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_Lecture_13 - Lecture 13 1-minute review allocative...

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Lecture 13 1-minute review allocative efficiency Edgeworth Box 1
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Exchange As an introduction to equilibrium we consider a simple situation: an exchange economy with no production. We first need to expand our description of consumers to include endowments – what they come to the market with. We have already done this in the labor/leisure discussion, now we just allow consumers to come to the market with any/all of the commodities. Exchange: Example There are two goods, let’s call them Daffodils and Roses D, R , two consumers Ann, Bill, with utility functions and endowments u A ( D, R ) = DR , e A = (100 , 0) u B ( D, R ) = DR 2 , e B = (0 , 200) Story: Ann grows Daffodils, Bill grows Roses, but both Ann & Bill like mixtures of flowers. First sketch an Edgeworth Box. Now solve for the efficient allocations ( D A , R A ) , ( D B , R B ). We must have MRS A = MRS B D A + D B = total Daffodils R A + R B = total Roses Computing gives R A D A = R B 2 D B D A + D B = 100 R A + R B = 200 Substituting gives R A D A = 100 - R A 2(200 - D A ) 2
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400 R A - 2 R A D A = 100 D A + R A D A D A = 400 R A 100 + R
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