Question

Britney is very fashionable. When she buys a new dress (D), she also needs to buy a hat (H)to match that dress and vice-versa. So, she views the two goods as perfect complements. The price of a dress is $15, the price of a hat is $10, and she has $85 to spend.

a) Write down a utility function that represents Britney's preferences over dresses and hats.

b) How many dresses and hats is she going to consume? (Hint: the first order conditions will not help; draw the budget constraint and the indifference curves and look at the highest one that intersects the budget constraint)

c) What is the exact value of Britney's indirect utility?

Answer 1

a)

Dress and Hat are perfect complements. Hence the utility function can be written as:

U = min(D, H)

Thus she should buy an equal number of dresses and hats. Keeping the number of one good the same and increasing other good would not increase the utility.

b)

We know that D = H

The budget line of the consumer can be written as:

D*Pd + H*Ph = M, where M is the income of the consumer

D*15 + H*10 = 85

Since H = D

D*15 + D*10 = 85

25D = 85

H = 3.4

D = 3.4

c)

The indirect Utility function is found by putting the value of D and H in the normal utility function.

U = min(D,H) = min(3.4, 3.4) = 3.4