HW3 - Homework 3 Jonathan Heathcote Due in Class on Tuesday...

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Homework 3 Jonathan Heathcote Due in Class on Tuesday February 28th In class we outlined two versions of the stochastic growth model: a planner’s problem, and an Arrow-Debreu competitive equilibrium. We were working to- wards showing that allocations in the two setups would be identical. 1. (a) Complete the proof that the sets of equations that characterize (i) the solution to the planner’s problem, and (ii) the competitive equi- librium are identical, and thus that one can solve for equilibrium allocations by solving the planner’s problem. (b) Now consider the following twist on the economy we described in class. Income (from both labor and capital) is taxed at rate τ t , where 0 t < 1 . There is no allowance for depreciation: thus the typical consumer’s budget constraint (in the sequence of markets formulation, without state-contingent claims) is c t + k t +1 =(1 τ t )( r t k t + w t n t )+(1 δ ) k t Revenues are used for non-valued government purchases G .Con
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HW3 - Homework 3 Jonathan Heathcote Due in Class on Tuesday...

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