4. Consider a representative agent with the utility function U = log Ct + t log(1 Nt)

The budget constraint is

Ct = wt Nt + Dt

where wt is the wage and Dt is non-wage income (i.e. a dividend from ownership in the firm). The agent lives for only one period (period t), and hence its problem is static.

1. (a)Derive an optimality condition characterizing optimal household behavior.
2. (b)Solve for the optimal quantities of consumption and labor.
3. (c)Suppose that the government implements a lump sum subsidy to all workers, Tt. It engages in no spending and has no budget con- straint to worry about, hence it can choose Tt however it pleases. The household's budget constraint is now:
4. Ct = wt Nt + Dt + Tt
5. How are the optimal quantities of Ct and Nt affected by the intro- duction of the subsidy? Specifically, do people consume more or less leisure? What is the economic intuition for this?