# problemset8 - Middle East Technical University Department...

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Middle East Technical University Spring 2011 Department of Economics ECON 201 Erol Çakmak TA: Osman Değer PROBLEM SET 8 1) Assume an economy characterized by two consumers, A and B, and two goods, X and Y. The price of good X is \$8 and the price of good Y is \$2. Consumer A purchases 2 units of good X and 5 units of good Y. Her marginal rate of substitution of good X for good Y at her goods combination is 2. Consumer B purchases 3 units of good X and 2 units of good Y. His marginal rate of substitution at his goods combination is 6. a. Is consumer A maximizing her utility when she purchases 2 units of good X and 5 units of good Y? b. Is consumer B maximizing his utility when he purchases 3 units of good X and 2 units of good Y? c. Is this allocation of goods purchased by the consumers Pareto optimal? d. Is this allocation of goods purchased by the consumers a competitive equilibrium? e. Can either consumer reallocate his or her spending on goods X and Y and increase his or her utility? If so, what should each consumer do? 2) (Morgan, Katz & Rosen, 12.11) Romeo and Juliet inhabit a pure exchange economy with 10 units of X and 20 units of Y. Denote Romeo s consumption of X and Y as x R and y R , respectively; denote Juliet s as x J and y J . Romeo s utility function is U R = x R ½ y R ½ ; Juliet s is U J = x J ¾ y J ¼ . Write down the expression for the contract curve in this economy. 3) In an exchange economy with two consumers A and B, the initial endowment of

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## This note was uploaded on 03/22/2012 for the course ECON 201 taught by Professor Çakmak during the Fall '10 term at Middle East Technical University.

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problemset8 - Middle East Technical University Department...

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