21011ps06 - lny . Their intitial endowments are e a = (1 ;...

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Econ 210A Fall 2011 Assignment #6 Due date: Monday, November 21 1. Ex. 13.8, p.232 in Varian. 2. Suppose Robinson ( R ) and Xena ( X ) R X has one unit of coconuts as endowment. They both have the same utility function described by U i ( c i ; f i ) = c i f 1 i ; i = R; X ; 2 (0 ; 1) Derive the Pareto frontier from the following problem: max c R ;f R c R f 1 R s.t. (1 c R ) (1 f R ) 1 ± U X (By solving this problem and obtaining the optimal levels of c R and f R , the maximized value of c R f 1 R would be a function of U X ; that function represents the Pareto frontier, the utility combinations of U R and U X that can be derived from all the Pareto optimal allocations.) 3. Consider a pure exchange economy with three agents, labelled a; b , and c; and two goods, x and y: U ( x; y ) = + (1 )
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Unformatted text preview: lny . Their intitial endowments are e a = (1 ; 0) ; e b = (0 ; 1) ; and e c = (1 ; 1) : Find the competitive equilibirum allocations for this economy. 4. Ex. 18.2, p.357 in Varian. 5. Consider a pure-exchange economy with 2 agents ( 1 and 2) and two goods, x and y: Their utility functions are as follows U 1 ( x 1 ; y 1 ) = min f x 1 ; y 1 g U 2 ( x 2 ; y 2 ) = & ln x 2 + (1 & a ) ln y 2 where x i and y i denote consumption levels for agent i = 1 ; 2 : Suppose the initial endowments are e x 1 = 0 ; e y 1 = 10 ; e x 2 = 10 ; and e y 2 = 0 : A. Calculate a competitive equilibrium for this economy. B. Can you &nd an allocation other than the competitive equilibrium allocation that is Pareto superior to the competitive equilibrium allocation? 1...
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