(a) Suppose that this individual lives for two periods, write down his/her lifetime expected utility function and intertemporal budget constraint. Carefully interpret each of these equations. Explain why the lifetime budget constraint must be satisfied as a strict equality. (b) Prove that Ct+1 = Ct + &t+1 from the permanent income hypothesis (PIH) to show that consumption follows a random walk. Discuss the full implication of this result. (c) How do changes in r affect expected consumption growth? Interpret the effect of r on expected consumption in the light of precautionary saving.

(a) Suppose that this individual lives for two periods, write down his/her lifetime expected utility function and intertemporal budget constraint. Carefully interpret each of these equations. Explain why the lifetime budget constraint must be satisfied as a strict equality. (b) Prove that Ct+1 = Ct + &t+1 from the permanent income hypothesis (PIH) to show that consumption follows a random walk. Discuss the full implication of this result. (c) How do changes in r affect expected consumption growth? Interpret the effect of r on expected consumption in the light of precautionary saving.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.7P

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Consider a forward-looking individual who aims at maximizing her lifetime utility from her lifetime resources. Assume the initial endowment of the individual isand her expected labour income is in the sequence Her utility function takes the form where is consumption in period and . Assume the real interest rate, is constant but not equal to the discount rate . Suppose that this individual lives for two periods, write down her intertemporal budget constraint and carefully interpret it. Explain why the lifetime budget constraint must be satisfied with a strict equality. From the intertemporal budget constraint, derive the permanent income hypothesis (PIH) and explain the drivers of consumption growth in this model.
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