w10_ps2_econ100

w10_ps2_econ100 - Economics 100BWinter 2010 Problem Set 2...

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Economics 100B—Winter 2010 Problem Set 2 Due January 19, 2010, 9 am 1. For each of the following utility functions, write down the marginal utility (for each good x and y), and state whether the function exhibits a diminishing marginal rate of substitution of good x for good y. a. U(X,Y) = X+2Y b. U(X,Y) = (1/X) + (1/Y 2 ) c. U(X,Y) = 2X .5 Y .5 d. U(X,Y) = .3ln(X) + .7ln(Y) e. U(X,Y) = X + 2Y + 3XY 2. Pat has an income of $30,000 that she allocates between books and pizza. The price of a book is $20; the price of a pizza is $12. a. Draw Pat’s budget line, labeling the intercepts and calculating the slope. Illustrate her preferred point of consumption using an indifference curve. b. What is the slope of Pat’s indifference curve at her preferred point of consumption? c. Show what happens to Pat’s consumption of books and pizza if the price of books doubles. d. Show what happens to Pat’s consumption if her income is reduced to $20,000 (but the original prices are in effect) 3.
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w10_ps2_econ100 - Economics 100BWinter 2010 Problem Set 2...

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