Consider the two-period model discussed in class. Suppose the lifetime utility function of consumer is given by cl-o cl-

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Consider The Two Period Model Discussed In Class Suppose The Lifetime Utility Function Of Consumer Is Given By Cl O Cl 1 (139.08 KiB) Viewed 39 times

Consider the two-period model discussed in class. Suppose the lifetime utility function of consumer is given by cl-o cl-o U(c, c') +B 0<B<1 0> 0 1 о 1 о where o is the inverse of the intertemporal elasticity of substitution, c is current con- sumption, d is future consumption and B is the subjective discount factor. Suppose the consumer's budget constraint in the current period is given by: cts=y where s is saving and y is the income endowment in the current period. The second period budget constraint is c' = y' + (1+r)s where r is the real interest rate and y' is the income endowment in the future period. (a) (15 points) Write down the Lagrangian of the consumer's optimisation problem. Find the optimality conditions and provide an economic interpretation for them. (b) (15 points) Use the conditions found on point (a) to express d as a function of c, 0, r and B. (c) (20 points) Suppose o increases. Is this increase going to amplify or to smooth the effect of a change in the real interest rate on the ratio of future consumption to present consumption ()? Put differently, as o rises, does the incentive of consumers to smooth consumption over time in response to a change in r become stronger or weaker? Explain your answer.