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# Economics 4808 Problem Set 6 1. Alice's utility is given by U ( x, y , l ) = x 0.2 y 0.2 (168 l ) 0.6 , x and y are goods and l is the amount of

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Economics 4808 Problem Set 6 1. Alice’s utility is given by 6 . 0 2 . 0 2 . 0 ) 168 ( ) , , ( l y x l y x U - = , x and y are goods and l is the amount of hours that Alice works. Alice can only spend what she earns by working at her job that pays her \$10 per hour and by spending her interest income from her trust fund, m > 0. a. Suppose the prices of x and y are \$12 and \$48 respectively. What is Alice’s budget constraint? b. Assume m = \$240. How much of each good does Alice buy and how many hours does she work? c. Assume m = \$1200. How much of each good does Alice buy and how much does she work? d. Suppose again that m = \$240, but now suppose she makes \$20/hr. Does Alice work more or less? Does this seem realistic? Suppose m = \$240, but she makes \$100,000/hr. Does Alice work more or less? Does this seem realistic? 2. Minimize 2 2 2 ) , , ( z y x z y x f + + = subject to 30 2 = + + z y x and 10 3 2 = - - z y x . Solve for * 2 * 1 *, *, *, λ λ and z y x . 3. Recall the regulation model where legislators apply regulations to garner votes. Votes are a function of producer utility (U R ) and consumer utility (U C ). The legislator’s vote/utility function is V = V(U R , U C ). If U R = R, and U C = K – R – L, where K is a constant and R and L are shown in the typical monopoly versus competitive market outcome below. \$ P m R L P c MC MR D Q Obviously, both U R and U C are affected by the eventual price (P) set by the legislator because both R and L are affected by that price. a. Now suppose the demand equation is given by Q P 5 . 0 100 - = , and MC = \$10. Write R as a function of the price and show that the price that maximizes producer utility is \$55. b. Find dP dR U V C and dP dR U V R .

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