163 300 600 162 300 650 171 300 700 188 300 750 215 300 800 250 300 850 295 300 900 348 300 950 411 300 1,000 482 300 1,050 563 300 1,100 652

10 Output (Q)

15

20

L 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300

Qu 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650 675 700

C 300 277 256 239 224 213 204 199 196 197 200 207 216 229 244 263 284

Marginal Cost Curves

1200

Linear Quadratic

1000

Cubic

800 Cost

0

Q 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

600 400 200 0 0

5

10 Output (Q)

15

20

Quantities

Linear

Shutdown

Quadratic

Cubic

1.00

0.00

8.33

Breakeven

53687092.20

7.75

11.88

Costs

Linear

Quadratic

Cubic

Shutdown

300.00

300.00

195.83

Breakeven

300.00

687.30

340.96

Change from Base Cost

Linear

Quadratic

Base Cubic

Shutdown

104.17

104.17

195.83

Breakeven

-40.96

346.33

340.96

Change from Base Costs

Linear

Quadratic

Jordan Simonson AAE 421 Homework 2 2/13/2012

Base Cubic

Shutdown

0.53

0.53

0.00

Breakeven

-0.12

1.02

0.00

Comparison of Breakeven and Shutdown Cost 800.00 700.00 600.00

Linear Quadratic Cubic

Costs

500.00 400.00 300.00 200.00 100.00 0.00 Shutdown

Breakeven

Jordan Simonson AAE 421 Homework 2 2/13/2012

Quadratic Cost Functions

2000

Formatted: Font: (Default) +Body, 18 pt

AC=Average Cost

1800

AVC=Average Variable Cost

1600

MC=Marginal Cost

1400 Cost

1200 1000 800 600 400 200 0 0

5

10

15

20

Output (Q)

Output 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TC=Total AC=Average AVC=Average MC=Marginal Cost Cost Variable Cost Cost 1,500 300 300 1,825 1,825 325 350 2,200 1,100 350 400 2,625 875 375 450 3,100 775 400 500 3,625 725 425 550 4,200 700 450 600 4,825 689 475 650 5,500 688 500 700 6,225 692 525 750 7,000 700 550 800 7,825 711 575 850 8,700 725 600 900 9,625 740 625 950 10,600 757 650 1,000 11,625 775 675 1,050 12,700 794 700 1,100

Jordan Jordan Simonson Simonson AAE 421 Homework 2-4 Rewrite AAE 421 Homework 2-4 Rewrite 3/4/2012 3/4/2012

BS and “truth”

Functions What You Want to Know In using the given total cost functions and the given demand function from figure 1, I was able to evaluate that profit is mazimized for my company when using the cubic cost function with a Q* of 4.67 and a maximum short-run profit of $3,714.00.

How I Got There:

Fig. 1: Given Functions Cubic: TC=1500+300Q-25Q2+1.5Q3 Quadratic: TC=1500+300Q+25Q2 Linear: TC=1500+300Q Demand: Q=10-0.004P

My company, BS and “truth” Functions was given three cost functions and a demand function to maximize

my company’s profits. Each of these cost functions was representative of the total cost of producting my homework if I used a strategic collection of these variable cost inputs: labor, capital, managerial and entrepeneurial abilities/skills. My company’s total fixed costs between books, tuition, rent and food is $1,500.00.

The total revenue (TR) came out to 2

be: TR=2500Q-250Q . I was then able to use the profit equation of ∏=TR-TC to

Fig. 2: Profit Equations

∏C=-1500+2200Q-225Q2-1.5Q3 ∏Q=-1500+2200Q-275Q2 ∏L=-1500+2200Q-250Q2

give me the following profit equations in figure 2.

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012 Graph 1

Cubic Function

AR=P MR

5,000

MC=Marginal Cost

Price

the cubic cost P* and Q*

1,000

function. When

0 0

2

-1,000

4

6

8

10

MC=MR profit is maximized.

Output (Q)

Quadratic Function

AR=P

3,500

MR

3,000

MC=Marginal Cost

2,500

Profit



P*=$1,500



Q*=4 Graph 2 shows

2,000

P* and Q*

1,500

Price

us the P* and Q* for

1,000

the quadratic cost

500 0 0

2

4

6

8

10

function. When MR=MC profit is

-1,000

Quantity

Linear Function

maximized.

AR=P

5,000

MR MC=Marginal Cost

4,000



P*=$1,400



Q*=4.40

Profit

3,000

Graph 3 shows us

Prices

P* and Q*

2,000

the P* and Q* for the

1,000

linear cost function.

0 -1,000

Q*=4.67

us the P* and Q* for

2,000

Graph 3



Graph 1 shows

3,000

-500

P*=$1,332

Profit

4,000

Graph 2



0

2

4

6

Quantity

8

10

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012 Furhtermore, I was able to find when the marginal cost (MC) and marginal revenue (MR) intersect, showing the value of the maximum profit of each cost function. Graph 1, 2 and 3 shows where MR=MC and the related profit maximization point. Using these equations, I was able to maximize profits. As seen in graph 4, the cubic function retains the most profits in the company with the quadratic cost function resulting is the least profits.

Graph 4

Profits

5,000

Cubic

4,000

Quadratic

Linear

Dollars

3,000 2,000 1,000

QC> QL > QQ

0 0

2

4

-1,000

6

8

10

Output (Q)

Furhtermore, I was able to find when the marginal cost (MC) and marginal revenue (MR) intersect, showing the value of the maximum profit of each cost function. Table 1 shows the varying maximum profits for each cost function as illustrated by each MR equaling each respective MC and the first order condition (FOC) being equal to zero.

Table 1

Output

Profit

AR = P

MR

MC FOC 4.67 $3,714.23 $1,332.32 165 165 $0 Cubic 4.00 $2,900.00 $1,500.00 500 500 $0 Quadratic The original equilibrium is with a –Q of 1,000 units and a P of $200. As 4.40 $3,340.00 $1,400.00 300 300 $0 Linear

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012 The guarantee that these values are maximums and not minimums, the second order derivative was also taken, shown in

Fig. 3: SOSC Profit Equations ∏C’’=-450-9Q ∏Q’’=-550 ∏L’’=-500

Figure 3, showing us that these functions are indeed maximum points because they are negative.

Comparison Across Profit Functions Graph 5

MC Compared to AR and MR

3,000

MC-C

2,500

MC-Q

MC-L

AR=P

MR

2,000

P* and Q* and MAX ∏

Dollars

1,500 1,000 500 0 -500

0

2

4

-1,000



6

8

10

Output (Q)

MAX ∏ is the MIN (MC) at Q*

Graph 5 gives us a comparison of the MR and AR for the MC of each cost function. There is not a lot of variation between the output that represents the maximum profit for each cost function, but there is a big discreptancy for the actual profits.

Table 2 is comparing the profits over the three cost functions. My company resorting to this quadratic cost function, would lead to a more than 20 percent reduction in profits, something I am not willing to do. The linear cost function

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012 would result in a $374 loss in the short run. If your out put increased to be above 12 units, your profit would be maximized by using the linear cost function. It would be worth it to lose $374 in the short run to make more in the long-run.

Especially when you would still be making profits in the short-run by using the linear cost function.

Table 2

Quantities Profits Cubic Quadratic Linear

Change Profits

% Change Profits

4.67

$3714.00

$0

0.00%

4

$2900.00

-$814.00

-21.92%

4.4

$3340.00

-$374.00

-10.07%

Table 3 shows the optimals prices over the three cost functions. With these cost functions and this demand function, selling more product at a cheaper price will result in an increase in profit. The optimal choice for the quadratic cost function results in an over 12 percent increase in the price and selling less output.

The linear cost function would result in a 5 percent increase in costs, with a reduced output of 4.4.

Table 3

Quantities Prices Cubic Quadratic Linear

Change Prices % Change Prices 0% $0

4.67

$1,332.00

4

$1,500.00

$168.00

13%

4.4

$1,400.00

$68.00

5%

Managerial Economics is Life From this data analysis, it was a simple decision toyou should choose the cubic cost function in the short run. and long run for the correct use of my variable and fixed costs.However, if you know you would like to raise your output above 12 units, you may want to forgo profits for the first 12 units to gain profits in the long run using the linear cost function. This makes sense because

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012 the more you use your inputs of: labor, capital, managerial and entrepeneurial abilities/skills, the more efficient you will be at using your time and getting homework done. I would want to produce and an output of about 4.67.

Homework 2-3 showed us the importance of using your MC and P* to find the breakeven and shutdown costs of my firm. This assignment allowed us to push the event further and find the MAX profits when MR=MC and then the respective P from the AR curve for each of these functions and the respective demand function.

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012

Appendix Cubic Cost Function

Cost = a + b*Q + c*Q^2 + d*Q^3 Total Cost = /

a+ 1500

b 300

*Q+ *Q+

c -25

*Q^2+ *Q^2+

d 1.5

*Q^3 *Q^3

b 300

+2*c -50

*Q+ *Q+

3*d 4.5

*Q^2 *Q^2

a' 2500

*Q+ *Q+

MC=dTC/dQ=

P = AR=

a' 2500

+b' -250

*Q *Q

Profit =

*Q+ -1500

2200

FOC: dΠ/dQ = 0

*Q+

AR=P 2,500 2,250 2,000 1,750 1,500 1,250 1,000 750 500 250 0

-450

*Q+

MR 2,500 2,000 1,500 1,000 500 0 -500 -1,000 -1,500 -2,000 -2,500

b' -250

*Q^2+ -225

*Q+ 2200

Q Profit 0 -1,500 1 474 2 1,988 3 3,035 4 3,604 5 3,688 6 3,276 7 2,361 8 932 9 -1,019 10 -3,500

TR =

*Q^2+ *Q^2

-4.5

MC 300 255 218 191 172 163 162 171 188 215 250

*Q^2

*Q^2 *Q^2

*Q^3 -1.5

*Q^3

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012

11 -6,522 12 -10,092 13 -14,221

-250 -500 -750

14 -18,916 -1,000 15 -24,188 -1,250 16 -30,044 -1,500

-3,000 -3,500 -4,000

295 348 411

-4,500 -5,000 -5,500

482 563 652

Q

Profit

AR = P

MR

MC

FOC

4.67

3,714

1,332

165

165

$0

4.67

3,714

1,332

165

165

$0

Quadratic Cost Function Cost = a + b*Q + c*Q^2 + d*Q^3 Total Cost =

a+ 1500

b 300

MC=dTC/dQ=

*Q+ *Q+ b

c 25 +2*c

*Q^2+ *Q^2+ *Q+

d 0 3*d

*Q^3 *Q^3 *Q^2

300

50

*Q+

0

*Q^2

Profit =

*Q+ 1500

2200

FOC: dΠ/dQ = 0

Profit -1,500 425 1,800 2,625

-275

*Q+ 2200

Q 0 1 2 3

*Q+

*Q^2+

AR=P 2,500 2,250 2,000 1,750

-550

MR 2,500 2,000 1,500 1,000

*Q+

MC 300 350 400 450

*Q^2+ *Q^2

0

*Q^2

*Q^3 0

*Q^3

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012 4 5 6 7 8 9 10 11 12 13

2,900 2,625 1,800 425 -1,500 -3,975 -7,000 -10,575 -14,700 -19,375

1,500 1,250 1,000 750 500 250 0 -250 -500 -750

500 0 -500 -1,000 -1,500 -2,000 -2,500 -3,000 -3,500 -4,000

500 550 600 650 700 750 800 850 900 950

14 15 16

-24,600 -30,375 -36,700

-1,000 -1,250 -1,500

-4,500 -5,000 -5,500

1,000 1,050 1,100

Q

Profit

AR = P MR

MC

4.00

2,900

1,500

500

500

4.00

2,900

1,500

500

500

FOC $0 $0

Linear Cost Function

Cost = a + b*Q + c*Q^2 + d*Q^3 Total Cost =

a+ 1500

b 300

MC=dTC/dQ=

P=

a'

+b'

*Q

2500

-250

*Q

*Q+ *Q+ b 300

TR=

c 0 +2*c 0

*Q^2+ *Q^2+ *Q+ *Q+

d 0 3*d 0

*Q^3 *Q^3 *Q^2 *Q^2

a'

*Q+

b'

*Q^2

2500

*Q+

-250

*Q^2

Jordan Simonson AAE 421 Homework 2-4 Rewrite 3/4/2012 Profit =

*Q+ -1500

2200

FOC: dΠ/dQ = 0

Profit

*Q+

-250

*Q+ 2200

Q

*Q^2+

-500

*Q^2+

*Q^3 0

*Q^2

*Q+

0

AR=P

MR

MC

*Q^2

0

-1,500

2,500

2,500

300

1

450

2,250

2,000

300

2

1,900

2,000

1,500

300

3

2,850

1,750

1,000

300

4

3,300

1,500

500

300

5

3,250

1,250

0

300

6

2,700

1,000

-500

300

7

1,650

750

-1,000

300

8

100

500

-1,500

300

9

-1,950

250

-2,000

300

10

-4,500

0

-2,500

300

11

-7,550

-250

-3,000

300

12

-11,100

-500

-3,500

300

13

-15,150

-750

-4,000

300

14

-19,700

-1,000

-4,500

300

15

-24,750

-1,250

-5,000

300

16

-30,300

-1,500

-5,500

300

Output

Profit

AR = P

MR

MC

FOC

4.40

3,340

1,400

300

300

$0

4.40

3,340

1,400

300

300

$0

*Q^3

Jordan Jordan Simonson Simonson AAE 421 Homework 3-4 Rewrite AAE 421 Homework 3-4 Rewrite 2/25/2012 2/26/2012

BS and “truth”

Functions What You Want to Know Using the given quantity demand (QD) and quantity supplied (QS) equations, my firm was able to map out its equilibrium prices and quantities in the short-run and long-run. The initial equilibrium was with a quantity (Q) of 1,000 units and a price of $200. In the short-run, equilibrium is with a Q of 1,250 units and a price of $225. In the long-run, equilibrium Q is 1,500 units and a price of $250.

Fig. 1: Given Functions QD1 = 3,000 – 10P QS1 = -1,000 + 10P QD2 = 3,500 - 10P QS2 = -500 + 10P

Comparitive Statics Analysis: My company, BS and “truth” Functions was given two QD and two QS functions as shown in Figure 1 to find the short-run and long-run equilibrium price and quantity. From these equations, I was able to derive a price equation for each as shown in Figure 2. In order to find the equilibrium you must then set

Fig. 2: Price Equations PD1= 300 – 0.1Q PS1= 100 + 0.1Q PD2= 350 – 0.1Q PS2= 50 + 0.1Q

each demand function equal to each supply function (i.e. QD1=QD2, QD2=QS1).

From this we were able to determine each respective equilibrium.

We assume that the model is currently in equilibrium with a Q of 1,000 units and a P of $200. As seen in Table 1, when comparing D1 and S1 at the Q of 1,000 units, you find that they are the same value of $200. This Q is representative of my first homework assignment. The Q was 1,000 units of homework at a P of $200.

Jordan Simonson AAE 421 Homework 3-4 Rewrite 2/25/2012 Moving to my short-run eqilibrium there was a change in the model when more knowledge was demanded and there was disequilibrium. When equilibrium was restablished, my Q was 1,250 units at a price of $225, as seen in Table 1 where S1 and D2 are at the same price at Q of 1,250. From this we can gather that there was a shortage of knowledge and my demand curve shifted to the right, or in the terms of my firm, the Table 1

Quantity 0 500 1000 1250 1500 2000 2500 3000 3500 4000

D1 300 250 200 175 150 100 50 0 -50 -100

S1 100 150 200 225 250 300 350 400 450 500

D2 350 300 250 225 200 150 100 50 0 -50

S2 50 100 150 175 200 250 300 350 400 450

demand was increased on the second homework.

The homework was more taxing, took longer and required more “bandwidth.� My supply

curve, however did not shift and so my cost increased. In the short-run I had to put in more time because I was increasing my bandwidth by learning things on excel, learning what you want in the homework and learning any holes in my economic know-how. I needed to devote more time, so I could be more efficient later.

You may also notice from Table 1 that at Q of 1,250 units, there may have been a surplus of knowledge where my cost was also at an equilibrium of $175 for D1 and S2. However, when using some economic intuitiion, we can infer that this cannot be an equilibrium for my firm because my time spent on my second homework was more than the time spent on homework 1. This would suggest

Jordan Simonson AAE 421 Homework 3-4 Rewrite 2/25/2012 that I had a surplus of knowledge, which I did not, so it is not a true equilibrium point for this situation.

After a time I had a surplus in knowledge causing disequilibrium in the long run. When equilibrium was reached my Q was 1,500 units and my price was $200. This is confirmed by using Table 1 where you can see that S2 and D2 is at a price of $200 with a Q of 1,500 units. This would suggest that the demand curve remained constant, but my supply curve shifted out, reducing my costs in the long-run. My third homework took me considerably less time and I understood it much better. The lab was much easier to understand and I was now becoming fluent in excel. These things allowed me to increase my quantity, while requiring less cost than my short-tun equilibrium, thus increasing my firm’s efficiency.

If you then graph these equations, as seen in Graph 1, you can then see that these equilibriums are congruant with the equilibriums present on the graph.

600

Graph 1

Equilibrium Prices and Quantities

500 400

D1

Costs

300

S1

200

D2

100

S2

0 -100 -200

0

500

1000

1250

1500

2000

Quantities

2500

3000

3500

4000

Jordan Simonson AAE 421 Homework 3-4 Rewrite 2/25/2012 When comparing the original equilibrium point to the long-run equilibrium point, we can see that the costs are the same, but the output has increased. My firm increased its MPL to produce a higher Q at the same P. By increasing my MPL, I was then able to decrease my marginal cost and increase my firm’s profits.

Managerial Economics is Life When looking at my short-run life, I can see that my demand curve has significantly shifted outwards. I have a 20 hour weekly job, am involved in two student organizations, have college and am married. I have a lot of responsibility and things that need to be completed in a week. At times, I have had to grind through a week just to get everything done, maybe not the most efficient way, but got things done. My costs right now are very high and the homework that is worth my time is very limited. My time is at a premium. However, I have increased my efficiency tremendously. I learn what I need to do to get a good grade in a class quickly in the semester, create a schedule and get things done. It is how I am most efficient at this time.

In the long-run, this will change. I will become more efficient and be able to complete more things in a shorter amount of time, while maintaining the same quality. I am putting in the time now, so I can be more efficient in the future. Just like I had to put in time to learn excel for this class and now my future homework assignments. While these assignments may take the same amount of time as before, because I have learned excel this homework will not take me as long as if I had done it in week one of my firm’s existance.

Jordan Simonson AAE 421 Homework 3-4 Rewrite 2/25/2012

Appendix Demand 1 Q= P=

ad1 3000 300 a'd1

bd1 -10 -0.1 b'd1

Demand 2 Q= P=

ad1 3500 350 a'd1

Quantity

D1 300 250 200 175 150 100 50 0 -50 -100

0 500 1000 1250 1500 2000 2500 3000 3500 4000 600

*P *Q

Supply 1 Q= P=

ad1 -1000 100 a'd1

bd1 10 0.1 b'd1

*P *Q

bd1 -10 -0.1 b'd1

*P *Q

Supply 2 Q= P=

ad1 -500 50 a'd1

bd1 10 0.1 b'd1

*P *Q

S1 100 150 200 225 250 300 350 400 450 500

D2 350 300 250 225 200 150 100 50 0 -50

Equil 1: Equil 2: Equil 3:

Q 1000 1250 1500

P 200 225 200

S2 50 100 150 175 200 250 300 350 400 450

Equilibrium Prices

500 400

Costs

300

D1 S1

200

D2 100

S2

0 0

500

1000

1250

1500

2000

-100 -200

Quantities

2500

3000

3500

4000

Jordan Simonson AAE 421 Homework 3-4 Rewrite 2/25/2012

Jordan Jordan Simonson Simonson AAE 421 Homework 3-6 3-6 AAE 421 Homework 3/3/2012 3/3/2012

BS and “truth”

Functions What You Want to Know

Fig. 1: Given Demand Function

Using the given demand function, Figure 1, and given conditions, Figure 2, my firm was able to find the maximum profit of Joy’s Frozen Yougurt, finding that she should increase her price by over 500 percent to $9.44. This price

Q = 200300P+120I+65T250AC+400AJ

increase allows advertising effectiveness to increase from a dismal $400 loss for every $1,000 of advertising to $2,775 profit for every $1,000 spent on advertising,

Q=number of cups served per week P=avg. price paid for each cup I=per capita income given market($1000) T=avg. outdoor temperature AC=Competition’s monthly advertising expenditures ($1,000) AJ=Joys’ own monthly advertising expenditures ($1,000)

a return on investment of 277.5 percent. When Joy’s Yogurt was faced with competitors increasing their advertising by $5,000, the only feasible option is to increase their advertising by $3,125 to remain at the same profit level. All other options were not feasible or reliable.

Maximum Current, Total Revenue and Profit Prices and Quantities: My company, BS and “truth” Functions was given a demand function and conditions to satisfy the demand function.

Graph 1

AR and MR Curve

20

P=$1.50 T=60˚F AJ=10

I=10 AC=15

AR MR

15

MR and AR curve in order to find the TR MAX Q and

10

Prices ($)

Fig. 2: Given Conditions

Graph 1 shows the

P.

TR MAX P

5

TR MAX

0

-5 -10

0

 TR MAX Q=2,775

500 1000 1500 2000 2500 3000 3500 4000 Quantity

 TR MAX P=$9.25

Jordan Simonson AAE 421 Homework 3-6 3/3/2012 Graph 2

20

Graph 2 shows the

AR and Profit Max Curve

15

AR Profit Max

MR and AR curve in

∏ MAX Q

Q and P.

order to find the ∏ MAX

Prices

10 ∏ MAX P

5 0 -5

0

500 1000 1500 2000 2500 3000 3500 4000

-10

Table 1

Quantity

SOSC

SOSC TR SOSC ∏

Values

-0.0033

-0.0033

 ∏ MAX Q=2,719  ∏ MAX P=$9.44

Table 1 shows the second order derivatives of the maximum TR and ∏.

Since both of these are negative we

know that these are for sure maximums.

Table 1 compares the current price with the TR mazimizing price and ∏ Table 2

maximizing price.

Current Price Max TR Max Profit Change TR Max vs. Current Change ∏ Max vs. Current % Change TR Max vs. current %Change ∏ Max vs. current

Quantity Price TR 5100 $1.50 $7,650.00 2775 $9.25 $25,668.75 2718.75 $9.44 $25,658.20 -2325 $7.75 $18,018.75 -2381.25 $7.94 $18,008.20 -45.59% 516.67% 235.54% -46.69% 529.17% 235.40%

Profit Elasticity $5,737.50 -0.09 $24,628.13 -1.00 $24,638.67 -1.04 $18,890.63 $18,901.17 329.25% 329.43%



∏ maximizing price has 329.43% increse in profits from the current price



∏ maximizing price shows a decrease of 46.60% of QD This table shows that Joy has seriously under-priced her frozen yogurt.

Her P* is $9.44 and Q* is 2,718.75 frozen yogurts assuming ceteris paribus

Jordan Simonson AAE 421 Homework 3-6 3/3/2012 conditions. Also notice, that the elasticity for TR is 1.00, showing that this is truly the maximum TR. Advertising Effectiveness Table 3

Advertising Effectiveness Current Price MAX TR MAX Profit

MRAdv= $1.50 $9.25 $9.4375

P* dQ/dA= ($400.00) $2,700.00 $2,775.00

MCADV= Breakeven dQ/dA Price 666.6666667 $2.50



$400 is lost for every $1,000 spent on advertising using the current price



$2,775.00 is gained for every $1,000 spent on advertising using P*



At price of $2.50, you will gain $1,000 for every $1,000 spent on advertising, the breakeven price for advertising

Table 3 shows us the effectiveness of our advertising. At the current price, advertising would not be an effective use of resources as it would lose Joy’s Yogurt money. This is due to not operating at an optimal price and quantity.

Whe operating at P* and Q*, advertising is very effective, the return on investment is 277.5%.

Elasticity Table 4

Elasticities Interpretation Own Price e= -0.0882 rel inelastic Income ($1000) e2= 0.23529 rel inelastic Avg. Temp e3= 0.76471 rel inelastic Comp Adv ($1000) e4= -0.7353 rel inelastic Own Adv ($1000) e5= 0.78431 rel inelastic #6 e6= 0 perfect in  All of these outlets are relatively inelastic 

Joy’s price is the most inelastic outlet

Jordan Simonson AAE 421 Homework 3-6 3/3/2012 

The most elastic outlet is our own advertising, even more than competitor advertising Table 4 is a representation of the elasticities for each outlet. As you can

see, all of these outlets are relatively inelastic. Changing the price is the most inelastic outlet in the demand function, meaning the demand function for this outlet is very close to vertical. There is not much of a demand change for an increase in price. Average temperature, even though it is relatively inelastic is one of the more effective ways of creating demand. If the temperature increases, you should expect demand to increase. Something interesting to note is that our advertising is more elastic than our competitors advertising. This means we can spend less money on advertising to get the same amount of demand as our

Fig. 3: New Conditions P=$1.50 T=60˚F AJ=10

I=10 AC=20

competitors.

Competitors Increase Advertising Joy’s Yogurt competitors have increase their advertising by $5,000. This has significantly hurt the demand and profit for Joy’s Yogurt.

Table 5 Current Price Max TR Max Profit Change TR Max vs. Current Change ∏ Max versus Current % Change TR Max versus current %Change ∏ Max versus current

Quantity Price TR 3850 $1.50 $5,775.00 2150 $7.17 $15,408.33 2093.75 $7.35 $15,397.79 -1700 $5.67 $9,633.33 -1756.25 $5.85 $9,622.79 -44.16% 377.78% 166.81% -45.62% 390.28% 166.63%

Profit Elasticity $4,331.25 -0.12 $14,602.08 -1.00 $14,612.63 -1.05 $10,270.83 $10,281.38 237.13% 237.38%



Joy’s Yogurt has lost over $10,000 in profits



P* has been reduced to $7.35 and Q* is reduced to 2093.75.



Elasticities for the current price and max profit increased

Jordan Simonson AAE 421 Homework 3-6 3/3/2012 Table 5 shows that the competitors increasing their advertising has led to a decrease in profits and a reduction in P* and Q*. The current price of $1.50 is still very low and Joy would benefit from increasing her price to $7.35, a 237.38% increase in profits.

Shocking the System

20

D1

Equilibrium 1

15

-10

causes fall in price to equilibrium 2

Quantity

5500

5000

4000

3500

3000

2500

As Graph 3 shows, the

2000

1500

1000

Equilibrium 2 0

-5

advertising creates surplus and

MC

500

Costs

0

Competitors increase in

D2

10 5



Demand Curves

4500

Graph 3

competitors increase in advertising has reduced the demand for Joy’s

Yogurt, creating a surplus in the market. Joy’s Yogurt was then reduced its price to $7.35 to reach equilibrium.

Table 6 Change Own Adv Change Own P Change Temp Change Income

Change $3,125 -$4.17 19.23˚F $10,420

To return profits back to Joy’s Yogurt, something must be done. Table 6 shows there are four ways you can increase your profits. You could reduce your price by

$4.17, which is not feasible since you are currently at a price of $1.50, which would mean youwould be losing money. You could also hope for an increase in temperature of 19.23˚F, which is unpredictable so that is not a good alternative.

Plus, if the average temperature rises, this also means the temperature rises for your competition and thus their demand increases as well. You could also increase your income by nearly $10,420 to make the same amount of profit. The

Jordan Simonson AAE 421 Homework 3-6 3/3/2012 final choice would be to increase your advertising by $3,125 to gain the same profit. This is the best solution since it is the most elastic solution out of these choices as shown in Table 7. Table 7 shows the adjusted elasticities for these outlets when the competitor for Joy’s Yogurt increases their advertising by $5,000.

Table 7

Elasticities Own Price Income ($1000) Avg. Temp Own Adv ($1000)

e= e2= e3= e5=

-0.11688312 0.311688312 1.012987013 1.038961039



Own advertising is the most elastic outlet



Changing the price is the most inelastic

Interpret rel inelastic rel inelastic elastic elastic

Table 7 shows that increasing advertising is the most economical way to attract customers because with a change in the advertising, it results in a 1.04 change in QD. It is the most elastic outlet and so demand responds the best to increases in Joy’s Yogurt

-10

advertising of $3,125 bring

MC

5500

5000

4500

4000

3500

3000

2500

equilibrium back to the previous

2000

1500

1000

500

Equilibrium 1 0

-5

An increase in own

D2

10 0



D1

Equilibrium 2

15 5

advertising.

Demand Curves

20

Costs

Graph 4

demand curve.

Quantity

Now that Joy’s Yogurt has

increased its advertising by $3,125, it now has a shortage and can return to the original P* and Q* as shown in Graph 4.

Jordan Simonson AAE 421 Homework 3-6 3/3/2012

Table 8

Advertising Effectiveness Current Price MAX TR MAX Profit

MRAdv= P* dQ/dA= MCADV= $1.50 ($400.00) Breakeven $7.17 $1,866.67 dQ/dA Price $7.35 $1,941.67 666.66667 $2.50



The breakeven Q and P remain the same.



Advertising effectiveness decreased for maximum profit and TR As shown in Table 8, the breakeven point remains constant. In order to break

even on the costs of advertising, you would need to sell 666.66 frozen yogurts at a price of $2.50.

Managerial Economics is Life Joy’s Yogurt is priced at $1.50 and her QD is 5,100 units. After computing her MAX TR and MAX ∏, BS and “truth” Functions discovered her frozen yogurt was significantly underpriced, by nearly 530%. At her current price, her advertising effectiveness was very terrible as she actually lost $400 for every $1,000 she spent. Using her MAX ∏ P* and Q*, she gained $2,775 for every $1,000 spent, a ROI of 277.5%. Joy’s competitors decided to increase their advertising by $5,000, reducing the demand for Joy’s Yogurt and creating a surplus in the market. In response, Joy’s Yogurt reduced its price in the short-run to $7.35 to reach equilibrium. To regain profits, Joy’s Yogurt would be able to return to its present profit level if it increased its advertising by $3,125. This

Jordan Simonson AAE 421 Homework 3-6 3/3/2012 would create a shortage in the market and shift out the demand curve to its previous position.

When analyzing Joy’s Yogurt and it’s demand function, I noticed many similarities between her firm and my own. In the beginning I was running a lowprice, high quantity business. I was spending a lot of time on 100 point homeworks and not getting the best initial grades on my homework. I did not fully understand my market, it took me a while to get an appendix going, to understand where to pull information from, to learn excel and what to write. I used test trials to build up my knowledge of the market. I can’t tell you when you are going to have a baby like target can, but I understand what you want in our tables and charts. Now I have learned that I can increase my price (grade) while also decreasing my quantity (time). My elasticity has increased, for every unit of time I put in, my demand increases. While I was increasing my profits, my competitors were learning more about me and what I was doing to get a better grade, just like I was learning more about them. We were working in groups, opensourcing to complete the lab and best understand it. We all understood our competition and many people were increasing their advertising so they could make more profits and take-away their competitors profits. You, as the buyer, are a collector, someone that likes to buy high-priced homework. You are not afraid to “shell out” a good grade, but it has to be high quality. You demand that high quality and if it is not high quality, you are not willing to pay a high price, as evidenced by some of my homework that doesn’t have an appendix. When other people are advertising to you, they are making their product appear to be higher in

Jordan Simonson AAE 421 Homework 3-6 3/3/2012 quality. If this advertising (page layout, graphs look good, etc) is not done well and doesn’t increase the quality you will deduct from the overall grade, but if done correclty you will look into the quality a little more to determine the price you are willing to pay. My advertising must be as impressive as my competitors in order to remain at my profitable levels. I must keep improving the look of my homework and using an appendix. These things will help set me apart from my competitors. At least, I hope it does for now.

Jordan Simonson AAE 421 Homework 3-6 3/3/2012

Appendix Part A: HWK 3-6a Ceteris Paribus Conditions Quantity Intercept

Units Independent Variables Regressive Coefficients

1 1 200

Own Price ($)

Comp Own Income Avg. Adv Adv ($1000) Temp ($1000) ($1000)

1 $1.50 -300

1000 $10.00 120

60 65

1000 $15.00 -250

1000 $10.00 400

Quantity Demanded at Current Price 5100 units Demand Curve Q= 5550 -300 *P Average Rev. Curve P= 18.5 -0.003333 *Q Marginal Rev. MR= 18.5 -0.006667 *Q

Q P Current Price 5100 $1.50 Max TR 2775 $9.25 Max Profit 2718.75 $9.44 ∆ TR Max vs. Current -2325 $7.75 ∆ ∏ Max vs. current -2381.25 $7.94 % ∆TR Max vs. current -45.59% 516.67% % ∆ ∏ Max vs. current -46.69% 529.17%

TR $7,650.00 $25,668.75 $25,658.20 $18,018.75 $18,008.20 235.54% 235.40%

Profit ɛ $5,737.50 -0.09 $24,628.13 -1.00 $24,638.67 -1.04 $18,890.63 $18,901.17 329.25% 329.43%

Advertising Effectiveness Current Price MAX TR MAX Profit

MRAdv= P* dQ/dA= MCADV= $1.50 ($400.00) Breakeven 9.25 $2,700.00 dQ/dA Price 9.4375 $2,775.00 666.66667 $2.50

Jordan Simonson AAE 421 Homework 3-6 3/3/2012

Elasticities Own Price

Avg. Temp Comp Adv ($1000) Own Adv ($1000)

e= e2 = e3 = e4 = e5 =

#6

e6

Income ($1000)

Quantity 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500

0.0882 0.2352 0.7647 0.7352 0.7843

Other Calculations Enter Retail Markup 4 Enter TFC= $50.00 Assume MC=AVC 0.375

Interpret rel inelastic rel inelastic rel inelastic rel inelastic rel inelastic

TVC

0 perfect in

D1 D2 MC 18.5 14.33333333 0.375 16.83333 12.66666667 0.375 15.16667 11 0.375 13.5 9.333333333 0.375 11.83333 7.666666667 0.375 10.16667 6 0.375 8.5 4.333333333 0.375 6.833333 2.666666667 0.375 5.166667 1 0.375 3.5 -0.666666667 0.375 1.833333 -2.333333333 0.375 0.166667 -4 0.375

Q P

TC

1912.5 $1,962.5 0

TR Total Profits

7650 $5,687.5 0

a 5550 18.5 a'

b -300 0.003333 b'

Jordan Simonson AAE 421 Homework 3-6 3/3/2012

Demand Curves

20

D1 D2 MC

15

Costs

10 5 0 -5 -10

Quantity 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500

AR

MR

18.5 16.83333 15.16667 13.5 11.83333 10.16667 8.5 6.833333 5.166667 3.5 1.833333 0.166667

18.5 15.16666667 11.83333333 8.5 5.166666667 1.833333333 -1.5 -4.833333333 -8.166666667 -11.5 -14.83333333 -18.16666667

Demand Curve 20

20

AR

15

MR

AR

15

Prices

Profit Max

5

-10

Quantity

4000

3500

3000

2500

2000

1500

-5

1000

4000

3500

3000

2500

2000

1500

500

0

1000

Quantity

500

0

0

0

Prices

5

-10

AR and Profit Max Curve

10

10

-5

Profit Max 18.125 14.791667 11.458333 8.125 4.7916667 1.4583333 -1.875 -5.2083333 -8.5416667 -11.875 -15.208333 -18.541667

Jordan Simonson AAE 421 Homework 3-6 3/3/2012

Part B: HWK 3-6c Ceteris Paribus Conditions Quantity Intercept

Units Independent Variables Regressive Coefficients

Income Avg. ($1000) Temp

1 1 1 $1.50 200 -300

Quantity Demanded at Current Price Demand Curve Q= Average Rev. Curve P= Marginal Rev. MR=

Current Price Max TR Max ∏ ∆ TR Max vs. Current ∆ ∏ Max versus Current % ∆ TR Max versus Current % ∆ ∏ Max versus Current

Own Price ($)

1000 $10 120

60 65

Comp Adv ($1000)

1000 $20 -250

1000 $10 400

3850 units 4300 -300 *P 14.33333333 -0.003333333 *Q 14.33333333 -0.006666667 *Q

Q P TR ∏ ɛ 3850 $1.50 $5,775.00 $4,331.25 -0.12 2150 $7.17 $15,408.33 $14,602.08 -1.00 2093.75 $7.35 $15,397.79 $14,612.63 -1.05 -1700 $5.67 $9,633.33 $10,270.83 -1756.25 $5.85 $9,622.79 $10,281.38 -44.16% 377.78% 166.81% 237.13% -45.62% 390.28% 166.63% 237.38%

Advertising Effectiveness Current Price MAX TR MAX Profit

Own Adv ($1000)

MRAdv= P* dQ/dA= MCADV= $1.50 ($400.00) Breakeven 7.166667 $1,866.67 dQ/dA Price 7.354167 $1,941.67 666.66667 $2.50

Jordan Simonson AAE 421 Homework 3-6 3/3/2012

Other Calculations Elasticities Own Price Income ($1000) Avg. Temp Comp Adv ($1000) Own Adv ($1000)

e2= e3=

Interpret rel -0.11688312 inelastic rel 0.311688312 inelastic 1.012987013 elastic

e4=

-1.2987013 elastic

e5=

1.038961039 elastic

e=

Change Own Adv Change Own P Change Temp Change Income

Change $3,125 -$4.17 19.23ËšF $10,416

Retail Markup TFC= Assume MC=AVC TVC TC TR Total Profits

4 $50.00 0.375 $1443.75 $1,493.75 5775 $4,281.25

Jordan Simonson Simonson AAEJordan 421 Homework 4-7/4-8 AAE 421 Homework 4-7/4-8 3/9/2012

3/9/12

BS and “truth”

Functions What You Want to Know for 4-7

Fig. 1: Given P, Q and ɛ QMAX=80,000 Q1=50,000 P1=$30.00 ɛ1=-4 Q2=60,000 P2=$27.00

Using the given P, Q and ɛ, in Figure 1, the BS and “truth” Functions firm was able to find the max profit of selling tickets for the Mesa Redbirds football team. Max profits are found when P*=$26.25 and Q*=75,000 units. This is nearly a $100,000, 1.25x increase in profits from the current P=$30.00 and Q=50,000. In order to fill the stadium (Q=80,000), P=$25.50. If the Mesa Redbirds football team decreased the price to $27.00 and were able to sell 60,000 tickets, their elasticity would change to -1.73.

Maximum Current, Total Revenue and Profit Prices and Quantities: My company, BS and “truth” Functions was given a P, Q and ɛ to satisfy the profit maximizing condition.

Graph 1

40 35 30

MC Compared to AR and MR MR

P* and Q* and MAX ∏ MAX Q

25 Price ($)

AR=P MC

20 15

MAX TR

10 5 0 -5 Quantity



Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 MAX ∏ when P*=$26.25 and Q*=75,000 found when MR=MC



MAX TR when P=$18.75 and Q=125,000, but above the MAX Q and found when MR=0



MAX Q=80000 and P=$25.50 at that quantity

Graph 1 shows the MC compared to the MR and AR curve in order to find the ∏ and TR MAX Q and P. Table 1

SOSC Values

SOSC TR -0.0003

SOSC∏ -0.0003

Table 1 shows the second order derivative of the maximum TR and ∏. Since both of

these are negative we know that these are for sure maximums. .

Table 2 compares the current price and MAX Q value with the TR Table 2

mazimizing price and ∏ maximizing price.

Current Price MAX Q TR MAX Profit MAX Change TR MAX vs. Current Change Profit Max vs. Current % change TR max vs. current % change Profit max vs current

Quantity Price 50000 $30.00 80,000 $25.50 125000 $18.75 75000 $26.25 75000 -$11.25 25000 -$3.75 150.00% -37.50% 50.00% -12.50%

TR Profits Elasticity $1,500,000.00 $750,000.00 -4 $2,040,000.00 $840,000.00 -2.125 $2,343,750.00 $468,750.00 -1 $1,968,750.00 $843,750.00 2.33333333 $843,750.00 -$281,250.00 $468,750.00 $93,750.00 56.25% -37.50% 31.25% 12.50%



∏ maximizing price has 1.25x increse in profits from the current price



∏ maximizing price shows an increase of 50% of QD



MAX TR is not true because the Q is above the MAX Q of 80,000 seats This table shows that the tickets for the Mesa Redbirds are overpriced.

The P* is $26.25 and Q* is 75,000 tickets assuming ceteris paribus conditions.

The TR is not a viable option since the maximum capacity of the stadium is 80,000 seats and the TR MAX Q is 125,000 seats. Also notice, that the elasticity

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 for TR is 1.00, showing that this is truly the maximum TR if there were enough seats. Since this is not an option, the MAX TR is actually when you fill the seats at Q=80,000 and P=$25.50. To find the MAX ∏ we assumed that the mark-up was 200% and then found that the MC=$15.00/unit. The demand function is very elastic as seen from the absolute values being larger than one. This means that a price change has a large affect on demand.

MAX TR and ∏ when P=$26.00 and Q=60,000 My company, BS and “truth” Functions was given a P, Q and ɛ to satisfy the profit maximizing condition.

Graph 2

50

MC Compared to AR and MR

40

P*, Q* MAX ∏ MAX Q

30 Price ($)

20

MR AR=P MC

MAX TR

10 0 -10 -20 -30

Quantity



MAX ∏ when P*=$28.07 and Q*=55,909 found when MR=MC



MAX TR when P=$21.32 and Q=81,818, but above the MAX Q and found when MR=0



MAX Q=80,000 and P=$21.79 at that quantity

Graph 1 shows the MC compared to the MR and AR curve in order to find the ∏ and TR MAX Q and P.

Table 3

Arc ɛ

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 Table 3 is the Arc ɛ from the current P

-1.72

($30.00) to the new price ($27.00). This shows you that at this equation is elastic. This means a change in price really affects the demand.

Table 4

SOSC Values

SOSC TR -0.0005

SOSC∏ -0.0005

Table 4 shows the second order derivative of the maximum TR and ∏. Since both of these

are negative we know that these are for sure maximums. .

Table 5 compares the current price and MAX Q value with the TR Table 5

mazimizing price and ∏ maximizing price.

Original Price Current Price Expected Q MAX Q TR MAX Profit MAX Change TR MAX vs. Current Change Profit Max vs. Current % change TR max vs. current % change Profit max vs current

Quantity Price 50000 $30.00 60000 $27.00 70000 $27.00 80,000 $21.79 81818 $21.32 55909 $28.07 21818 -$5.68 -4091 $1.07 36.36% -21.05% -6.82% 3.95%

TR Profits Elasticity $1,500,000.00 $750,000.00 -2.30 $1,620,000.00 $810,000.00 1.72 $1,890,000.00 $840,000.00 2.57 $1,743,157.89 $663,157.89 1.045 $1,744,019.14 $639,473.68 -1 $1,569,132.78 $814,360.05 1.93 $124,019.14 -$170,526.32 -$50,867.22 $4,360.05 7.66% -21.05% -3.14% 0.54%



∏ maximizing price has .5x increse in profits from the current price



∏ maximizing price shows an decrease of 6.82% of QD



MAX TR is not true because the Q is above the MAX Q of 80,000 seats This table shows that the tickets for the Mesa Redbirds are underpriced.

The P* is $28.07 and Q* is 55,909 tickets assuming ceteris paribus conditions.

The TR is not a viable option since the maximum capacity of the stadium is 80,000 seats and the TR MAX Q is 81,818 seats. If we were using the previous elasticity, the expected Q for a price of $27.00 would be 70,000 tickets with a

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 profit of $840,000. Also notice, that the elasticity for TR is 1.00, showing that this is truly the maximum TR if there were enough seats. Since this is not an option, the MAX TR is actually when you fill the seats at Q=80,000 and P=$21.79. To find the MAX ∏ we assumed that the mark-up was 200% and then found that the MC=$13.50/unit. The demand function is very elastic as seen from the absolute values being larger than one. This means that a price change has a large affect on demand.

What You Want to Know for 4-8

Fig. 2: Given P, Q and ɛ QS1=100 QS2=120 PS1=$400.00 PS2=$350.00 QG1=50 QG2=56 PG1=$400.00 PG2=$350.00

Using the given P and Q in Figure 2, the BS and “truth” Functions firm was able to find the max profit of selling the Spreadsheet and Graphic program for for the Efficient Software Store. MAX profits are found when Ps*=$304.21 and QS*=141 units. This is nearly a $1,000, 2.35% increase in profits from the current P and Q. MAX profits are found for the Graphics program when PG*=381.99 and QG*=52 units. This is nearly a $140.00, 0.71% increase in profits from the current P and Q. MAX TR and Profit for Spreadsheet: My company, BS and “truth” Functions was given a P and Q to satisfy the 450 400 350 300

MR AR=P MC

250 Prices ($)

Graph 3

MC Compared to AR and MR

Graph 1

200 150

P*, Q*, MAX ∏ and TR

100 50 0 -50 -100

90

100

110

120 Quantities

130

140

150

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 profit maximizing condition. 

MAX ∏ when P*=$304.42 and Q*=141 found when MR=MC



MAX TR when P=$303.33 and Q=142

Graph 3 shows the MC compared to the MR and AR curve in order to find the ∏ and TR MAX Q and P. Table 6

SOSC Values

SOSC TR -4.28

SOSC∏ -4.28

Table 6 shows the second order derivative of the maximum TR and ∏. Since both of

these are negative we know that these are for sure maximums. .

Table 7 compares the current price and MAX Q value with the TR Table 7

mazimizing price and ∏ maximizing price.

Previous Price Current Price TR MAX Profit MAX Change TR MAX vs. Current Change Profit Max vs. Current % change TR max vs. current % change Profit max vs current

Quantity Price TR Profits Elasticity 100 $120.00 $12,000.00 $11,800.00 -0.56104 120 $350.00 $42,000.00 $41,790.00 -1.36364 141.8182 $303.33 $43,018.18 $42,770.00 -1 141.4091 $304.21 $43,017.82 $42,770.36 -1.00579 21.81818 -$46.67 $1,018.18 $980.00 21.40909 -$45.79 $1,017.82 $980.36 18.18% -13.33% 2.42% 2.35% 17.84% -13.08% 2.42% 2.35%



∏ maximizing price has 17.84% increse in profits from the current price



∏ maximizing price shows an decrease of 13.08% of QD

This table shows that the Spreadsheet program for the Efficient Software Store is underpriced. The P* is $304.21 and Q* is 141 programs assuming ceteris paribus conditions. Also notice, that the elasticity for TR is 1.00, showing that this is truly the maximum. To find the MAX ∏ we assumed that the mark-up was 200% and then found that the MC=$1.75/unit. The demand function is elastic at all prices except $100 as seen from the absolute values being larger than one.

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 This means that a price change has a large affect on demand as long as price is not $100.

Table 8

Arc ɛ

-1.36

Table 8 shows us the cross-price arc elasticity for the Spreadsheet Program is elastic.

This shows us that the price of the Graphics Program has a large effect on the QD of the Spreadsheet Program.

MAX TR and ∏ for Graphic Program My company, BS and “truth” Functions was given a P and Q to satisfy the

Graph 4

MC Compared to AR and MR

500

P*, Q*, MAX ∏ and TR

400

Prices ($)

300

MR

200

AR=P

100

MC

0 40

-100 -200

50

60

Quantities

profit maximizing condition. 

MAX ∏ when P*=$381.99 and Q*=52 found when MR=MC



MAX TR when P=$381.11 and Q=52

Graph 4 shows the MC compared to the MR and AR curve in order to find the ∏ and TR MAX Q and P. Table 8

Arc ɛ

-.85

Table 8 shows us the cross-price arc elasticity for

h2

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 the Graphics Program is relatively inelastic. This shows us that the price of the Spreadsheet program does not have a large effect on the QD of the Graphics Program.

Table 9

SOSC Values

SOSC TR -4.28

SOSC∏ -4.28

Table 9 shows the second order derivative of the maximum TR and ∏. Since both of these

are negative we know that these are for sure maximums. .

Table 10 compares the current price and MAX Q value with the TR Table Table210

mazimizing price and ∏ maximizing price.

Previous Price Current Price TR MAX Profit MAX Change TR MAX vs. Current Change Profit Max vs. Current % change TR max vs. current % change Profit max vs current

Quantity Price TR 50 $400.00 $20,000.00 56 $350.00 $19,600.00 51.77358 $381.11 $19,731.49 51.65472 $381.99 $19,731.38 -4.22642 $31.11 $131.49 -4.34528 $31.99 $131.38 -7.55% 8.89% 0.67% -7.76% 9.14% 0.67%

Profits Elasticity $19,900.00 -1.09 $19,502.00 -0.85 $19,640.88 -1.0 $19,640.99 -1.0 $138.88 $138.99 0.71% 0.71%



∏ maximizing price has 0.71%. increase in profits from the current price



∏ maximizing price shows a decrease of 7.76% of QD This table shows that the Graphics Program for the Efficient Software

Company is overpriced at its current price. The P* is $381.99 and Q* is 52 programs assuming ceteris paribus conditions. TR is very close to the MAX profit with P=$381.11 and Q=52. Also notice, that the elasticity for TR is 1.00, showing that this is truly the maximum TR. To find the MAX ∏ we assumed that the mark-up was 200% and then found that the MC=$1.75/unit. The demand function is very elastic except when at the current price as seen from the absolute

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 values being larger than one. This means that a price change has a large affect on demand except at the current price.

Managerial Economics is Life Through assuming some crucial values, the BS and “truth” Function firm was able to actually find the maximum profit for the Mesa Redbirds. We assumed that the MU for the tickets was 200%. This allowed us to find the MC by taking the current P and dividing it by this MU value.

Homework 4-7 and 3-6 are similar to 3-4 because they all introduce market disequilibrium and the effects of it on the supply and price. For instance in 4-7, we were asked what would happen if the Redbirds has a lower price of $27, essentially stating that the demand Figure 3

for tickets would decrease. In this case, the QD would decrease to 55,909 seats.

This would be an example of a decrease in demand, leading to a surplus and forcing the Redbirds to decrease their price. Figure 3 shows us that a surplus of tickets would lead to a decrease in price.

Homework 4-7 relates to Joy’s situation because the Redbirds also are not at a MAX profit price or quantity. The Redbirds, however are overpriced, leading their ticket sales to be lower than they should be, thus having less people in their seats. This also has a dramatic effect on the amount of concessions they sell, typically where ballparks make most of their money. For this reason, it is

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 probably best to increase the number of people in the stands, which means they should decrease their price to $25.50 to maximize ticket sales and profits on their concessions.

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12

Appendix 4-7 P= Q= e= MU= MC=

$30.00 50,000 -4 200% $15.00

dollars units % chg dollars/unit

a Estimated Demand Curve: Estimated AR Curve: Estimated MR:

Current Price MAX Q TR MAX Profit MAX Change TR MAX vs. Current Change Profit Max vs. Current % change TR max vs. current % change Profit max vs current

Q= AR=P MR=

250,000 $37.50 37.5

Quantity Price 50000 $30.00 80,000 $25.50 125000 $18.75 75000 $26.25 75000 -$11.25 25000 -$3.75 150.00% -37.50% 50.00% -12.50%

b

6666.666667 *P -0.00015 *Q -0.0003 *Q

TR Profits Elasticity $1,500,000.00 $750,000.00 -4 $2,040,000.00 $840,000.00 -2.125 $2,343,750.00 $468,750.00 -1 $1,968,750.00 $843,750.00 -2.33 $843,750.00 -$281,250.00 $468,750.00 $93,750.00 56.25% -37.50% 31.25% 12.50%

Implied elasticity if current price is profit maximizing (given P, Q, MC) Implied MC if current price is profit maximizing (given P, Q and Elasticity)

Q

MR 0 10000 20000 30000 40000 50000 60000 70000 80000 90000

37.5 34.5 31.5 28.5 25.5 22.5 19.5 16.5 13.5 10.5

AR=P MC $37.50 $36.00 $34.50 $33.00 $31.50 $30.00 $28.50 $27.00 $25.50 $24.00

$15.00 $15.00 $15.00 $15.00 $15.00 $15.00 $15.00 $15.00 $15.00 $15.00

-2 22.5

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 100000 110000 120000 130000

40 35

7.5 4.5 1.5 -1.5

$22.50 $21.00 $19.50 $18.00

$15.00 $15.00 $15.00 $15.00

MC Compared to AR and MR

30 Price ($)

25 20

MR

15

AR=P

10

MC

5 0 -5 Quantity

4-7(b) Q1 Q2 % Change P1 P2 % Change Arc E

50000 60000 20.00% 30 27 -10.00% -1.72727273

a Estimated Demand Curve: Estimated AR Curve: Estimated MR:

Q= AR=P MR=

163,636 $42.63 42.63158

b -3838.38 *P -0.00026 *Q -0.00052 *Q

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 Original Price Current Price Expected Q MAX Q TR MAX Profit MAX Change TR MAX vs. Current Change Profit Max vs. Current % change TR max vs. current % change Profit max vs current

Quantity Price 50000 $30.00 60000 $27.00 70000 $27.00 80,000 $21.79 81818.18 $21.32 55909.09 $28.07 21818.18 -$5.68 4090.91 $1.07 36.36% -21.05% -6.82% 3.95%

TR Profits Elasticity $1,500,000.00 $750,000.00 -2.30 $1,620,000.00 $810,000.00 -1.72 $1,890,000.00 $840,000.00 -2.57 $1,743,157.89 $663,157.89 1.045 $1,744,019.14 $639,473.68 -1 $1,569,132.78 $814,360.05 -1.927 $124,019.14 -$170,526.32 -$50,867.22 $4,360.05 7.66% -21.05% -3.14% 0.54%

Implied elasticity if current price is profit maximizing (given P, Q, MC) Implied MC if current price is profit maximizing (given P, Q and Elasticity)

Q 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000 120000 130000

MR AR=P MC 42.63158 $42.63 37.42105 $40.03 32.21053 $37.42 27 $34.82 21.78947 $32.21 16.57895 $29.61 11.36842 $27.00 6.157895 $24.39 0.947368 $21.79 -4.26316 $19.18 -9.47368 $16.58 -14.6842 $13.97 -19.8947 $11.37 -25.1053 $8.76

$13.50 $13.50 $13.50 $13.50 $13.50 $13.50 $13.50 $13.50 $13.50 $13.50 $13.50 $13.50 $13.50 $13.50

-2 11.36842105

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12 50

MC Compared to AR and MR

40

20

MR

10

AR=P 130000

120000

110000

100000

90000

80000

70000

60000

50000

40000

30000

20000

-10

10000

0 0

Price ($)

30

MC

-20 -30

Quantity

Quantity Demanded at Current Price Demand Curve Q= Average Rev. Curve P= Marginal Rev. MR=

Current Price Max TR Max ∏ ∆ TR Max vs. Current ∆ ∏ Max versus Current % ∆ TR Max versus Current % ∆ ∏ Max versus Current

3850 units 4300 -300 *P 14.33333333 -0.003333333 *Q 14.33333333 -0.006666667 *Q

Q P TR ∏ ɛ 3850 $1.50 $5,775.00 $4,331.25 -0.12 2150 $7.17 $15,408.33 $14,602.08 -1.00 2093.75 $7.35 $15,397.79 $14,612.63 -1.05 -1700 $5.67 $9,633.33 $10,270.83 -1756.25 $5.85 $9,622.79 $10,281.38 -44.16% 377.78% 166.81% 237.13% -45.62% 390.28% 166.63% 237.38%

Advertising Effectiveness Current Price MAX TR MAX Profit

MRAdv= P* dQ/dA= MCADV= $1.50 ($400.00) Breakeven 7.166667 $1,866.67 dQ/dA Price 7.354167 $1,941.67 666.66667 $2.50

Jordan Simonson AAE 421 Homework 4-7/4-8 3/9/12

Other Calculations Elasticities Own Price Income ($1000) Avg. Temp Comp Adv ($1000) Own Adv ($1000)

e2= e3=

Interpret rel -0.11688312 inelastic rel 0.311688312 inelastic 1.012987013 elastic

e4=

-1.2987013 elastic

e5=

1.038961039 elastic

e=

Change Own Adv Change Own P Change Temp Change Income

Change $3,125 -$4.17 19.23ËšF $10,416

Retail Markup TFC= Assume MC=AVC TVC TC TR Total Profits

4 $50.00 0.375 $1443.75 $1,493.75 5775 $4,281.25

Jordan Simonson Jordan AAE 421 Simonson Homework 4-14 AAE 421 Homework 4-14 3/21/2012

3/21/12

BS and “truth”

Functions What You Want to Know As your consultant, BS and “truth” functions went through the information you provided us: the price of Aceword, quantity of Aceword, family income and the price of Goodwrite with the intention of assessing how you have been doing on your pricing strategy over the past 10 months. I am sorry to say, but you are currently in a tough spot as you missed potential profits, currently have an inelastic demand and are downright getting killed by your competitor, Goodwrite.

For these reasons you should innovate your product so you have a point of differentiation over your competitor. Here is a summary of where you went wrong.

An Amazing Month 4 Table 1: AoD Month 4

Previous Price Current Price TR MAX Profit MAX ∆ TR MAX vs. Current ∆ ∏ Max vs. Current % ∆ TR max vs. current % ∆ ∏ max vs current

Q P 220 $120 240 $110 240 $110 180 $137.50 0 $0.00 -60 $27.50 0.00% 0.00% -25.00% 25.00%

TR $26,400 $26,400 $26,400 $24,750 $0 -$1,650 0.00% -6.25%



At point of TR MAX, P=$110, Q=240, ɛ=-1



Were only $1,650, 12.5% away from ∏ MAX

∏ $13,200 $13,200 $13,200 $14,850 $0 $1,650 0.00% 12.50%

ɛ -1.19 -1 -1 -1.67

Aceword was doing great in this month. It was at a point of TR max, which also means ɛ=-1. This was achieved by a decrease in price and everything else

Jordan Simonson AAE 421 Homework 4-14 3/21/12 was CP. Aceword was elastic meaning you could reduce your price and their would be an increase in TR. Aceword was only $1,650 away from profit maximization, something that could have been closer by becoming more efficient, decreasing MC and increaseing the mark-up.

Got Greedy in Month 5 Table 2: AoD Month 5

Previous Price Current Price TR MAX Profit MAX ∆ TR MAX vs. Current ∆ ∏ Max vs. Current % ∆ TR max vs. current % ∆ ∏ max vs current

Q 240 230 252 184 22 -46 9.57% -20.21%

P $110.00 $114.00 $104.84 $133.34 -$9.16 $19.34 -8.04% 16.96%

TR $26,400 $26,220 $26,422 $24,469 $202 $1,750 0.77% -6.68%



Q=230, P=$114, ɛ=-1.19



Lost $90 in profit to increase price by $4

∏ $13,200 $13,110 $12,056 $14,009 -$1,053 $899 -8.04% 6.86%

ɛ -1.10 -1.19 -1 -1.74

In month 5, your company got a little greedy and decided to increase the price by $4 as shown in Table A1. At CP conditions, it was a small increase in price, but it had effects on profits as you reduced profits by $90. Aceword became more elastic, now at -1.19. In order to maximize profits, you would need to increase your price by about $20, something you typically do not want to do. You should not have changed your price, but instead reduced your MC to increase profits that way.

Goodwrite Kills You in Month 6 Table 3: AoD Month 6

Previous Price Current Price TR MAX Profit MAX ∆ TR MAX vs. Current ∆ ∏ Max vs. Current % ∆ TR max vs. current % ∆ ∏ max vs current

Q 230 215 159 133 -55 -81 -25.82% -37.91%

P $114 $115 $176.41 $205.16 $61.41 $90.16 53.40% 78.40%

TR $26,220 $24,725 $28,134 $27,387 $3,409 $2,662 13.79% 10.77%

∏ $13,110 $12,363 $18,964 $19,711 $6,601 $7,349 53.40% 59.44%

ɛ -0.45 0.48 -1 1.39

Jordan Simonson AAE 421 Homework 4-14 3/21/12



Q=215, P=115, ɛ=0.48



Further loss of $750 in profit



$90, 78.40% difference between profit max and current price

Your price increase of $4 led Goodwrite to decrease their price by $20, a 15% reduction in their price. You also increased your price by $1, but this had little overall effect on the changes in the market. These caluculations were not done at CP, but through calculations we were able to discover that the decrease in Goodwrite’s price explained the majority of change. These things hurt you significantly, you lost profits, are relatively inelastic (meaning you need to increase prices in order to increase TR) and to profit maximize you need to increase your price by $90. A price increase of that magnitude would allow Goodwrite to gain valuable market share in your industry, something you do not want. For these reasons, BS and “truth” Functions suggests your company innovates the Aceword software. This will differentiate your product from your competitor, increasing demand and allowing you to either increase or reduce the price to compete.

Jordan Simonson AAE 421 Homework 4-14 3/21/12 10 Month Overview

Graph 1: Prices and Relative Prices

$150

Prices and Relative Prices

Relative Prices

$140 Prices

$130 $120 $110

Price Aceword Price Goodwrite Relative Price

$100 $90 1

2

3

4

5 6 Months

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

7

8

9

10



At month 4 where at MAX TR, relative price was the lowest



As relative price increased, profit and TR decreased as also shown in Graph A2

Table 4: Change in Elasticities at CP

Change in Elasticities at CP Ep %∆ Ei %∆ Exp %∆ -1.00 0 0.95 0 0.45 0 -1.19 19.15% 0.49 -48.16% 0.79 76.94% -0.49 -58.97% 0.48 -2.10%



An increase (decrease) in price makes Aceword more (less) elastic



An increase in family income makes Aceword less elastic



A decrease in Goodwrite’s price makes Aceword more elastic

Managerial Economics is Life In the AAE 421 class we have been increasing our MPL, shifting around our prices, etc. My firm needs to continue to maximize profits in this class. In order to do this, my firm is constantly scoping the landscape for ways to innovate.

To create differentiation between my firm and its competitors. One way I have

Jordan Simonson AAE 421 Homework 4-14 3/21/12 innovated is by being prepared for the lab. I have found that I learn more in lab when I come prepared and also get through more parts of the lab. My product has also evolved to include an appendix, stream-lined content and a better look. I have done all of this while reducing my MC on each paper, something Aceword should have done to increase profits instead of continuing to play with their price, which got them into trouble. It takes me less time to get a better grade on the homework and I now know my way around Excel and placing the graphs into word. This homework shows that changing your price is not always the best way to increase profits, sometimes you need to innovate, reduce MC or increase MPL.

Jordan Simonson AAE 421 Homework 4-14 3/21/12

Table A2: Elasticities

Appendix Month 1 2 3 4 5 6 7 8 9 10

Q 200 210 220 240 230 215 220 230 235 220

PA $120 $120 $120 $110 $114 $115 $115 $105 $105 $105

IncomeF $4,000 $4,000 $4,200 $4,200 $4,200 $4,200 $4,400 $4,400 $4,600 $4,600

PG $130 $145 $145 $145 $145 $125 $125 $125 $125 $115

TR $24,000 $25,200 $26,400 $26,400 $26,220 $24,725 $25,300 $24,150 $24,675 $23,100

Month %∆Q %∆P %∆I %∆ XP 1 2 4.88% 0.00% 0.00% 10.91% 3 4.65% 0.00% 4.88% 0.00% 4 8.70% -8.70% 0.00% 0.00% 5 -4.26% 3.57% 0.00% 0.00% 6 -6.74% 0.87% 0.00% -14.81% 7 2.30% 0.00% 4.65% 0.00% 8 4.44% -9.09% 0.00% 0.00% 9 2.15% 0.00% 4.44% 0.00% 10 -6.59% 0.00% 0.00% -8.33%

∆ TR $0 $1,200 $1,200 $0 -$180 $1,495 $575 -$1,150 $525 $1,575

Elasticity XP Inc P P Not CP Inc P Inc XP

%∆ 0.00% 5.00% 4.76% 0.00% 0.68% 5.70% 2.33% 4.55% 2.17% 6.38%

arc ɛ 1 2 3 4

0.45 0.95 1.00 1.19 0.48 0.49 0.49 0.48 0.79

5 6 7 8



The Arc Elasticity was becoming more elastic until Goodwrite decreased their price



Notice month 6 is not CP

Graph A1: Prices and Relative Prices

$150

Prices and Relative Prices

$140 Prices

$130 $120 $110

Price Aceword Price Goodwrite Relative Price

$100 $90 1

2

3

4

5 6 Months

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

Relative Prices

Table A1: Monthly Changes

7

8

9

10

RP 92.31% 82.76% 82.76% 75.86% 78.62% 92.00% 92.00% 84.00% 84.00% 91.30%

Jordan Simonson AAE 421 Homework 4-14 3/21/12 Change in Elasticities

Graph A2: TR and Relative Prices

%∆

Ei 0.95 0.49 0.48

0 19.15% -58.97%

%∆ 0 -48.16% -2.10%

Exp %∆ 0.45 0 0.79 76.94%

TR and Relative Prices

$27,000 $26,000

90.00%

Prices

$25,000 $24,000

85.00%

$23,000

80.00%

$22,000

TR

$21,000 1

$27,000

75.00%

Relative Price

$20,000

Graph A3: TR vs. Family Income

2

3

4

5 6 7 Months

70.00% 8

9

10

TR vs. Family Income

$26,000 $25,000 TR

95.00%

$24,000 TR Family Income Linear (TR) Linear (Family Income)

$23,000 $22,000 $21,000 1

2

3

4

5 6 7 Months

Relative Prices

Ep -1.00 -1.19 0.49

8

9 10

$4,700 $4,600 $4,500 $4,400 $4,300 $4,200 $4,100 $4,000 $3,900 $3,800 $3,700 $3,600

Family income

Table A3: Changes in Elasticities

Jordan Simonson AAE 421 Homework 4-14 3/21/12 AoD A1: Month 4 to 5

Aceword Q1= Q2= % Change= P1= P2= % Change= Arc Elasticity:

Month 4 to 5 Price Goodwrite 240 P1= 230 P2= -4.26% % Change= Family $110 Income $114 I1= 3.57% I2= -1.19 % Change Current P= Q= e= MU: MC=

114 230 -1.19 200.00% $57.00

a

TR $145 $26,400 $145 $26,220 0.00% -0.68%

$4200 $4200 0.00% Previous 110 $ 240 units -1.19 200.00% $55.00 $/unit

b 504 2.403882046 *P $209.68 0.415993789 *Q $209.68 0.831987578 *Q

Estimated Demand Curve: Estimated AR Curve: Estimated MR:

Q= AR=P MR=

Previous Price Current Price TR MAX Profit MAX ∆ TR MAX vs. Current ∆ ∏ Max vs. Current % ∆ TR max vs. current % ∆ ∏ max vs current

Quantity Price TR Profits ɛ 240 $110 $26,400 $13,200 -1.10 230 $114 $26,220 $13,110 -1.19 252 $104.84 $26,421 $12,056 -1 183 $133.34 $24,469 $14,009 -1.74 22 -$9.16 $201 -$1,053 -46 $19.34 -$1,750.82 $899 9.57% -8.04% 0.77% -8.04% -20.21% 16.96% -6.68% 6.86%

Implied elasticity if current price is profit maximizing (given P, Q, MC) Implied MC if current price is profit maximizing (given P, Q and Elasticity)

-2 18.32

Jordan Simonson AAE 421 Homework 4-14 3/21/12

AoD A2: Month 5 to 6

Aceword Q1= Q2= % Change= P1= P2= % Change= Arc Elasticity:

Month 5 to 6 Price Goodwrite 230 P1= 215 P2= -6.74% % Change= $114 Family Income $115 I1= 0.87% I2= -0.48 % Change Current P= Q= e= MU: MC=

Estimated Demand Curve: Estimated AR Curve: Estimated MR:

Previous Price Current Price TR MAX Profit MAX ∆ TR MAX vs. Current ∆ ∏ Max vs. Current % ∆ TR max vs. current % ∆ ∏ max vs current

Q= AR=P MR= Q 230 215 159 133 -55 -81 -25.82% -37.91%

TR $145 $26,220 $125 $24,725 -14.81% -5.87% $4200 $4200 0.00%

$115 215 0.483563179 200.00% $57.50

Previous $114 $ 230 units 0.483563179 200.00% $57.00 $/unit

a

b 319 0.904052901 *P $352.82 1.106129961 *Q $352.82 2.212259922 *Q P $114 $115 $176.41 $205.16 $61.41 $90.16 53.40% 78.40%

TR $26,220 $24,725 $28,134 $27,387 $3,409 $2,662 13.79% 10.77%

∏ $13,110 $12,362 $18,964 $19,711 $6,601 $7,349 53.40% 59.44%

Implied elasticity if current price is profit maximizing (given P, Q, MC) Implied MC if current price is profit maximizing (given P, Q and Elasticity)

ɛ -0.45 -0.48 -1 -1.38

-2 -122.818

Jordan Simonson AAE 421 Homework 4-14 3/21/12

Spreadsheets Q1= Q2= % Change= P1= P2= % Change= Arc Elasticity:

Month 6 to 7 Price Goodwrite 215 P1= 220 P2= 2.30% % Change= $115 Family Income $115 I1= 0.00% I2= -0.49 % Change

P= Q= e= MU: MC=

Q= AR=P MR=

Previous Price Current Price TR MAX Profit MAX ∆ TR MAX vs. Current ∆ ∏ Max vs. Current % ∆ TR max vs. current % ∆ ∏ max vs current

Q 215 220 164 137 -55 -82 25.29% 37.64%

$4200 $4400 -4.65%

Current Previous $115 $115 $ 220 215 units 0.49 -0.49 200.00% 200.00% $57.50 $57.50 $/unit

a Estimated Demand Curve: Estimated AR Curve: Estimated MR:

TR $125 $24,725 $125 $25,300 0.00% 2.30%

b 329 $347.67 $347.67 P $115 $115 $173.84 $202.59 $58.84 $87.59 51.16% 76.16%

-0.94 *P -1.06 *Q -2.12 *Q TR $24,725 $25,300 $28,573 $27,791 $3,273 $2,491 12.94% 9.85%

∏ $12,362 $12,650 $19,122 $19,903 $6,472 $7,253 51.16% 57.34%

Implied elasticity if current price is profit maximizing (given P, Q, MC) Implied MC if current price is profit maximizing (given P, Q and Elasticity)

ɛ -0.51 -0.49 -1 -1.40

-2 117.674

Jordan Simonson

Jordan Simonson AAE 421 5-3a AAE 421 5-3a 4/25/2012 4/25/12

BS and “truth”

Functions Goodness of Fit Table 1: Goodness of Fit

R2

0.55



55% of the variation in the demand for the low

ADJ R2

0.671

calorie microwave food is accounted for by the

Prob (>F)

0.44%

regression equation, 67% when adjusted

Critical T

2.09



There is a 44% chance that the regression

equation is not statistically significant  The estimated coefficient is significant at the 0.05 level  There are several other regression coefficients that could account for the variability

Slope Analysis Table 2: Slope Analysis

Demand Factors

Average Null Elasticity Hypothesis

Own Price ($)

-1.19

Comp Price

0.68

Income Monthly Adv Exp Number of Microwaves Sold

1.62

One Tailed t-Test: (b Beta)/SE

Probability of Null Hypothesis

Inelastic Weak Substitute

-0.38

35%

0.85

20%

0.80

22%

0.11

Normal Good Mprofit(Adv) > MC(Adv)

-2.22

2%

0.07

Strong Competitor

-7.21

0%

Jordan Simonson AAE 421 5-3a 4/25/12



The is a 35% chance that low-calorie microwaveable food is inelastic



Our competitor is most likely not a substiture



Low-calorie microwaveable food is probably not a normal good



There is a low chance that our marketing will make us money



There is no chance that the number of microwaves sold is a competitor

AoD Table 3: AoD

Q Current Price MAX TR MAX Profit ∆ TR MAX vs. Current ∆ ∏ MAX vs. Current % ∆ TR MAX vs Current % ∆ ∏ MAX vs Current 

P

TR

∏

ɛ

17,650 $5.00

$88,250

$44,125

-1.19

19,325 $4.60

$88,918

$40,606

-1.00

14,075 $5.85

$82,356

$47,168

-1.75

1,675 $0.40

$668

$3,519

-3,575 $0.85

-$5,894.49

$3,043

9.5%

-8%

0.8%

-8.0%

-20.3%

17%

-6.7%

6.9%

P*=$5.85 and Q*=14,075. This would require a 17% increase in price for a $3,000 profit leading to a 7% increase in profits.



All values are elastic so can decrease price to increase revenue BS and “truth” Functions suggests you do not change your price from your

current price. For maximum TR you would reduce your price because you are currently elastic, but you would reduce your profits. To obtain P* and Q* you would need to increase your price, something you do not want to do.

Jordan Simonson AAE 421 5-3a 4/25/12

BE Advertising Table 4: BE Advertising

BE Price Analysis

P

R

TR-Cost

∏

BE Advertising Price: MC Adv=MR Adv

$5

$1

$0.00

-$0.50

BE Advertising Price: MC Adv=Mprofit

$7.50

$1.50

$0.50

$0



Your advertising agency should be fired.



At the current price, the price we suggest you stay at, your advertising agency is losing you $0.50 for every $1 you spend on advertising.



In order to just break-even on the money you spend on advertising, you would need to raise your price to $7.50, something you cannot do.

Breakeven Cross-Price Advertising and Price Table 5: Breakeven Cross-Price

Q

C

TR-Adv

∏

-20

$0

-$100

-$50

∆

C

TR-Adv

∏

100 -$0.48

-$100

$100

-$50

-$8,405

$100

-$8,355

$3.80

0

$100

50

80

0

$100

50

Cross Price Slope/MR Analysis 1 unit decrease in Competitor Price generates BE Changes (Adv or P) Advertising Required to Offset Revenue Losses Price Change " Income Change

“ “

“ “

“

Change In Number of Microwaves



“

You better hope your competitor doesn’t reduce their price because for every penny they reduce their price, you lose $50 in profit.



You can’t advertise to make up for the loss in profit and revenue because your advertising agency sucks.



You would need to reduce your cost by $0.48 and a loss in profits of $8,355 in order to offset the revenue losses.



You could also hope for 80 more microwaves to be bought or an income increase of $3.80.

Jordan Simonson AAE 421 5-3a 4/25/12

Problem Context Business Summary Your microwaveable food company is having severe problems and needs to make severe changes. The first problem with your product is that your marketing is ineffective. You either need to reassess your marketing strategy or reduce advertising in general. You should probably just fire your advertising agency.

You should also push to reduce your MC. The more you reduce your MC, the closer your TR can move to max profits and you are more poised to reduce your price. This would help in the case of a price war.

Your product is most likely an inferior good, which means you would stand to gain sales if income is reduced. You would have higher sales during a recession.

You are priced fairly well and I would stay at the current price. This is your greatest strength and are able to reduce price if you get in a price-war with your competitor.

Jordan Simonson

Jordan Simonson AAE 421 5-3a AAE 421 5-3a 4/25/2012 4/25/12

BS and “truth”

Functions Goodness of Fit Table 1: Goodness of Fit

R2

0.91

F Test

311.4

Prob (>F)

0%

Critical T

1.98



91% of the variation in the demand for the low

calorie microwave food is accounted for by the regression equation 

There is a 0% chance that the regression

equation is not statistically significant  The estimated coefficient is significant at the 0.05 level 

Figure 1: Confidence Intervals

The mean

quantity is 29,420. 

We are 95%

confident that the quantity lies between 23,889 and 34,951.

23,889

29,420

34,951

Jordan Simonson AAE 421 5-3a 4/25/12

Slope Analysis Table 2: Slope Analysis

Demand Factors

Average Elasticity

P

Null Hypothesis

One Tailed tTest: (b Beta)/SE

Probability of Null Hypothesis

-0.63

0.27

1.27

0.10

-2.06 Inelastic

A

M∏(ADV)> 1.02 MC(ADV)

I

Normal 0.34 Good

H

Weak 0.17 Compliment

Pc

Weak 0.17 Substitute



There

is a 27% chance that toaster ovens are inelastic

-5.24

0.00

3.09

0.00



Our

competitor is most likely not

-0.26

0.40

a substitute



Toaster ovens are a normal good



There is a low chance that our marketing will make us money



Number of household sales is a strong compliment

BE Advertising Table 3: BE Advertising

Advertising Slope/MR Analysis

Q

Rev

TR-Adv

Profits

1 unit of additional advertising (MC) generates

1500

$82,500

$82,418

$61,792

Critical Advertising Slope: MC Adv=MR Adv

1.500

$82.50

$0

-$20.63

Critical Advertising Slope: MC Adv=M∏ Adv

1.58

$87.94

$5.44

-$16.54

BE Price Analysis BE Advertising Price: MC Adv=MR Adv BE Advertising Price: MC Adv=M∏

P

Rev

TR-Cost

Profits

$55

$82.50

$0

-$20.63

$58.40

87.60

$5.10

-$15.52



Your advertising agency is kick-butt.



At the current price your advertising agency is gaining you $1.50 for every $1 you spend on advertising.



Your MCADV=M∏ when you are priced at $58.40.

Jordan Simonson AAE 421 5-3a 4/25/12

Breakeven Cross-Advertising and Cross-Price Cross Price Slope/MR Analysis

Table 4: Breakeven Cross-Price

Q

1 unit decrease in Competitor Price generates

C

-0.100 ∆

BE Changes (Adv or P) Advertising Required to Offset Revenue Losses Price Change Required to Offset Revenue Losses

∏

TR-Adv $0

-$5.50

C

-$5.16 ∏

TR-Adv

0.067 -$66.67 -$0.091 -2.67

$0.067

-$66.33

$100

-$2.33

Income Change

$313

0

$100

99.67

Household Change

$200

0

$100

99.67



Your competitor is not very strong because for every dollar they drop their price, your company loses $5.16.



You can either increase advertising by 0.067 or decrease your price by $0.091 to make up the loss in revenues. .



You could also hope for an income increase of $313 or a change in households by $200.

AoD Table 5: AoD

Q Current Price MAX TR MAX Profit ∆ TR MAX vs. Current ∆ ∏ MAX vs. Current % ∆ TR MAX vs Current % ∆ ∏ MAX vs Current 

P

∏

TR

29,420

$55 $1,618,100 $1,213,575

44,960

$40.87 $1,837,638 $1,219,438

37,398

$47.75 $1,785,646 $1,271,430

15,540 -$14.13

$219,537

$5,862

7,978

-$7.25

$167,545

$57,855

52.8%

-26%

13.6%

0.5%

27.1%

-13%

10.4%

4.8%

P*=$47.75 and Q*=37,398. This would require a 13% decrease in price for a $58,000 increase in profit leading to a 4.8% increase in profits.



ɛ -2.06 -1.00 -1.40

All values are elastic so can decrease price to increase revenue BS and “truth” Functions suggests you change your price to the profit

maximizing price of $47.75. Even though this would only result in a 4.8%

Jordan Simonson AAE 421 5-3a 4/25/12 increase in profits, this relates to a $58,000 increase in profits. We know this move would be worth the price reduction not only for the increase in profits, but also because you would only need to lower your price. At your current price you are elastic, meaning you can reduce your price and increase revenues. You should continue to work on lowering your MC because the lower it is the lower you can reduce your price while still maintaining the same profit margins. This will allow you to better withstand a price war with your competitors.

Problem Context Business Summary Your toaster is well positioned in the market to be very successful. All variables are showing that your company is doing very good advertising your toaster. In fact for every $1,000 you spend on advertising, you sell 1,500 toasters, resulting in an extra $60,000 in profits.

You are also well positioned for success in the case of a price war. You can respond very well to your competitors pricing changes. You are currently elastic and so can reduce price to increase revenues. You lose very little in profits for each dollar reduction in your competitor’s price. Further reductions in MC will further allow you to increase profit margins and withstand sizeable competition.

Jordan Simonson Jordan AAE 421 Simonson 6-2 Extra Credit AAE 421 6-2 Extra Credit 5/7/2012

5/7/2012

BS and “truth”

Functions Production Graph 1: Production Data

800



Production Data

700

people

Production

600



500 400

TP AP MP

300 200

Stage 1

Stage 2

Stage 3

0 1

2

3 4 5 6 Number of Workers

7

8

9

5 < Stage 2 <

8 

100 -100 0

Stage 1 < 5

Stage 3 > 8

people 

This appears

to be a cubic production function  Max MP is at 3 workers

Goodness of Fit for Cubic Production Function Table 1: Regression Analysis Figure 1: Regression

Regression Statistics Multiple R 0.98 R Square 0.96 Adjusted R Square 0.94 Standard Error 0.66 Observations 9.00

Y=-0.174+0.027X-7.3E-05X2+7.19E-08X3

 96% of the variation in the production function is accounted for by the regression equation

Profit Maximizing Labor Inputs 1,200

Profit Max

1,000

MLC MRP ($2.75) MRP ($3.50) MRP ($5.00)

800 600 $

Graph 2: Profit Max Labor Inputs

400 200 0

-200

1

2

3

4

5

6

Number of Workers

7

8

9

 Profit max when MLC=MRP

Jordan Simonson AAE 421 6-2 Extra Credit 5/7/2012  When operating at a price of $2.75 you should use 7 workers  When operating at a price of 3.50 or $5.00 you should use 8 workers Table 2: Isoquants and Expansion Path

Table 3: Returns to Scale

Labor 9 8 7 6 5 4 3 2 1

L K 1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

710 725 700 665 590 450 300 110 50 1

1420 1450 1400 1330 1180 900 600 220 100 2

2130 2175 2100 1995 1770 1350 900 330 150 3

Q

% Chg L/K

% Scale Chg ɛ Q

Scale

1.00 0.50 0.33 0.25 0.20 0.17 0.14 0.13

3.40 3.09 1.00 0.64 0.35 0.23 0.18 0.10

900 and 2100 IRTS IRTS  The expansion path is IRTS IRTS DRTS, as you add more capital IRTS IRTS and labor, production decreases IRTS  To max production per DRTS

50 220 900 1800 2950 3990 4900 5800 6390

2840 2900 2800 2660 2360 1800 1200 440 200 4

3.40 6.18 3.00 2.56 1.76 1.37 1.29 0.81

3550 4260 3625 4350 3500 4200 3325 3990 2950 3540 2250 2700 1500 1800 550 660 250 300 5 6 Capital (Boats)

4970 5075 4900 4655 4130 3150 2100 770 350 7

5680 5800 5600 5320 4720 3600 2400 880 400 8

6390 6525 6300 5985 5310 4050 2700 990 450 9

 The expansion path is in yellow, with shown isoquants of

person per boat, the owner should have eight workers on eight boats

MEIL: 1000 Tuna Challenge Getting 1,000 tuna for every boat is pretty much impossible for your current setup. At max TP the highest you can get is a little more than 700 tuna with 8 workers. You current boat is setup to be a boat that uses nets to fish. This means you probably have a boat with netting and other gear that is not conducive to hook

Jordan Simonson AAE 421 6-2 Extra Credit 5/7/2012 and line fishing. I would suggest getting rid if all of this extra cargo to make room for more fishermen. Hopefully this will allow more room on the boat to fish from. Looking towards to future, you need to buy boats better equipped to fish with hook and line. These are probably bigger boats with simple attachments to help hook and line fishermen succeed. Increasing your technology is another way to increase production. Using fish locators, sharper hooks, and stronger line will allow you to find more fish and keep more on the line.

In relation to the BS and â&#x20AC;&#x153;truthâ&#x20AC;? Functions firm I am continually working to cut things out of my life that bring no value. I have found several forms of BS in this class that I have learned how to remove so I can work the most efficient way possible. Sometimes this is not enough and I need to better my technology. For instance, right now my Microsoft Word program is having issues and keeps shutting down on me. This summer I will be getting that fixed so I can work faster while writing a report. This class has taught me how to cut through the BS, when I have maximized my production and when I need to change my technology.

Jordan Simonson Jordan AAE 421 Simonson 6-5 Extra Credit AAE 421 TH MT 2 Sec5/7/2012 3

5/7/2012

BS and “truth”

Functions Production Resources Graph 1: Total Cost Production

1,500,000.00 1,300,000.00

Production

 The firm is

1,100,000.00

not allocating its

TC

900,000.00 700,000.00

TC Mexico

500,000.00

TC Taiwan

300,000.00

TC Canada

100,000.00

production resources optimally

-100,000.00

 It should not Hours

produce its goods

in Canada because the TC there is always higher than the lowest TC  With the information we have, there are time you would produce in Mexico and other times you would produce in Taiwan

Manufacturing in One Facility If the company wants to manufacture in one location, it really depends on how many electronics they need to produce and how many people they need to produce that amount. If they can produce what they need with less than 410 employees working 24 hours all year, then they should produce electronics in Taiwan. If they cannot do this, they should produce in Mexico. Consideration should also be given to other factors as well. For instance, transportation may be more expensive from Taiwan.

Jordan Simonson

Jordan Simonson AAE 421 6-10 AAE 421 6-10 5/2/2012 5/2/2012

BS and “truth”

Functions Goodness of Fit Table 1: Goodness of Fit

Table 2: Coefficient Significance

R Square Adjusted R Square F Prob (>F) Standard Error Observations

0.99 0.99 358 0.005 0.041 11



99% of the variation in production for the

Brady Corporation is accounted for in the regression equation, it fits well



There is less than a 1% chance that the regression equation is insignificant



The standard error is very low Regression Equation:



LN(Q)=-0.3106+0.3458Ln(K)+0.8251Ln(L)

the form of LN

Intercept Ln(L) Ln(K)

Coefficients -0.3106 0.3458 0.8251

t Stat -0.2415 2.1941 2.5228

P-value 0.8152 0.0595 0.0357



The regression equation is in

The LN(L) and LN(K)

coefficients are statistically significant at the 0.05 level



The intercept is not statistically significant and has a probability of 0.8152 to be equal to zero

Predicted Production Table 3: Predicted Production

Observation

Predicted

1

226.1014

Actual 245

2

251.5796

3 4

Error

% Change

-18.9

-7.71%

240

11.58

4.82%

300.0174

300

0.02

0.01%

330.7262

320

10.73

3.35%

5

400.0429

390

10.04

2.58%

6

459.5183

440

19.52

4.44%

514.6165

520

-5.38

-1.04%

518.8208

520

-1.18

-0.23%

564.4284

580

-15.57

-2.68%

586.013

600

-13.99

-2.33%

596.8742

600

-3.13

-0.52%

7 8 9 10 11



Plant 2 and 6 are

the least efficient because they produce

Jordan Simonson AAE 421 6-10 5/2/2012 under the predicted value by over 4% 

Plant one is very efficient because it produces over the predicted amount by nearly 8%

Graph 1: Returns to Scale

0.30



Returns to Scale

0.25

function is slightly

Returns to Scale

Q

0.20

K and L

0.15

This production

IRTS because b + c > 1 Ln(L) Ln(K)

0.10

0.3458 0.8251

0.05



0.00 1

2

3

4

5 6 Plants

7

8

9

Both labor and

10

capital are inelastic, but

together form a production function that is IRTS

MCL with Respect to MPL Graph 2: MPL with K Fixed

0.12

MPL (K fixed)

MPL (K fixed)

0.12



0.12

MPL (K fixed)

0.12

Holding K

fixed we are able to determine that the

0.12 0.12

Brady Corporation is

0.12

experiencing

0.12 1

2

3

4

5

6 7 Plants

8

9

10 11

diminishing marginal

returns 

Using the equation P*MPL=MCL, we can infer that MCL is also decreasing, keeping P constant



It seems to even out at the seventh plant where they produce 520 units

Jordan Simonson AAE 421 6-10 5/2/2012

Production Function Estimation Iso-Quant Curve at 500: K = 156,860,091.19 * L^ -2.39



Iso-Quant Curve at 1,000: 1,164,367,041.29 * L^ -2.39

Quant is at 500 is about

Iso-Cost Curve: K = 296.34 - 0.5 * L

415 and K* is 87.

Expansion Path: 0.419 * -0.5 * L



curve is at 1,000, L*=750, K*=157 and Cost*=$25,350 800 700 600 500 400 300 200 100 0 -100 300 -200

Production Function Estimation Iso-Cost Curve

Expansion Path Iso-Quant at 1,000

Capital

Graph 3: Production Function Estimation

Iso-Quant at 500

400

500

600

700

Labor

L* when the Iso-

800

900

1000

When the Iso-Quant

Jordan Simonson AAE 421 6-10 5/2/2012

Appendix Capital

Labor

30.00 34.00 44.00 50.00 70.00 76.00 84.00 86.00 104.00 110.00 116.00

250.00 270.00 300.00 320.00 350.00 400.00 440.00 440.00 450.00 460.00 460.00

Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

MPL Quantity Ln(K) Ln(L) Ln(Q) MPL MPK (K fixed) 245.00 3.40 5.52 5.50 0.34 1.43 0.12 240.00 3.53 5.60 5.48 0.31 1.23 0.12 300.00 3.78 5.70 5.70 0.35 1.19 0.12 320.00 3.91 5.77 5.77 0.35 1.12 0.12 390.00 4.25 5.86 5.97 0.39 0.97 0.12 440.00 4.33 5.99 6.09 0.38 1.01 0.12 520.00 4.43 6.09 6.25 0.41 1.08 0.12 520.00 4.45 6.09 6.25 0.41 1.06 0.12 580.00 4.64 6.11 6.36 0.45 0.98 0.12 600.00 4.70 6.13 6.40 0.45 0.95 0.12 600.00 4.75 6.13 6.40 0.45 0.90 0.12

0.994459969 0.988950631 0.986188288 0.041411831 11

ANOVA df Regression Residual Total

Intercept

2 8 10

Coefficients 0.310597003

SS 1.227936685 0.013719518 1.241656202

MS 0.613968 0.001715

F 358.0116

Standard Error

t Stat

P-value

1.286025723

-0.24152

0.81523

Significance F 1.49056E-08

Jordan Simonson AAE 421 6-10 5/2/2012 Ln(L) Ln(K)

Observation

0.345781985 0.825054754

0.15759225 0.327041413

2.194156 2.522784

0.059534 0.035654

Predicted Y

Residuals

Predicted

Actual

Error

245 240 300 320 390 440 520 520 580 600 600

-18.89864822

1

5.420983358

0.080274853

226.1014

2

5.527759591

-0.047120668

251.5796

3

5.703840446

-5.79718E-05

300.0174

4

5.801290737

-0.032969741

330.7262

5

5.991571713

-0.025424973

400.0429

6

6.130178876

-0.043404149

459.5183

7

6.24342205

0.010406762

514.6165

8

6.251558472

0.00227034

518.8208

9

6.335813463

0.027214641

564.4284

10

6.373341991

0.023587664

586.013

11

6.391706412

0.005223243

596.8742

%K

L

0.017392032 10.72616505 10.04286847 19.51834999 -5.383455466 -1.179237585 -15.57164238 -13.98698973 -3.125775493

%L and %K

Production 25.48

%Production 0.11

4.00

0.13

20.00

0.08

0.11

48.44

0.19

10.00

0.29

30.00

0.11

0.20

30.71

0.10

6.00

0.14

20.00

0.07

0.10

69.32

0.21

20.00

0.40

30.00

0.09

0.25

59.48

0.15

6.00

0.09

50.00

0.14

0.11

55.10

0.12

8.00

0.11

40.00

0.10

0.10

4.20

0.01

2.00

0.02

0.00

0.00

0.01

45.61

0.09

18.00

0.21

10.00

0.02

0.12

21.58 10.86

0.04 0.02 1.04 0.10

6.00 6.00

0.06 0.05

10.00 0.00

0.02 0.00 Sum Average

0.04 0.03 1.07 0.11

Sum Average

K

11.57963783

%L

Jordan Simonson AAE 421 6-10 5/2/2012 0.30

Returns to Scale

0.25 Returns to Scale

Production

0.20

K and L

0.15 0.10 0.05 0.00 1

2

3

4

5 6 Plants

7

8

9

10

MPL (K fixed)

0.12 0.12

MPL (K fixed)

0.12 0.12 0.12

MPL (K fixed)

0.12 0.12 0.12 1

1a &2a:

2

4

5

6 7 Plants

8

9

10

11

K = (Q/a)^(1/b)*L^(c/b)

K= K=

1b&2b

3

156860091.19 1164367041.29

*L^ *L^

-2.39 -2.39

K = C/P(k) - P(l)/P(k) * L k=

lc&2c k= k=

296.34

-0.5

*L

P(l)/P(k) = MP(l)/MP(k) or P(l)/MP(l) = P(k)/MP(k) c/b p(l)/P(k_ *L 0.419101864 0.5 *L 0.209550932 *L

Jordan Simonson AAE 421 6-10 5/2/2012 2d K= k= k=

156860091.19 -29634 0.209550932

L= 2a=2c 2a) K= 2c) K=

*L^ -0.5

417.6523451 0 87.51943814 87.51943814

-2.39 *L *L

0.00

2e K= k= k=

1164367041.29 -29634 14817

L= 2a=2c 2a) K= 2c) K=

a: b: c: k: l: Q= Q2= P(l)= P(k)= cost=

754.9578949 0 158.2007921 158.2021305

0.73300922 0.82505475 0.34578199 1 1 500 1000 $ 25.00 $ 50.00 $14,817.00

800

Production Function Estimation Iso-Cost Curve

600 Capital

*L^

Expansion Path Iso-Quant at 1,000

400

Iso-Quant at 500

200 0 -200

300

400

500

600

700

Labor

800

900

1000

-0.5

0.00

-2.39 *L *L

Jordan Simonson

Jordan Simonson AAE 421 7-9 AAE 4214/29/2012 7-9 4/29/12

BS and “truth”

Functions Trend Analysis Graph 1: Total Cost

200

Table 1: Returns to Scale

Total Cost

RTS 3 2 2.5

TC

150

3

100

3.5 5

50

Total Cost

5.5

0

8.5 10 20 30 40 50 Q 60 70 80 90 100

13

Before doing a goodness of fit model, it appears this is a cubic cost function.

The graph shows this, but it is most easily seen in the returns to scale table. The first four columns of the table show that there was decreasing returns to scale (DRTS) and then the cost function switched the increasing return to scale (IRTS).

This is very typical of a cubic cost function. A cubic cost function typically has plateaus and so we should maximize production on these plateaus to minimize costs and maximize profits.

Goodness of Fit Table 2: Regression Analysis

Regression Statistics R Square Adjusted R Square Standard Error Observations

Cubic 0.999032 0.998548 0.556797 10

Quadratic 0.987768 0.984274 1.832664 10

Linear 0.909411 0.898087 4.665354 10



The R2 statistic

and adjusted R2 statistic

Jordan Simonson AAE 421 7-9 4/29/12 show that the cubic cost function accounts for 99% of the variability, more than any other cost function

ď&#x201A;§

The standard error is also smaller for the cubic cost function, giving further reason to believe this is a cubic cost function The results from table 2 confirm our initial recommendation using a cubic cost

function. Given this data, a linear cost function is least likely to be representative of this cost curve.

Concerns It this data was representative of data over ten months, I feel we do not have enough data to have a representative sample. Using the current data and that assumption would lead you to believe that the company either was working to increase their production or there was some seasonality to the cost of producing your good. If you were working to increase production, these cost values are taken in the short-run. Along the way your company may have become more efficient resulting in the DRTS seen in the function. If there is some seasonality, perhaps an input to your production is more expensive during the summer, we would need to do analysis across the seasons to see what the cost function is.

Both of these would represent a short run pattern.

If this data was taken from 10 different plants, we can then assume this is not in the short run. Using ten plants would allow you to see the various costs associated with different output levels. Since each plant has probably been working at the same production level for a long period of time, you can assume

Jordan Simonson AAE 421 7-9 4/29/12 they are relatively efficient and have been running at the same cost in the long run. You would also have corrected for seasonality.

Cost Curves 1.4

Graph 2: Marginal Cost



MC

1.2

less than 30 a

Quadratic < 30 30 < Cubic < 62 Linear > 62

1

quadratic cost

Linear

MC

0.8 0.6

Quadratic

0.4

Cubic

function would be

0.2 0 -0.2

If output is

the minimal MC. 

0 10 20 30 40 50 60 70 80 90 100 Quantity

If output is

greater than 30, but less than 62, a cubic cost function would be the minimal MC.  Graph 3: Average Variable Cost

If output is greater than 62, a linear cost function would be the minimal MC. 1.2 1

Linear Quadratic Cubic

0.8



AVC

The quadratic

has the lowest AVC until Q~110.

AVC

0.6



0.4 0.2

When Q > 110

the linear cost curve

-0.2

Graph 4: Total Cost

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

0 Quantity

160

TC

150 130 TC

 28 < Linear > 87

Linear Quadratic Cubic

140 120

has the lowest AVC

 28 < Quadratic < 55  55 < Cubic < 87

110 100 90

Linear

80 0

10

20

Quadratic 30

40 50 60 Quantity

Cubic 70

Linear 80

90 100

Jordan Simonson AAE 421 7-9 4/29/12  Depending on your output you will use different cost functions to reduce your cost.

BE and SD Price Analysis Graph 5: BE and SD

Table 4: Percentage Change BE and SD Price

1.5 Costs

Table 3: BE and SD Price

BE and SD Analysis

2

0%

Cubic Quadratic Linear

1

0.5

-7%

55.75%

0%

Min. C Cost SD BE -69%

Base C 0.00% 0.00%

SD BE

-143%

0

C

Shutdown

C ($) 0.30 1.49

Q ($) -0.13 1.38

L ($) 0.46 0.46

% ∆ from Base Q L -143% 56% -7% -69%

Breakeven

-0.5



The quadratic cost function has a negative shutdown cost of -$0.13, a 143% decrease from the cubic cost function.



The linear cost function has the largest shutdown price of $0.46, which is also the lowest breakeven price by 69% from the cubic function.



The cubic cost function has the largest BE price at $1.49

Time Comparison 140

Time Comparison

120 Time (Minutes)

Graph 6: Time Comparison Table 5: Time Comparison

2-4 (Min) 7-9 (Min) ∆ (Min) %∆

100 80

Hwk 2-4 (Min)

60

Hwk 7-9 (Min)

40

C 120 7 113 94%

Q

L

8 4 4 50%

3 2 1 33%

.  Homework 2 for the

20 0 Cubic

Quadratic

Linear

cubic cost function took the

largest amount of time with 120 minutes. This time was primarily to create the template.

Jordan Simonson AAE 421 7-9 4/29/12  There was a 113 minute, 94% decrease in time from a similar cubic cost function tabulation for homework 7-9.  As more cost functions were run, I was able to reduce my MPL by using linked functions and previous templates to speed up the process. I increased my efficiency by 98% from the first time to the last time I used this template.

This is a prime example of putting in your time first to reap the rewards later. If I hadn’t linked everything initially, it would have taken a considerably longer time to recreate those templates. As I completed more cost function tabulations, I was also able to increase efficiency each time once I had the template, further reducing MPL.

Jordan Simonson AAE 421 7-9 4/29/12

Appendix: Cubic Cost Regression Analysis Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.99 0.99 0.99 0.56 10

ANOVA df Regression Residual Total

3 6 9

Intercept Quantity (Linear) Quantity (Quadratic) Quantity (Cubic)

SS 1920.265 1.86014 1922.125

MS 640.0883 0.310023

F 2064.646

Significance F 1.98E-09

Coefficients 99.5 0.51

Standard Error 1.08 0.08

t Stat 92 6.3

P-value 1.11E-10 0.000748

-0.0084 8.37E-05

0.0017 1E-05

-5.07 8.36

0.002284 0.00016

Cubic Cost Function Cost = a + b*Q + c*Q^2 + d*Q^3 Total Cost =

a+ 99.5 a 99.5

AC=TC/Q=

b 0.51 *1/Q *1/Q

ACV=(TC-a)/Q= MC=dTC/dQ=

Output

TC

AC

*Q+ *Q+ +b 0.51 b 300 b 300

AVC

MC

0.51

0.51

0

99.50

10

103.84

10.38

0.43

0.37

20

106.98

5.35

0.37

0.27

30

109.43

3.65

0.33

0.23

c -0.008 c -0.008 +c 25 +2*c 50

*Q^2+ *Q^2+ *Q+ *Q+ *Q+ *Q+ *Q+ *Q+

d 8.37E-05 d 8.37E-05 d 8.37E-05 3*d 0

*Q^3 *Q^3 *Q^2 *Q^2 *Q^2 *Q^2 *Q^2 *Q^2

Jordan Simonson AAE 421 7-9 4/29/12 40

111.70

2.79

0.30

0.23

50

114.28

2.29

0.30

0.29

60

117.68

1.96

0.30

0.40

70

122.39

1.75

0.33

0.55

80

128.93

1.61

0.37

0.76

90

137.79

1.53

0.43

1.02

100

149.48

1.49

0.50

1.33

Cubic

12

AC=Average Cost

10

AVC=Average Variable Cost

8 Cost

MC=Marginal Cost

6 4 2 0 0

20

40

60 Quantity

80

100

Q

Cost

50.60

Shutdown (Q) = MIN AVC:

0.295

104.75

Breakeven (Q) = MIN AC:

120

Changing Cells

1.491 Target Cells

Appendix: Quadratic Cost Regression Analysis Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.993865 0.987768 0.984274 1.832664 10

ANOVA df Regression Residual Total

2 7 9

SS 1898.614 23.51061 1922.125

MS 949.3072 3.358658

F 282.6448

Significance F 2.02E-07

Jordan Simonson AAE 421 7-9 4/29/12 Intercept Quantity (Linear) Quantity (Quadratic)

Coefficients 106.6833 -0.1272

Standard Error 2.155491 0.090022

t Stat 49.49374 -1.41295

P-value 3.6E-10 0.200557

0.005341

0.000798

6.696521

0.000278

Quadratic Cost Function Cost = a + b*Q + c*Q^2 + d*Q^3

AC=TC/Q=

a+ 106.68 a 106.68

b -0.13 *1/Q *1/Q

AVC

MC

0

-0.127

ACV=(TC-a)/Q= MC=dTC/dQ=

Output

TC

AC

0

107

10

106

11

0

-0.020

20

106

5

0

0.086

30

108

4

0

0.193

40 50

110

3

0

0.300

114

2

0

0.406

60

118

2

0

0.514

70

124

2

0

0.621

80

131

2

0

0.727

90

138

2

0

0.834

100

147

1

0

0.941

Shutdown (Q) = MIN AVC: Breakeven (Q) = MIN AC:

*Q+ *Q+ +b -0.13 b 300.00 b 300.00

Q 0.00 141.33

c 0.01 c 0.01 +c 25.00 +2*c 50.00

*Q^2+ *Q^2+ *Q+ *Q+ *Q+ *Q+ *Q+ *Q+

15

*Q^3 *Q^3 *Q^2 *Q^2 *Q^2 *Q^2 *Q^2 *Q^2

AC=Average Cost

10

AVC=Average Variable Cost MC=Marginal Cost

5 0 0

50

100 Output

-5

Cost $0 $1

Appendix: Linear Regression Analysis Regression Statistics Multiple R 0.95363 R Square 0.909411 Adjusted R Square 0.898087 Standard Error 4.665354

d 0.00 d 0.00 d 0.00 3*d 0.00

Quadratic

Cost

Total Cost =

150

Jordan Simonson AAE 421 7-9 4/29/12 Observations

10

ANOVA df

SS 1748.001 174.1242 1922.125

Regression Residual Total

1 8 9

Intercept Quantity (Linear)

Coefficients 94.93 0.46

MS 1748.001 21.76553

Standard Error 3.19 0.05

F 80.31051

t Stat 29.79 8.96

Significance F 1.91E-05

P-value 0.00 0.00

Linear Cost Function AAE421 HOMEWORK 2: Math Appendix, Problem 3a (Cubic Cost Function) Cost = a + b*Q + c*Q^2 + d*Q^3 a+ b *Q+ c *Q^2+ d *Q^3 Total Cost = 94.93 0.46 *Q+ 0.00 *Q^2+ 0.00 *Q^3 a *1/Q +b c *Q+ d *Q^2 AC=TC/Q= 94.93 *1/Q 0.46 0.00 *Q+ 0.00 *Q^2 b +c *Q+ d *Q^2 ACV=(TC-a)/Q= 300.00 25.00 *Q+ 0.00 *Q^2 b +2*c *Q+ 3*d *Q^2 MC=dTC/dQ= 300.00 50.00 *Q+ 0.00 *Q^2

TC

AC

AVC

MC

0.46

0.46

0

94.93

10

99.54

9.95

0.46

0.46

20

104.14

5.21

0.46

0.46

30

108.74

3.62

0.46

0.46

40

113.35

2.83

0.46

0.46

50

117.95

2.36

0.46

0.46

60

122.55

2.04

0.46

0.46

70

127.15

1.82

0.46

0.46

80 90

131.76

1.65

0.46

0.46

136.36

1.52

0.46

0.46

100

140.96

1.41

0.46

0.46

Shutdown (Q) = MIN AVC: Breakeven (Q) = MIN AC:

15

Linear AC=Average Cost

10

AVC=Average Variable Cost

Cost

Output

MC=Marginal Cost 5

0 50 Output 100

0

Q 0.00 â&#x2C6;&#x17E;

Cost $0 $0

150

Jordan Simonson AAE 421 7-9 4/29/12

Comparisons Cubic 0.509926 0.365579 0.271465 0.227584 0.233936 0.290521 0.397339 0.55439 0.761674 1.019192 1.326943

AVC Linear 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303 0.460303

Cubic 0.509926 0.433566 0.373951 0.33108 0.304953 0.295571 0.302933 0.32704 0.36789 0.425486 0.499825 0.590909 0.698737 0.82331 0.964627 1.122688

AC Linear 0 10 5 4 3 2 2 2 2 2 1

Quadratic -0.1272 -0.07379 -0.02038 0.03303 0.086439 0.139848 0.193258 0.246667 0.300076 0.353485 0.406894 0.460303 0.513712 0.567121 0.62053 0.673939

Quad

Cubic 0 11 5 4 3 2 2 2 2 2 1

0 10 5 4 3 2 2 2 2 2 1

1.4

MC

1.2 1 0.8

Linear

0.6

Quadratic

0.4

Cubic

0.2 0 -0.2

0 10 20 30 40 50 60 70 80 90100

1.5

AVC

Linear Quadratic Cubic

1 AVC

Marginal Costs Linear Quadratic 0.460303 -0.1272 0.460303 -0.02038 0.460303 0.086439 0.460303 0.193258 0.460303 0.300076 0.460303 0.406894 0.460303 0.513712 0.460303 0.62053 0.460303 0.727348 0.460303 0.834167 0.460303 0.940985

0.5 0 0

-0.5

12 10 8 6 4 2 0

20

40

60

80

100 120 140

Quantity

Linear Quadratic Cubic

0 10 20 30 40 50 60 70 80 90 100

Jordan Simonson AAE 421 7-9 4/29/12 Quad 107 106 106 108 110 114 118 124 131 138 147

Cubic 100 104 107 109 112 114 118 122 129 138 149

160

TC

140 120

TC

TC Linear 95 100 104 109 113 118 123 127 132 136 141

Linear Quadratic Cubic

100 80 0

10 20 30 40 50 60 70 80 90 100 Quantity

SD and BE Prices Minimum Q Quantities Shutdown Breakeven Minimum Cost Cost Shutdown Breakeven

Cost Shutdown Breakeven

Costs Shutdown Breakeven

Cubic

Quadratic 0.00 141.33

Linear

50.60 104.75

Cubic 0.295540628 1.490882887

Quadratic -0.1272 1.382486

Linear 0.46030303 0.460303259

Base Cubic 0.30 1.49

Change from Base Quadratic Linear -0.42 0.16 -0.11 -1.03

0.00% 0.00%

% Change from Base Quadratic Linear -143.04% 55.75% -7.27% -69.13%

Base Cubic

0.00 Infinity

Costs

Jordan Simonson AAE 421 7-9 4/29/12 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4

0%

BE and SD Analysis

0%

Cubic Quadratic Linear

-7%

55.75%

-69%

Shutdown -143%

Breakeven

Time Comparison Cubic Hwk 2-4 (Min) Hwk 7-9 (Min) Change % Change

140

Linear

120

8

3

7 113 94.17%

4 4 50.00%

2 1 33.33%

Time Comparison

120 Time (Minutes)

Quadratic

100

Hwk 2-4 (Min)

80 60

Hwk 7-9 (Min)

40 20 0 Cubic

Quadratic

Linear