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Imagine an individual who lives for two periods. The individual has a given pattern of endowment...

Imagine an individual who lives for two periods. The individual has a given pattern of endowment income (y1 and y2) and faces the positive real interest rate, r.

Lifetime utility is given by U(c1, c2)= ln(c1)+β ln(c2)

Suppose that the individual faces a proportional consumption tax at the rate Ԏc in each period. (If the individual consumes X in period i then he must pay XԎc to the government in taxes period). Derive the individual's budget constraint and the F.O.C for the optimal consumption profile. What are the optimal values of consumption in the two periods? What is savings?

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