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ECON201PS3 - WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS...

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WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS ECONOMICS 201-03 JOHNSON Problem Set #3 (due IN LECTURE Friday, September 26 th ) 1. A utility maximizing consumer has the following utility function: U ( X , Y ) = (3/2)X 2/3 + Y a. Are these preferences strictly monotonic? Strictly convex? Explain. b. Assuming our utility maximizer faces a linear budget constraint of the form P X X + P Y Y = I , derive his/her optimal demands X*( P X , P Y , I ) and Y*( P X , P Y , I ) . You may use any method you prefer, but please show your work. If these demands are piecewise functions, then state each piece clearly (namely, is a corner solution possible, and, if so, what would X* and Y* be then?) c. Assuming an interior optimum, what is the own-price elasticity of demand for X? The cross price elasticity of demand for X with respect to P Y ? d. Assuming an interior optimum, graph the Engel curve for Y. Label intercept and slope values carefully. e. Suppose, initially, that I = 100 , P X = 2 and P Y = 2. Graph this consumer’s initial optimum point (A) in a well-labeled graph. Your indifference curve should show whether strict convexity holds and whether it can hit an axis (or both). f. The price of X falls to 1. Find the consumer’s new optimum point (C) and label it on the same graph as in (e). Draw another indifference curve to show this new optimum. g. Find the coordinates of the substitution effect point (B) of this price change. Label it and draw the compensated budget line tangent to the original indifference curve through point A. [Hint: What do we know about good X for interior solutions here?] 2. In a two good world, a utility maximizer with strictly convex preferences has a perfectly inelastic demand curve for good X. Derive this demand curve in a
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