# HW4 - Homework 4 Econ 606 Jonathan Heathcote Due in class...

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Homework 4, Econ 606 Jonathan Heathcote Due in class, Tuesday March 28th Consider the following economy Each period a continuum of mass (1 δ ) agents are born at age 0 Agents survive from age a to a +1 with constant probability δ. The total population is (1 δ )(1 + δ + δ 2 + ... )=1 Assume the environment is stationary, so we need not worry about time subscripts Agents maximize expected utility, which is given by E P a =0 ( βδ ) a u ( c a ) where u ( c )= c 1 γ 1 γ Agents are subject to idiosyncratic wage shocks that are iid across agents. Agents supply one unit of time per period. The initial wage at age zero is lognormally distributed: ln( w 0 α 0 ˜ N ³ v 0 2 ,v 0 ´ Wages subsequently evolve according to α a +1 = α a + ω a +1 a 0 ω a +1 ˜ N ³ µ v ω 2 ω ´ where the actual (level) wage is w a =exp( α a ) . The market structure is as follows. Agents are endowed with zero wealth at birth. Then they can trade bonds at a constant price q.

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HW4 - Homework 4 Econ 606 Jonathan Heathcote Due in class...

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