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ans to problem set4 f07

Intermediate Microeconomics: A Modern Approach, Seventh Edition

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Econ 301 – F07 Answers to PROBLEM SET 4 - due in class on Thursday Oct 25 Wissink 1. Derive/recall the demand functions for x & y for the utility function u(x, y) = xy. Calculate the own- price elasticity of demand for x using the demand function for x you derived. Calculate the cross-price elasticity of demand for x with respect to Py. Calculate the income elasticity of demand for x. [ANSWER] With the utility function, u(x,y)=xy, we get x*=I/2Px and y*=I/2Py. The own price elasticity of demand for x, the cross-price elasticity of demand for x with respect to Py, and the income elasticity of demand for x are in the followings: 1 2 / 2 1 0 0 1 2 / 2 , , 2 , = × = × = = × = × = = × - = × = Px I I Px x I I x x Py x Py Py x Px I Px Px I x Px Px x D I x D y x D Px x η η η 2. Suppose there are two markets: the market for Butter, B, and market for Guns, G. Suppose the demand curve in each market is linear where P=price and Q=quantity. That is: P B = K – sQ B and P G = F - tQ G . Suppose these two demand curves intersect the price axis at the same value, i.e., K = F. Using the exact point elasticity formula, show that if quantities are selected such that prices are equal in these two markets, then so are their own-price elasticities of demand. [ANSWER] With K=F, we get sQ B =tQ G. from the following: P B =P G => K-sQ B = F – tQ G => sQ B =tQ G. The own-price elasticity of demand for Butter is |-1/s|*P B /Q B = P B /(s*Q B ) and the own-price elasticity of demand for Guns is |-1/t|*P G /Q G = P G /(t*Q G ) = P B /(s*Q B ) since sQ B =tQ G and P B =P G . 3. Suppose that on January 1st 2007, the Ithaca Transit Authority increased fares on all its bus lines from 40 cents to 60 cents. Private bus companies in Ithaca did not change their fares. The Daily Sun of January 8th reports that the total number of rides on city-owned buses decreased from 2200 to 1800 per day; on those city lines competing with private bus lines, the number of rides decreased from 1150 to 850 per day. a. Compute the own price elasticity of demand (over the one-week period) for all city-owned bus lines. Compute the own price elasticity of demand for city-owned lines competing with private companies. b. Is the demand for bus rides elastic or inelastic? Explain.

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