ECO 320L-HW2 Due March 23, 2010 Classtime 1. Consider the consumption-saving problem of a consumer. His current income is y and his future income is y0 . The real interest rate is r . Consumer’s utility function is ln( C ) + ln( C0 ) . The government taxes capital income to raise tax revenues. There are no other taxes. The capital income tax is t k (i.e. Consumer pays t k units of consumption good for each unit he earns from savings). (a) Write down the ﬁrst period and second period budget constraint for the consumer. (b) Write down the lifetime budget constraint. (c) What is the relative price of future consumption in terms of current consumption? How does it depend capital income tax t k ? (d) Write down the optimality condition. (e) Using the optimality condition and the lifetime budget constraint, solve the optimal C , C0 , and savings s as functions of y,y0 ,r, and t k . (f) Now assume that y = 100 and y0 = 50 . r = 20% and t k = 50% . Calculate C , C0 , s, and government’s tax revenue in the future period. 2. Consider the consumption-saving problem of a consumer. His current income is
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