17.1 An individual has a fixed wealth (W) to allocate between consumption in two periods ( and 2). The individual's utility function is given by U(92), and the budget constraint is W = + 1+ where is the one-period interest rate.

a. Show that, in order to maximize utility given this budget constraint, the individual should choose and such that the MRS (of c for 2) is equal to 1+r.

b. Show that a/ar0 but that the sign of de/ar is ambiguous. If ac/ar is negative, what can you conclude about the price elasticity of demand for

c. How would your conclusions from part

(b) be amended if the individual received income in each period (y, and y2) such that the budget constraint is given by