hw2-solutions - Intermediate Microeconomics Econ 3101,...

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Unformatted text preview: Intermediate Microeconomics Econ 3101, Section 002 Homework 2-Solutions Timothy Lim Uy NOTE: Partial points are only to be awarded if the answers given are incorrect. Question 1. Demand I. Consider the case where there are two goods, x and y , with prices p x and p y respectively. Sup- pose the consumer has income m . (a) [10] Given that the consumer’s utility function is given by u ( x, y ) = min { 2 x, 3 y } , determine the consumer’s demand for goods x and y . Ans: The consumer’s problem is given by max u ( x, y ) = min { 2 x, 3 y } s.t. p x x + p y y = m . Given this particular function, the consumer’s optimal choice requires y = 2 x 3 . Plugging this into the budget constraint yields the demand functions x * = 3 m 3 p x +2 p y , y * = 2 m 3 p x +2 p y . (b) [10] Suppose now the consumer’s utility function is u ( x, y ) = 2 x + 3 y instead. Derive the consumer’s demand for goods x and y . Ans: The consumer’s problem is given by max u ( x, y ) = 2 x + 3 y s.t. p x x + p y y = m , x ≥ 0, y ≥ 0. Demand is given by: • For p x p y > 2 3 , x * = 0; y * = m p y • For p x p y < 2 3 , x * = m p x ; y * = 0 • For p x p y = 2 3 , ( x * , y * ) = { ( x, y ) : p x x + p y y = m, x ≥ , y ≥ } (c) [5] What is the optimal consumption bundle for the consumer in part(b) if...
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hw2-solutions - Intermediate Microeconomics Econ 3101,...

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