Midterm 08

Midterm 08 - Economics 104A Solution for Midterm Exam...

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Economics 104A Solution for Midterm Exam Winter 2008 1. (a) (5pt) Let u ( x 1 ,x 2 ) = x 1 + x 2 be a utility function for a consumer. Are the two goods perfect substitutes for the consumer? Explain why or why not. Draw the IC with utility level 1. Answer: Notice MU 1 ( x ) = MU 2 ( x ) = 1 2 x 1 + x 2 . It follows MRS ( x ) = 1 which in turn implies that the consumer is always willing to substitute one good for another at a 1-1 ration. The IC with utility level 1 is the straight line x 1 + x 2 = 1 (see Figure 1). (b) (5pt) Andy purchases only two goods, kumquats (K) and oranges (O). He has an income of $40 and can buy kumquats at $4 per pound and oranges at $2 per pound. His utility function is u ( K,O ) = 5 K + 3 O . What bundle of kumquats and oranges should he purchase to maximize utility? Why? Answer: The given utility function implies MU K ( x ) = 5 and MU O ( x ) = 3. Hence, MRS ( x ) = 5 3 which implies that kumquats and oranges are perfect substitutes for Andy. Since p
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Midterm 08 - Economics 104A Solution for Midterm Exam...

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