homework5

# homework5 - ECO 475 Homework 5 Jay H Hong Due WEDNESDAY...

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ECO 475 Homework 5 Jay H. Hong Due: Oct 13, 2010 WEDNESDAY Review Session 1 Computing the equilibrium Consider an island where two individuals ( i = 1 , 2) live forever who maximize their lifetime utility given by X t =0 β t ln( c i t ) . Let e i t denote the time t endowment of type i consumer, which is non-storable . (1) Define carefully a competitive equilibrium. (2) Solve the competitive equilibrium when the endowment process of each agent in the island is given by e 1 t = 12 if t = even 6 if t = odd e 2 t = 6 if t = even 3 if t = odd (3) Formulate the Social Planner’s problem where the planner’s weight on consumer 1 is α . Use μ t for the multiplier of time t constraint. (4) Formulate the transfer function for i = 1 , 2. (5) Using the Negishi’s method, compute the competitive equilibrium for this economy. Verify that your equilibrium you construct using the Negishi’s is identical to the equilibrium you derive from (2). (6) Suppose the government of the island introduces a lumpsum tax/transfer ( τ i t ) so that the effective

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