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Unformatted text preview: Intermediate Microeconomics, 2008 Problem Set No 5 due: Monday / Tuesday, Jan, 28 / 29 We strongly suggest you do the problem set before class on Monday, so that you can familiarize yourself with the topics and the new concepts. Problems 1) Please, do the following problems from chapter four of the book: 7) 11) 15) 16) 17) 2) Why can&t all goods be inferior? 3) A consumer faces prices for hot dogs and hamburgers of $1 each. Con- sumption of the two commodities at various weekly income levels are shown below. a. Use the information to sketch the income consumption curve on a graph. b. Draw the Engel curves for hot dogs and hamburgers. Income Hot Dogs Hamburgers $10 3 7 15 6 9 20 10 10 c. What is the income elasticity of hot dogs for this consumer as income increases from $10 to $15? 4) For each of the following statements, de¡ne all of the bold terms. Then, explain why the statement is true or false. a. If a consumer views two goods as perfect substitutes then their optimal choice will be a corner solution . b. The substitution e/ect from a price increase states that the consumer will always choose a smaller amount of that good to consume. However, the income e/ect states that consumption can move in either direction. 1 c. Suppose Alf and Bo have convex indi/erence curves . Alf likes units of "X&more than units of "Y&but Bo likes units of "Y&much more than units of "X& . Then, in the optimum, Alf&s marginal rate of substitution will be di/erent from Bo&s even if they face the same prices. d. All Gi/en goods are normal goods , but not all normal goods are Gi/en goods. e. Economists assume that preferences are ordinal . This implies that given two utility functions and one is a monotonic transformation of the other, then they represent the same preferences over bundles of goods. 5) Suppose the price of X goes up and a consumer goes on consuming the exact same amount of X as before. Then X cannot be an inferior good. True or False? Explain your answer. 6) We considered preferences represented by the following utility function in class: U ( q 1 ;q 2 ) = q 1 q 2 . We assume that income is ¡xed at Y = 2 and the price of good two is ¡xed as p 2 = 1 (so you can drop these variables as parameters from the functions, to save notation). 6a) Derive demand of good one, D 1 ( p 1 ) . At p 1 = 1 4 , how much q 1 and q 2 is demanded? What is the utility level? 6b) Derive Hicks demand function of good one and two, H 1 & p 1 ; & U ¡ and H 2 & p 1 ; & U ¡ at & U = 4 . To ¡nd H , ¡nd the bundle is minimizes costs X ( q 1 ;q 2 ) s.t. U ( q 1 ;q 2 ) = 4 ....
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This note was uploaded on 06/18/2008 for the course ECON 401 taught by Professor Kuhn during the Winter '08 term at University of Michigan.
- Winter '08