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# HW5 - Homework 5 Econ 606 Jonathan Heathcote Due in class...

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Homework 5, Econ 606 Jonathan Heathcote Due in class, Tuesday April 4th Consider the following consumption-savings problem: An individual faces two possible realizations for their wage in each period, w { w l ,w h } where 0 <w l <w h . At time zero, w 0 may be high or low with equal probability. In subsequent periods, wages evolve stochastically according to a Markov process de f ned by the transition probability matrix π. The individual must choose consumption c t , savings in a non-contingent bond a t +1 and hours worked, n t at each date t to maximize expected lifetime utility, where utility associated with an allocation { c t ,n t } t =0 is given by P t =0 β t u ( c t ,n t ) u ( c t ,n t )= 1 1 γ " c t ψn 1+ 1 ε t 1+ 1 ε # 1 γ where ψ,ε,γ > 0 (these are known as Greenwood, Hercowitz and Hu f mann preferences) Suppose that initial wealth at time zero is given by a 0 and that borrowing is not permitted: φ =0 . Hours and consumption must be non-negative (there

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HW5 - Homework 5 Econ 606 Jonathan Heathcote Due in class...

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