Exercise 3

Every month, a family of three spends $2,000 on food (F) and other items (O). The family's preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1.
a) Find this family's monthly food expenditure.

The family could join a consumers' club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8).

b) Suppose the club did NOT charge a membership fee: how much money would the family spend on food? How much food would the family buy?

c) Would the family be willing to pay more than $80 to join the consumers' club? Clearly justify your answer.

d) In a diagram where you measure food along the horizontal axis, illustrate the budget constraint and optimal bundle of this family if it doesn't join the consumers' club. In the same diagram, illustrate the highest fee the family is willing to pay to join the consumer's club (reminder: as the unit price of other items is $1, you can measure the dollar fee along the vertical axis).