Economics for CAPE

ECONOMICS CAPE for

Dave Ramsingh

i ncludes cd-rom

5 Elasticity of demand

LEARNING OBJECTIVES

• Define elasticity of demand.

• Explain price, cross, and income elasticity.

• Calculate price, cross and income elasticity.

• Identify and explain the three types of elasticity.

• Explain the uses of the three types of elasticity.

• Apply the concepts of elasticity.

REQUIRED KNOWLEDGE

• Income and substitution effects

• Factors of demand

• Calculating percentages and calculating gradients.

TOPIC VALUE

This aspect of demand gives some insight into the reasons why people respond to changes in price in the way that they do. Some price changes result in significant changes in demand.

Introduction

Elasticity of demand is defined as the degree of responsiveness of quantity demanded of a good or service in response to changes in the three main influences on demand, namely price, income, and prices of substitutes and complements. Since elastic infers ‘stretching’, quantity demanded may ‘stretch’ or contract when price, income and prices of other related goods change.

Price elasticity

Refer to figure 5.1, which illustrates the changing equilibrium of a price change. In indifference curve theory you would observe that both income and substitution effects cause a significant change in quantity demanded. According to figure 5.1, the change is from Y1 to Y2 units of good Y.

While the change seems significant, this response can in fact be measured quite accurately. There are two ways to calculate the elasticity or ‘responsiveness’ of quantity demanded due to price changes. They are:

1. By formula

2. By change in total expenditure from a price change.

Calculating elasticity by formula

The formula used to measure price elasticity of demand is:

percentage change in quantity demanded of good A percentage change in price of good A

If the formula is applied, then a change from $4 to $5 (see f igure 5.2) is now expressed as change in price, $4 to $5 = 1.

Percentage change = 5 − 4 4 × 100 = 25% or 0.25

Related change in quantity 3 to 2 = 1

Percentage change = 3 − 2 3 × 100 = 1 3 × 100 = −33 1 3 % or −0.33

% Δ in Qd = −33 1 3 % or −0.33

% Δ in Price = +25% or + 0.25

Price elasticity of demand therefore = −0.33 0.25 = −1.33

Note a negative change in quantity equal to −0.33 is divided by a positive change in price of + 0.25, giving a negative answer of −1.33 (i.e., a $1 decrease in price leads to a 33 per cent increase in quantity demanded). All price elasticities of demand and downward sloping demand curves carry a negative sign but by convention the sign and the positive value is given. The negative sign is to indicate the inverse relationship between price and quantity demanded.

Two important aspects of the coefficient are the sign and the size. A coefficient therefore of −1.33 with a negative sign indicates that the slope is negative and the good in question is normal according to price.

The sign therefore indicates the category of the good, which may be normal or inferior. The size refers to the value 1.33 in the above example. If it is greater than 1 then the interpretation is an elastic response. An example of a good that is elastic in demand is branded lines of clothing or footwear.

When the coefficient is less than one, the price elasticity of demand is said to be inelastic. In figure 5.3, a fall in price of good X from $10 to $5 induces a quantity change of 1(4 –5). Applying the formula will give the

coefficients change along the points of the demand curve. Calculating price elasticity of demand is done for a segment or arc of the curve in percentage terms.

It is important to note that in figure 5.3 calculating price elasticity of demand from A to B is different for a price rise, compared to a price fall. When price falls from $10.00 to $5.00 the coefficient value is 0.5. However, a rise from $5.00 to $10.00 gives a different coefficient, that is, from $5.00 to $10.00 = 5 5 =1

The change in quantity is from 5 to 4 = 1

The % change is 1 5 or 20%. The coefficient is 20% = − 1 5 or − 0.2

Dividing −20 100 % = – 0.2

For the same segment A B there are two coefficients, i.e., − 0.5 and − 0.2

To get around this problem the average or midpoint price elasticity of demand formula is applied by dividing formula 1 and formula 2 as follows:

1. change in quantities × 100 sum of quantities

2. change in price × 100 sum of prices

3. Divide formula 1 by formula 2 to find point elasticity Summary

Elasticity of demand measures the responsiveness of quantity demanded to changes in price. Coefficients greater than 1 are elastic responses, while coefficients less than 1 are inelastic.

Since a rise and fall in price over a segment of the curve yield two different coefficients, this is solved using the midpoint or average formula. The sign preceding the coefficient is important because it reflects the type of good. A negative sign implies a normal good according to price while a positive sign implies a Giffen good. The size refers to the degree of responsiveness, that is, where the coefficient is elastic, inelastic, unitary, zero or infinite.

The total revenue method of estimating price elasticity of demand

The second method of estimating price elasticity of demand is the change in total revenue or total expenditure of consumers for a price rise or fall.

An example of a good that is inelastic in demand is electricity. Since the coefficient is less than 1 it is inelastic in demand. Note again that the sign categorises the type of good (normal) and size, plus the degree of responsiveness.

Common error

Guard against confusing the elasticity of demand of a point on the curve and elasticity of demand between two points. A demand curve that is a straight line has a constant slope mathematically, but the elasticity

Total revenue (TR) is calculated as price multiplied by quantity. The basic rule of thumb is if an increase in price causes total revenue to fall, demand is said to be elastic. For a price fall, an increase in revenue indicates that price elasticity of demand is similarly elastic. See figure 5.4. A price rise from $5.00 to $8.00 yields a fall in TR as follows:

15 × $5 = $75

4 × $8 = $32

From a rise of $5 to $8 the fall in TR = $43

Figure 5.2 An elastic response measured

Figure 5.3 An inelastic response measured for good X

5.4

A fall in price will cause TR to rise by $43.00. In figure 5.5 a price rise or fall yields opposite results. A price rise in this instance causes TR to rise instead and a price fall causes TR to fall.

Example: 5 × $10 = $50.00 4 × $20 = $80.00

Increase in TR = $30.00

Likewise, a price fall will cause TR to fall by $30. In this case, price elasticity of demand is said to be inelastic. There are instances when there is neither a rise nor fall but a constant coefficient = 1; in this case, it is called unitary elasticity.

In figure 5.6 any price multiplied by quantity would yield a TR of $24.00 whether prices are rising or falling. This is a unique feature of unitary elasticity. For example, at a price of $12.00 and quantity of two units, TR = $24.00. If the price falls to $6, the corresponding quantity would be 4. Therefore, TR = 6 × 4 = $24.00. Any price increase or fall will yield a TR = $24.00.

Extremes in elasticity

There are two extremes in price elasticity of demand. They are zero or perfectly inelastic demand and infinite or perfectly elastic demand.

Zero elasticity

As the coefficient implies the value is always equal to zero. Figure 5.7 shows that a rise in price will yield a coefficient as follows:

For a price rise of $2 to $3

Change in quantity = 0

% Δ in P = 0.5 or 50%

% Δ in Qd

% Δ in price = 0 0.5 = 0

For a price fall $3 to $2

% Δ in Qd = 0

% Δ in P = 1 3 or 0.3

% Δ in Qd

% Δ in P = 0 0.3 = 0

Any value divided by zero is equal to zero. An example of this type of elasticity may be observed for the price changes of insulin for persons suffering from diabetes. They would purchase the drug whatever the changes in price.

Perfect elasticity

In the case of perfect elasticity the price does not change but quantity does change. In fact, at a price of $10.00 an unlimited amount is demanded. Hence price elasticity of demand is infinite (∞). Figure 5.8 shows a horizontal demand curve at a price of $10.00. The curve is perfectly elastic.

Figure

An elastic response: total revenue method

Figure 5.5 An inelastic response: TR method

Figure 5.7 Perfect inelasticity

Key point

There are two methods of estimating price elasticity of demand. They are the formula method and the change in TR method. They are invaluable to an entrepreneur who has to price his product according to the price elasticity of demand. An important point to note is that price elasticity of demand changes throughout the points of a linear demand curve.

Changing values of point elasticity of demand

The midpoint of the linear demand curve in figure 5.9 has a price elasticity of demand equal to 1. Note that price elasticity of demand starts at zero at point D on the horizontal axis and increases in value to point A on the vertical axis. Points to the right of B above have a value less than 1, while to the left of B values are greater than 1. At point B, the value is equal to 1. Although price elasticity of demand at a point can be calculated by algebra, a quick way to measure it is at a single point, for example at point B. In order to estimate the elasticity at that point the distance BD is divided by distance BA, which is equal to 1. Price elasticity of demand at C will then be CD/CA = <1.

Table 5.2 Factors affecting elasticity of demand

1. Availability of substitutes

2. The absolute price of the good

3. Proportion of income spent on the good

When there are good substitutes, a change in price will cause demand to fall significantly, e.g., soft drinks.

The higher the price of a good, e.g., automobile or laptop computer, the more elastic for a price rise or fall.

House buying elicits a significant response to price changes, since a mortgage is a large proportion of income.

4. Time periodOver time consumers adjust their expenditure to alternative products. Price elasticity of demand is >1.

5. Durability of a goodIf the good lasts for a short time people would need it quickly. Price elasticity of demand is >1.

6. AdvertisingGoods not promoted tend to have an elasticity >1.

7. Habit-forming goods and services

For goods that are not addictive or habit forming, e.g., clothing, price elasticity of demand is usually >1.

8. Necessities and luxuriesLuxuries, e.g., swimming pool, price elasticity of demand > 1.

Gasoline does not have many good substitutes as a car fuel. A price rise will not cause a large change in demand.

Low-price items like lead pencils elicit insignificant quantity changes when price changes.

Buying erasers whose prices have risen and fallen are unlikely to elicit a significant quantity change.

Little time does not allow information on price changes to affect demand.

Products like television sets and refrigerators are not changed easily and price elasticity of demand will be <1.

Advertising may cause brand loyalty to increase. Price changes are not likely to affect quantity significantly.

Alcohol, tobacco and coffee are habit forming and not sensitive to price changes, therefore price elasticity <1.

Electricity and gasoline are necessities and not sensitive to price changes.

Figure 5.8 Perfect elasticity

Table 5.1 Price elasticity of demand and changes in TR

Summary

Price elasticities of demand differ along different points on a curve. In a straight line linear curve the midpoint has a value of 1. To the left of the midpoint, values are greater than 1 in ascending value. Similarly, to the right of midpoint, values are less than 1 in descending value. A simple formula for determining point elasticity is the inverse of slope multiplied by price at any point of measurement.

The usefulness of price elasticity

›If price elasticity of demand is elastic, decreasing prices via discounts or bargain sales yield an increase in TR.

›If price elasticity of demand for a good or service is inelastic, a firm may raise prices to increase profit, e.g., alcohol, cigarettes, gasoline, electricity.

›Firms may separate markets with different elasticities to price discriminate, e.g., home and foreign markets or night rates for internet users versus daytime rates.

›Advertising creates brand loyalty, making demand inelastic as well as increasing market share for a firm. Successful advertising shifts the demand curve to the right.

›The government may raise taxes on habitforming goods and services in order to raise tax revenues, e.g., gasoline, alcohol, tobacco and gambling.

›Unions may bargain for higher wages in industries whose products have an inelastic demand, e.g., water or electricity.

›A government may lower (devalue) the price of its currency to encourage an inflow of foreign revenue from the sale of exports with an elastic demand. Refer to chapter 33 for more information on exchange rates.

Cross elasticity of demand

If you were thinking of buying a watch but found out that the battery is just as expensive as the watch, you

would rethink your purchase of the watch. The same goes for computers and printers, ink or compact discs.

Your concerns have to do with another significant influence on demand, that is, the change in the price of one good and how it affects the quantity demanded of a good related to it; for example, computers and printers are known as complements or goods used jointly. Relatedly, how does the price of frozen goat meat affect the quantity demanded of fresh goat meat, given that they are substitutes?

These concerns are all related to cross elasticity of demand (CED) or cross price elasticity of demand, which is defined as the degree of responsiveness of quantity demanded of one good in response to the price change in another related good. It is expressed in the formula:

CED = % Δ in Qd of good A

% Δ in price of good B

Once again the sign and size are very critical in categorising the good and measuring its price responsiveness. If the coefficient is a negative sign, the category of the good is said to be a complement.

See figure 5.10. When the price of a flashlight falls from $100 to $50, the quantity of batteries demanded increases from 50 to 125 units since more flashlights will be bought with a price fall, then CED of batteries is expressed as:

Δ in Qd of batteries = 125 − 50 = 75.

The % change is 75/50 × 100 =150%

Δ in price of flashlight = $50 − $100 = $−50 or % Δ = − 50 × 100 100 = −50%

CED therefore +150% −50% = −3

Figure 5.10 Complementary goods

Note the sign and the size denote a complement that is very responsive. Similarly, for substitutes, consider wheat flour and cornmeal flour. Refer to figure 5.11. If the price of a bag of wheat flour rises from $10 to $15 the demand for wheat flour will fall. The demand for a substitute, cornmeal flour, will rise.

The CED of cornmeal = % Δ in Qd of cornmeal

= 20 − 10 10 × 100 = +100%

Figure 5.9 Point price elasticity of demand

% Δ in price of wheat flour = 15 − 10 10 × 100 = +50%

+100% +50% = +2

CED = +2

Price (Wheat flour)

Quantity demanded (Cornmeal)

Note again the positive sign associated with the category that is a substitute when whole wheat prices change and the quantity of cornmeal demanded increases. The size denotes how responsive cornmeal is as a good substitute for wheat flour.

Independent goods

Refer to figure 5.12. When goods are not related in any way they are said to be independent and carry a coefficient of zero.

Example: % Δ in Qd of coconuts = 0

% Δ in price of gold jewellery = −10%

Therefore CED = 0

Price (Jewellery)

Summary

Quantity (Coconuts)

Cross elasticity of demand measures the percentage change in quantity demanded of one good when the price of another related good changes. For complements, the sign is negative; for substitutes, it is positive; and for independent goods, the coefficient is equal to zero.

›The main factor affecting cross elasticity of demand is the extent to which goods are close complements or substitutes.

›A high negative CED suggests very close complements; for example, CD players and CDs, although a fall in price of CDs may not impact strongly on the quantity demanded of CD players. Similarly, a CED with a high positive value suggests very close substitutes; for example, a peanut drink and chocolate milk drink, or two competing brands of toothpaste, or soap powder.

The value of cross elasticity of demand to a firm

It is important for a firm to know CED values for complements and substitutes. If there is high CED between hot dog sausages and hot dog bread, for example, and there is a price rise for hot dog sausages, firms may counteract the expected fall in demand for hot dog sausages by offering hot dog bread on sale, or selling them together at a bargain price. For example, you may observe that coffee is sometimes sold with cream in the same package for one price.

Similarly, if CD players increase in price a firm may counteract the expected fall in demand for CD players by offering free compact discs.

Cross elasticity of demand is largely influenced by the closeness in the relationship of substitutes and complements. A high value in both instances refers to a very close relationship between the products.

Income elasticity of demand

Since income is a main influence on demand, a change in real income, that is, a price fall or income rise without inflation, will very likely increase demand for goods and services.

Recall that an increase in income will cause a shift in the demand curve to the right for normal goods, whereas an increase in price induces changes along the curve. It was also noted that when incomes increased, there was a fall in demand for some type of goods called inferior goods.

Income elasticity of demand (YED) measures the percentage change in quantity demanded of goods and services in response to changes in income. Expressed in formula it is:

% Δ in Qd

% Δ in Income

A coefficient greater than 1 is said to be elastic, less than 1 inelastic and zero elastic if there is no change in quantity demanded when income changes. Once more the sign and size are important. A positive sign indicates a normal good according to income. See figure 5.13. A negative sign indicates an inferior good, as shown in figure 5.14.

Figure 5.11 Substitute goods

Figure 5.12 Independent goods

Table 5.3 The relationship between type of good, price elasticity of demand, sign

Note that there are occasions when real changes in income cause no change in quantity demanded. This is also called a zero income-elastic response. Moreover, a single good may, over time, experience all three types of income elasticities as illustrated in the Engel curve in figure 5.15.

If a newly employed person travels by bus to work, small income increases will cause his or her demand for bus travel to be stable. They may demand 20 hours a month of bus travel if their income is $5,000 monthly.

Yet, despite an improved income of $7,000, their bus travel stays at 20 hours, with perhaps carpooling as well. After 7 or 8 years and multiple income increases they may purchase a car and use less bus travel. Bus travel, therefore, could be a normal good with respect to income, zero elastic and an inferior good over a period of time.

Goods that respond positively to increases in real income are sometimes called superior or incomeelastic goods. Some examples are houses, automobiles, swimming pools, expensive jewellery, plasma television sets, satellite dishes, upscale restaurant dining and foreign travel. There is an upsurge in activity in these markets when an economy is enjoying high-income changes in buoyant economic conditions.

Factors affecting income elasticity of demand

It is assumed that income responsive goods and services depend on levels of disposable income that are generally determined by rates of taxation. In addition, rates of inflation and expectation of inflation would temper consumers’ demand for income-elastic goods. Expectations in an economy may also be a determining factor when crime rates are high and political stability not assured.

If a country has a high standard of living, as in developed countries, and consumers are accustomed to the purchase of income-elastic goods their income elasticity of demand may be high, for example foreign holidays.

Wealthy individuals react to increases in real income differently from average or low-income earners, since low-income earners may purchase only basic necessities.

In developing countries with steady economic growth, demand for inferior goods falls in favour of superior goods, such as tertiary level education.

Figure 5.13 A normal good

Figure 5.14 An inferior good

Figure 5.15 The Engel curve

Value of income elasticity of demand and decision making

›A firm may benefit from a knowledge of income elasticity of demand when economic conditions are positive and incomes are rising. Cars, house buying, foreign travel, upscale dining and real estate markets record high profit levels.

›In a recession when incomes are falling, firms may concentrate on selling inferior goods, e.g., basic goods and services. Firms trading in superior goods may target high-income earners or advertise extensively. Insurance and other financial products experience high demand during an economic boom.

›Caribbean hotels target markets in foreign countries whose economic growth rates are rising, because real incomes in those countries are likely to be rising as well.

Summary

Income elasticity of demand (YED) measures the relationship between changes in real income and quantity demanded as is expressed in the formula:

% Δ in Qd % Δ in income

Negative and positive values of YED indicate inferior and normal/superior goods respectively. An Engel curve illustrates all three types of income elasticity.

Chapter summary

›Elasticity in economic language is the extent or degree of responsiveness of quantity demanded to a change in three significant determinants of demand: the absolute price of the good, level of income, and price of other related goods.

›It is calculated by formulae. For price elasticity of demand, changes in TR are also used.

›The average or midpoint formula is the most accurate measure of a segment of the curve because values are different for the same segment of a curve.

›Income elasticity measures the percentage changes in quantity demanded with respect to changes in income, while CED measures the extent to which goods are related.

›The sign and size are important in categorising and interpreting elasticities of demand.

›Elasticity is a useful tool of analysis for firms, governments and unions in predicting changes in the economic environment.

›Normal, inferior, Giffen, complements, substitutes and snob value goods all carry different PED,YED and CED.

Practice questions

Multiple choice questions

1. The price elasticity of demand of good X is 0.5. If the price of the good changes by 10 per cent what is the corresponding percentage change in quantity?

a. 10 per cent

b. 20 per cent

c. 5 per cent

d. 15 per cent

2. The demand for good X is perfectly elastic. 50 units are sold at Bds $3.00 per unit. If the price is raised to $4.00 expenditure on the good X will be:

a. $150.00

b. $200.00

c. $600.00

d. $0.00

3. The price elasticity of demand of a good is unitary. When the price of the good is $3.00, quantity demanded is 40 units. If the price of the good increases to $6.00, what will be the change in quantity demanded?

a. 24

b. 20

c. No change

d. 80

4. The price elasticity of demand of good B is unitary. What will increase if the price is reduced?

a. Total revenue

b. Expenditure on substitutes

c. Quantity demanded

d. Expenditure on good B.

Structured question

1. a. Define price, income and cross elasticity of demand. Support your answers with formulae, examples and appropriate diagrams.

b. The Caribbean is a popular tourist destination. Identify three factors that may influence the price elasticity of demand for hotel accommodation in Barbados in the month of July. What factors may determine YED for holidays in Jamaica in the month of August?

c. How may a hotelier in Antigua use a knowledge of CED to boost his profits during the month of August?