211-1 PS2 F07

# 211-1 PS2 F07 - MMSS 211-1 Problem Set 2 Fall 2007 1...

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MMSS 211-1 Problem Set 2 Fall 2007 1. Auerbach’s demand for frozen custard is given by P = 20 – 2Q A while that for Kotlikoff is given by P = 40 – 2Q B . Supposing that these are the only two consumers in this market, what is the market demand for frozen custard? 2. For each of the following utility functions U(x,y), calculate MU x , MU y , and MRS x,y and show whether the indifference curves are convex to the origin or exhibit some other shape. a) U = x 4 y 4 b) U = x .25 y .25 c) U = xy 2 d) U = 5x + 3y e) U = x 2 + 2xy + y 2 3. Tom spends all of his \$100 weekly income on two goods, X and Y. His utility function is given by U(X,Y) = XY. If P X = 4 and P Y = 10, how much of each good should he buy? 4. Same as #1 except now Tom’s utility function is given by U(X,Y) = X 1/2 Y 1/2 . 5. What is the relationship between your answers to Problems 3 and 4? 6. Let U(x,y) = 4x + y. a) Is the assumption of nonsatiation satisfied here? b) Does the marginal utility of x diminish, remain constant, or increase as more x is consumed? Explain. c) What is the MRS here? d) Is the MRS diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? 7.

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211-1 PS2 F07 - MMSS 211-1 Problem Set 2 Fall 2007 1...

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