Minimizing Cost with Calculus (If You Want Recognizing That More Isn’t Always Better with

86 Part II: Considering Which Side You’re On in the Decision-Making Process

Figure 5-5:

Utility maximizing number of tacos and pizza slices.

The customer’s goal is to maximize utility by going to the highest indifference curve touched by the budget constraint B a. For the indifference curve map in Figure 5-5, the highest indifference curve touched by the budget constraint B a is U a, which indicates the customer buys six tacos and zero slices of pizza.

Now, you decide to offer a special promotion: buy one slice of pizza and your second slice is free. Now, if customers buy one slice of pizza, they can still buy four tacos. And because the second slice of pizza is free, the customers can still buy four tacos with two slices of pizza. The resulting budget constraint is described in the last two columns of Table 5-2.

On the graph, this promotion has added a horizontal section to the budget constraint, shifting the budget constraint out at the point between one and two slices of pizza. (Remember, the second slice of pizza doesn’t cost customers anything.) The new budget constraint for the customer is Bb in Figure 5-6.

Again, your customers want to maximize utility by finding the highest indifference curve touched by the new budget constraint. This is the indifference curve Ub in Figure 5-6 and it indicates that the customers now buy four tacos and two slices of pizza. You’ve gone from selling no pizza to this customer to selling two slices! And as an added bonus, your customer is getting even more satisfaction than before.

Chapter 5: Consumer Behavior: A Market for Anything?

87

Figure 5-6:

Utility maximizing number of tacos and pizza slices for the buy one, get one free promotion.

Selling gift cards

Gift cards are used to bias customers toward your business over a competitor. Because the customer can use the gift card at only your business, gift cards affect the shape of the budget constraint.

Compare a situation where a customer has $50 in cash versus $25 in cash and a $25 gift certificate to your store. At first, these situations may seem essentially the same — but they’re not. The gift certificate can be used at only your store, so the maximum that can be spent at your competitor is now only $25.

Figure 5-7 compares the two budget constraints. The budget constraint B a is the budget constraint that exists if the customer can spend $50 cash at either your store or a competitor’s store. (I assume a price of $1 per unit for the good being purchased.) Given $50 cash, the customer maximizes utility on indifference curve U a, spending $38 at your competitor’s store and $12 at your store.

If the customer has a $25 gift certificate at your store, the maximum he can spend at the competitor’s store is $25, while he can spend a maximum of $50 at your store ($25 cash plus $25 gift certificate). The new budget constraint is Bb. Now the customer maximizes utility with indifference curve Ub, spending $25 at your competitor’s store and $25 at your store. That’s $13 more than he had previously spent at your store!