spring2009_midterm2_soln

spring2009_midterm2_soln - Second Midterm Exam Econ 150b....

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Unformatted text preview: Second Midterm Exam Econ 150b. Intermediate Microeconomics April 1, 2009 Please write your name and discussion-section time on each blue book. 1. (65 points.) Consider a pure exchange economy with two goods, labeled 1 and 2, and two consumers, labeled A and B . Write .! A 1 ;! A 2 / and .! B 1 ;! B 2 / for the endowments of con- sumers A and B , respectively. Suppose the consumers have utility functions u A .x A 1 ;x A 2 / and u B .x B 1 ;x B 2 / , which are smooth, monotonic and concave (i.e., indifference curves are convex). (a) (5 points.) Define feasible allocation . Soln.: Full credit: An allocation .x A 1 ;x A 2 ;x B 1 ;x B 2 / is feasible if x A 1 C x B 1 D ! A 1 C ! B 1 ; x A 2 C x B 2 D ! A 2 C ! B 2 : Partial credit: If answer with words, but with a precise definition, get 4 points. Demand equals supply is not an OK answer, for the variables x A and x B are not demands (there are no prices involved in the definition!). If answer x A 1 C x B 1 D ! 1 ; x A 2 C x B 2 D ! 2 ; without defining ! 1 and ! 2 in terms of .! A 1 ;! A 2 / and .! B 1 ;! B 2 / get 2.5 points. (b) (5 points.) Define Pareto efficient allocation and contract curve . Soln.: Full credit: A feasible allocation .x A 1 ;x A 2 ;x B 1 ;x B 2 / is Pareto efficient if there does not exist another feasible allocation .x A 1 ;x A 2 ;x B 1 ;x B 2 / such that u A .x A 1 ;x A 2 / u A .x A 1 ;x A 2 / and u B .x B 1 ;x B 2 / u B .x B 1 ;x B 2 /; with strict inequality for at least one consumer. The contract curve is the set of all Pareto efficient allocations. 1 Partial credit: An answer with words, but with a precise definition, gets 4 points. If omits the first feasible but includes the second one, then answer gets 2.5 points. If omits the second feasible and everything else is correct, get 1 point. If every- thing is correct but the strict inequality part, then get 2.5 points. If imposes strict inequality for both consumers, get 2.5 points. (c) (5 points.) Explain why the Pareto efficient allocations are the allocations that solve max .x A 1 ;x A 2 ;x B 1 ;x B 2 / u A .x A 1 ;x A 2 / subject to u B .x B 1 ;x B 2 / D u x A 1 C x B 1 D ! A 1 C ! B 1 x A 2 C x B 2 D ! A 2 C ! B 2 for some utility level u in consumer B s utility possibility set....
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spring2009_midterm2_soln - Second Midterm Exam Econ 150b....

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