eco200_problemset2_2009

# eco200_problemset2_2009 - UNIVERSITY OF TORONTO Faculty of...

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UNIVERSITY OF TORONTO Faculty of Arts and Science November 2009 PROBLEM SET 2 1 ECO200 - Section L0101 Carlos J. Serrano NOTE: THE DUE DATE OF PROBLEM SET 2 IS WEDNESDAY NOVEMBER 18, 2009 AT 2.00PM IN CLASS. ROOM LM 159 Question 1. (25 points) [Intertemporal consumption and taxes on savings returns] Consider an economy populated with individuals that last two periods. In period 1 the in- dividual is young, in period 2 the individual is old. The utility function of any individuals is ( 1   2 ) =  ( 1 )+ ln( 2 ) , where 1 and 2 represent consumption in period 1 and period 2, and (0 1) is a discount factor. Suppose that the individual earns 1 0 and 2 0 in period 1 and 2, respectively. Suppose that an individual can borrow or save in capital markets at the rate of interest   0 . Finally, suppose (as we did in the model we covered in class) that the nominal prices of consumption in each period are constant and are 1. The marginal utilities of consumption in period 1 and period 2 are  1 = 1  1  2 =  2 (a) Suppose that 1 = \$100 , 2 = \$50 , = 0 1 (i.e., 10%), and = 1 1+ . Write the utility maximization problem (including the utility function and a budget constraint in period 1 dollars? Calculate the optimal consumption in period 1, 1 , and in period 2, 2 What is the level of utility at ( 1   2 )?

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