The elasticity of substitution with constant-relative-risk-aversion utility. Consider an individual who lives for two periods and whose utility is given by equation (2.43). Let P1 and P2 denote the prices of consumption in the two periods, and let W denote the value of the individual’s lifetime income; thus the budget constraint is P1C1 + P2C2 = W.

(a) What are the individual’s utility-maximizing choices of C1 and C2, given P1, P2, and W?

 

(b) The elasticity of substitution between consumption in the two periods is ?[( P1/P2)/(C1/C2)][?(C1/C2)/?( P1/P2)], or  ln (C1/C2)/? ln ( P1/P2). Show that with the utility function (2.43), the elasticity of substitution between C1 and C2 is 1/?.