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Unformatted text preview: Problem Set 4 Solutions ECON 401, Winter 2008 Problems A. (3.1) Which of the following pairs of goods are complements (people like to consume them together), and which are substitutes (people are willing to trade off one good for the other)? Are the goods that are substitutes likely to be perfect substitutes for some or all consumers? a. A popular novel and a gossip magazine. Imperfect substitutes b. A camera and film. Complements c. An economics textbook and a mathematics textbook. Independent (neither complements nor substitutes) in some courses, but complements in 401 d. A Panasonic CD player and a JVC CD players Perfect substitutes for many consumers A. (3.4) Miguel considers tickets to the Houston Grand Opera and to Houston Astros baseball games to be perfect substitutes. Show his preference map. What is his utility function? The marginal rate of substitution between Opera and Astros tickets is always 1. Miguels utility function can therefore be expressed as U ( A,B ) = a ( A + B ); where a is a positive constant, A denotes number of tickets to the opera, and B denotes number of tickets to the baseball games. A. (3.6) Give as many reasons as you can for why economists believe that indifference curves are convex. 1 2 A reasonable description of tastes: People like a mix of goods. It seems reasonable that the absolute value of the MRS will decline as we move down an indifference curve. That is, holding utility constant, as X rises and Z falls, it seems likely that the marginal utility of consuming an additional unit of x falls and the marginal utility of consuming an additional unit of z rises. Consistent with observed choices: If consumers have concave indifference curves, then they will only consume one of the goods. A. (3.10) What happens to a consumers optimal choice of goods if all prices and income double? (Hint: What happens to the intercepts of the budget constraint) When all prices and income double, the budget constraint remains unchanged, and there fore the optimal choice of goods is unchanged. To verify that the budget constraint is unchanged, note that before the price change the budget constraint is p 1 q 1 + p 2 q 2 = Y and after the price change the budget constraint is (2 p 1 ) q 1 + (2 p 2 ) q 2 = 2 Y p 1 q 1 + p 2 q 2 = Y A. (3.16) In 2006, Michigan passed legislation that provides greater incentives to drivers who buy ethanol by lowering the state tax on each gallon of ethanolblended fuel to...
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