hw-01 - U ( c ) = s t =0 t u ( c t ) , (0 , 1) , where c t...

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Homework 1 Macroeconomic Theory I. Viktor Tsyrennikov Question 1. An individual seeks to maximize his utility U ( c 1 , c 2 ) = ln ( c 1 ) + βln ( c 2 ) , β (0 , 1) , where c 1 and c 2 are non-negative consumption levels of a perishable good in period 1 and 2 respectively. The individual receives income y 1 and y 2 in the two periods that he lives. He can save at interest rate r s > 0 and borrow at rate r b > r s . a) Write down the individual’s budget constraint for the case when he is a saver and when he is a borrower. b) Solve for the optimal consumption plan. Question 2. An individual seeks to maximize his utility
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Unformatted text preview: U ( c ) = s t =0 t u ( c t ) , (0 , 1) , where c t is a non-negative consumption level of a perishable good in period t . The individual receives income y t = 1 in even periods and y t = 0 in odd periods. His bank account initial balance is a = 0 and he can save and borrow at gross interest rate R = 1 / . a) Find an optimal consumption plan of an individual. b) Plot a time path of a t and h t . Would it matter if the individual could not borrow but only save? 1...
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