Unformatted text preview: iid income shocks y . Utility is exponential: u ( c ) =-e-γc . Note that c can be negative and the only constraint on assets is the No Ponzi condition. Agents face a constant interest rate r . (a) Show that if x t = y t + a t , then the optimal savings decision follows a t +1 = δx t + b , for some constants δ and b . (b) Use your expression for the policy function for assets to show that cash on hand is a random walk with drift. What does this imply about the boundedness of assets and consumption as t → ∞ when β (1 + r ) < 1? Give some intuition relative to the CRRA case discussed in class. 3. Prove that if lim c →∞ u 00 ( c ) u ( c ) = 0 and β (1 + r ) < 1, then assets are bounded. How does this apply to the case of CRRA utility versus exponential utility? 1...
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- Fall '07
- Utility, Probability theory, Stochastic process, ﬁrst order condition, ﬁrst period, random variable y2