# hw4 - c 1-γ . In addition, we assume that the investor...

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ECON 831 Homework #4 due in class Nov. 5th Exercise 1: (Consumption-savings problem) Consider the consumption-savings problem introduced in class on Oct. 27th. Finish the resolution by backward induction. Note: assume that the problem has been written with standard notations and that the regularity conditions have been checked. In other words, there is a little overlap between what I started in class and what you have to do here). Exercise 2: (Investor's problem) Let x t denote the value of an investor's assets and let c t be the consumption at time t , for t = 1 , ··· ,T < . Suppose that assets at time ( t + 1) are proportional to savings at time t , with a positive factor of proportionality depending on t , say α t > 0 . Assume that the initial assets x 1 are positive. The utility associated with a level of consumption c during one period is supposed to be
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Unformatted text preview: c 1-γ . In addition, we assume that the investor also receives some utility from the terminal value of the assets: more speci cally, if, at the end of the problem, the remaining assets are worth x then the associated utility is Ax 1-γ , where A is a positive constant and γ a constant such that < γ < 1 . The investor wants to maximize the discounted value of the sum of utility from con-sumption and terminal assets. De ne β = 1 / (1 + r ) , where r is the rate of discount. Assume that both savings and consumption must be positive each period. Solve the above problem by backward induction. Note: this means that you have to write the problem (explain your notations!), verify the regularity assumptions, and solve by backward induction. 1...
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## This note was uploaded on 02/19/2010 for the course ECON 831 taught by Professor Antoine during the Fall '09 term at Simon Fraser.

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