Suppose I run a fast-food restaurant and I know my customers come in on a limited budget. Almost everyone that comes in for lunch buys a soft-drink. Now suppose it costs me virtually nothing to serve a medium versus a large soft-drink, but I do incur some extra costs when adding items (like a dessert or another side-dish) to someone’s lunch tray.

A:

Suppose for purposes of this exercise that cups come in all sizes, not just small, medium and large; and suppose the average customer has a lunch budget B. On a graph with “ounces of soft-drink” on the horizontal axis and “dollars spent on other lunch items” on the vertical, illustrate a customer’s budget constraint assuming I charge the same price p per ounce of soft-drink no matter how big a cup the customer gets.

(a) I have three business partners: Larry, his brother Daryl and his other brother Daryl. The Daryls propose that we lower the price of the initial ounces of soft-drink that a consumer buys and then, starting at 10 ounces, we increase the price. They have calculated that our average customer would be able to buy exactly the same number of ounces of soft-drink (if that is all he bought on his lunch budget) as under the current single price. Illustrate how this will change the average customer’s budget constraint.

(b) Larry thinks the Daryls are idiots and suggests instead that we raise the price for initial ounces of soft-drink and then, starting at 10 ounces, decrease the price for any additional ounces.

He, too, has calculated that, under his pricing policy, the average customer will be able to buy exactly the same ounces of soft-drinks (if that is all the customer buys on his lunch budget).

Illustrate the effect on the average customer’s budget constraint.

(c) If the average customer had a choice, which of the three pricing systems—the current single price, the Daryls’ proposal or Larry’s proposal—would he choose?

B:

Write down the mathematical expression for each of the three choice sets described above, letting ounces of soft-drinks be denoted by x1 and dollars spend on other lunch items by x2.