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# homework9 - ECO 475 Homework 9 Jay H Hong Due 1 Computing...

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Unformatted text preview: ECO 475 Homework 9 Jay H. Hong Due: Nov 18, 2009 1 Computing the equilibrium Consider the simple two agent pure exchange economy. There are two individuals ( i = 1 , 2) who live forever and each individual enjoys utility from a sequence of consumption given by E ∑ ∞ t =0 β t ln( c i t ) . Each consumer receives a random endowment of non-storable consumption goods in each period which depends on the aggregate state of economy at time t , s t ∈ { A,B } . The process of random endowments is given by e 1 t = 2 if s t = A if s t = B e 2 t = if s t = A 2 if s t = B The aggregate state of economy is a random variable with Pr( s = A ) = π and Pr( s = B ) = 1- π (1) Carefully define and characterize an Arrow Debreu equilibrium. (2) Formulate Pareto problem where the planner’s weight on consumer 1 is α . ( Hint: μ s t is the multiplier for time t and state s constraint.) Using the Negishi’s method, compute the competitive equilibrium for this economy. Check if your equilibrium coincides the equilibrium you derive in (1).economy....
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