problem set 1 - following allocations Pareto optimal? a....

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Econ 102B (Summer 2008) Problem Set 1 (Due Monday, August 4 th ) 1) Consider a two-person pure exchange economy with two goods, A and B, and two consumers, 1 and 2. 1’s utility function is given by u=u(A 1 , B 1 ) and 2’s utility function is given by v=v(A 2 , B 2 ). The initial endowment bundles of 1 and 2 are given by (A 1 , B 1 ) and (A 2 , B 2 ), respectively. For each of the following specifications, compute the competitive equilibrium allocation as well as the prices (Be careful about the system of equations that you use as well as your derivations of the MRSs). a. u=A 1 2/3 B 1 1/3 , v=A 2 1/2 B 2 1/2 , and (A 1 =A 2 =B 1 =B 2 =10) b. u=A 1 2/3 B 1 1/3 , v=A 2 1/3 B 2 2/3 , and (A 1 =A 2 =B 1 =B 2 =10) 2) Given the two utility functions [ U=A 1 B 1 , V=A 2 B 2 ] and the initial aggregate endowment bundle [ W=(20, 20) ] for this pure exchange economy, are the
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Unformatted text preview: following allocations Pareto optimal? a. a={(12, 10), (10,10)} b. a={(7, 13), (13, 7)} c. a={(11, 11), (9, 9)} 3) Consider an economy with one producer and one consumer. There are two goods; food (F) and labour (L). The production function is given by F p =3L p , and the consumers marginal rate of substitution of labour for food is given by MRS LF = F c /(24-L c ). The aggregate initial endowment bundle in this economy is (0, 0). Compute the competitive equilibrium for this economy. 4) Explain to a friend of yours or to yourself the following concepts (no written answer necessary): a. Walras Law, b. An attainable allocation, c. Production efficiency, d. Exchange efficiency....
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