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WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS ECONOMICS 201-03 JOHNSON Problem Set #8 (due IN LECTURE Tuesday, December 2 nd ) 1. James and Karen (our friends from before remember?) are stranded on a desert island. Each has initial endowments of ham and cheese (neither is vegetarian or lactose intolerant!). James, the pickier of the two, insists upon consuming ham and cheese only in the ratio of two slices of cheese to every slice of ham (perhaps he likes a breadless ham “sandwich” with the cheese taking the role of the bread!). Thus, his utility function is given by: U J = min [ H J , C J / 2 ] Karen is less picky in her tastes and has a utility function of: U K = 4H K + 3C K Between the two of them, they have 100 slices of ham and 200 slices of cheese. a. Draw an Edgeworth box diagram that represents the possibilities for exchange equilibrium in this situation. What is the only price ratio that can prevail in any equilibrium here? Why? Can you describe the shape/slope/position of the contract curve here? b. Suppose initially that James has 40 slices of ham and 80 slices of cheese. What would the equilibrium position be here? Explain. c. Suppose, instead, that James initially has 60 slices of ham and 80 slices of cheese. What would the equilibrium position be here? Explain with ranges, as we won’t know AN exact answer here. [Extra Credit: What is the best equilibrium for James in this case? What will his utility be?] 2. Robinson Crusoe (such a great book!) produces and consumes fish (F) and coconuts (C). Assume that over a certain period he has decided to work 200 hours and is indifferent as to whether he spends his time fishing or gathering coconuts. His production function for fish is given by: F = L F 1/2 While his production function for coconuts is given by: C = L C 1/2
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Where L F and L C are the number of labor hours devoted to fishing and coconuting, respectively. Thus his labor constraint is: L F + L C = 200 Finally, his utility function for F and C is the following: U ( F , C ) = F 1/2 C 1/2 a. If Robinson is cut off from the rest of the world, how will he choose to allocate his labor? Start with deriving his PPF first. Use the two production functions and his labor constraint to arrive at an expression in only F and C. Then, given that PPF, where will he choose to be? Why? What will be the optimal levels of F and of C? What will his utility be? What will his MRT be? [Put Fish on the horizontal axis.] Explain. b.
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This note was uploaded on 06/15/2010 for the course ECON 201 taught by Professor Johnson during the Fall '08 term at Wellesley College.

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