PS5_Chapter10_soln

# PS5_Chapter10_soln - ECO 100B Problem Set 5 Solutions 1...

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ECO 100B Problem Set 5 Solutions 1. Alice and Bob consume milk, M , and cookies, C . Alice’s utility function is U A = M A C A and Bob’s is U B = M 0 . 5 B C B . Their initial endowments are M A = 10 ,C A = 20, and M B = 20, C B = 10. (a) Draw the Edgeworth Box. (b) What the marginal rates of substitution for each person? MRS A = C A M A , MRS B = 1 2 M - 1 2 B C B M 1 2 B = C B 2 M B . (c) What is the contract curve for this exchange economy? At the contract curve C A M A = C B 2 M B C A M A = 30 - C A 2 (30 - M A ) M A = 60 C A C A + 30 . (d) What is the core for this exchange economy? At the Core, C A M A 200 60 C 2 A C A + 30 200 C A 5 3 ± 37 + 1 ² Also, M 0 . 5 B C B 10 20 s ³ 30 - 60 C A C A + 30 ´ (30 - C A ) 10 20 (e) Solve for the market equilibrium. Let the price of milk = p and the price of cookies = 1. Then, C A = pM A 1

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C B = 2 pM B 30 = p ( M A + 2 M B ) = p (30 + M B ) . p
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PS5_Chapter10_soln - ECO 100B Problem Set 5 Solutions 1...

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