Britney is very fashionable. When she buys a new dress (D), she also needs to bu

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 $10, the price of a hat is $6, and she has $64 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?

Explanation / Answer

A. U = min{D,H} Here, we see that Britney only gets utility out of a dress or a hat if she has another to match. B. Budget: 10D + 6H = 64 solve for D 10D = 64 - 6H D = 6.4 - 0.6H Substitute this into the utility function. U = min{D,H} U = min{6.4 - 0.6H,H} Here, the minimum will occur when H = 6.4 - 0.6H. Solve for H. H = 6.4 - 0.6H 1.6H = 6.4 H = 64/1.6 H = 4 Substitute this into your budget constraint. 10D + 6H = 64 10D + 6*4 = 64 D = (64 - 6*4)/10 D = 4 So, Britney is going to consume 4 dresses and 4 hats. C. U = min{D,H} U = min{4,4} U = 4

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