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Unformatted text preview: Economics 208 Marek Kapi cka Macroeconomics Spring 2011 Problem Set 4 Answers 1 Ramsey Taxation Consider the following economy. There is a representative household whose utility function is given by X t =0 t ( c t- l 2 t 2 ) , < < 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 = 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 t . Thus, if the household works l t hours in period t, then it will pay t l t to the government in that period. 1. Write down the household present value budget constraint. Then, write down the agents maximization problem, i.e. utility maximization sub- ject to the present-value budget constraint....
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