208-2011-PS4

208-2011-PS4 - Economics 208 Macroeconomics Marek Kapika c...

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Economics 208 Marek Kapiˇ cka Macroeconomics Spring 2011 Problem Set 4 1 Ramsey Taxation Consider the following economy. There is a representative household whose utility function is given by X t =0 β t ( c t - l 2 t 2 ) , 0 < β < 1 , where c t is consumption in period t, and l t is labor supply in period t. The household can also borrow or lend at an interest rate r satisfying β = 1 1+ r . The wage rate is assumed to be one in all periods. The household has no other sources of income. The government needs to finance its spending given by G t in period t . The government receives revenue from flat labor taxes τ t . Thus, if the household works l t hours in period t, then it will pay τ t l t to the government in that period. 1. Write down the household present value budget constraint. Then, write down the agent’s maximization problem, i.e. utility maximization sub- ject to the present-value budget constraint. 2. Solve the agent’s maximization problem and derive the indirect utility
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This note was uploaded on 12/26/2011 for the course ECON 208 taught by Professor Staff during the Fall '08 term at UCSB.

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208-2011-PS4 - Economics 208 Macroeconomics Marek Kapika c...

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