# UW-Madison ECON 301 - Problem Set (2 pages)

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## Problem Set

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## Problem Set

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Econ 301 - Intermediate Economics
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Econ 301 Intermediate Microeconomics Prof Marek Weretka Problem set 3 due Thursday February 11th 10 before class Problem 1 Cobb Douglas Utility function Tony likes nuts x1 and berries x2 and his preferences are described by the following utility function U x1 x2 xa1 xb2 Find the following variables 1 the optimal fraction percentage of income spent on berries 2 the optimal amount of total cash dollars spent on berries 3 the optimal quantity of nuts consumed 4 the slope of the indi erence curve at the optimal bundle for the following values of parameters a a 4 b 8 p1 5 p2 10 m 60 b a 13 b 31 p1 4 p2 1 m 12 c a 12 b 32 p1 5 p2 1 m 20 Hint Instead of calculating optimal choices using two secrets of happiness take advantage of the demand formulas for Cobb Douglas utility that we derived in the class Problem 2 Benjamin spends his time either watching movies x1 he uses on demand option cable TV or listening to songs MP3 downloaded from the Internet x2 His preferences are described by U x1 x2 ln x1 ln x2 Answer the following questions a Derive Benjamin s demand for movies and MP3 les as a function of prices p1 p2 and his income m do not use Cobb Douglas formula but rather derive demand using two secrets of happiness b Fix the price of MP3 at p2 1 and income on m 10 Find the price o er curve give an exact formula x2 f x1 and plot it in the commodity space Find the demand curve x1 f p1 and plot it in the graph with p1 on vertical axis and x1 on horizontal axis c Is x1 an ordinary good or a Gi en good Explain d Now x p1 1 and p2 1 In the commodity space plot the income o er curve In addition in two separate graphs plot Engel curves for both movies and MP3 les Argue that the two commodities are normal not inferior e For the demand functions from point a determine whether the two goods are gross complements substitutes or neither Problem 3 Perfect Complements Consider Trevor from our previous problem set who begins his day with strawberry milkshake To prepare it he mixes milk x1

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