Question: Learning to Enjoy Spare Time A worker's instantaneous utility, u(), depends on the amount of market- produced goods consumed, c,, and also on the amount

Learning to Enjoy Spare Time A worker's instantaneous utility, u(), depends on the amount of market- produced goods consumed, c,, and also on the amount of home-produced goods, c2, (for example, entertainment, leisure). In order to acquire market- produced goods, the worker must allocate some amount of time, 4, to market activities that pay a salary of w,, measured in terms of consumption good. The worker takes wages as given and beyond the worker's control. There is no borrowing or lending. It is known that the market wage evolves according to the law of motion w+1 = h(w). The quantity of home-produced goods depends on the stock of "exper- tise" that the worker has at the beginning of the period, which we label a,. This stock of "expertise" depreciates at the rate & and can be increased by allocating time to nonmarket activities. To summarize the problem, the individual agent maximizes

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