Interest rates and saving with constant elasticity of substitution utility. A country?srepresentative individual has a constante relative risk aversion utility functionU(C) =C1??11 ?? 1where > 0 and maximizes U1 = U(C1) + U(C2) subject toC1 + RC2 = Y1 + RY2[where R 1=(1 + r)] and Y1 and Y2 are endowments.
(a) Derive the intertemporal Euler equation.
(b) What is the optimal level of C1 given the endowments, R, and ? What?s theoptimal level of C2?
(c) How?s C2 a¤ected if endowment Y1 decreases? How?s C2 a¤ected if the countrybecomes less patient (i.e., #)? Show mathematically and explain intuitively.