Microeconomic Theory 11th Edition by Walter Nicholson,Christopher Snyder

Exercise 1

An individual has a fixed wealth (W) to allocate between consumption in two periods ( c 1 and c 2 ). The individual's utility function is given by
and the budget constraint is

where r is the one-period interest rate.
a. Show that, in order to maximize utility given this budget constraint, the individual should choose c 1 and c 2 such that the MRS (of c 1 for c 2 ) is equal to 1 + r.
b. Show that
is negative, what can you conclude about the price elasticity of demand for c 2 ?
c. How would your conclusions from part (b) be amended if the individual received income in each period ( y 1 and y 2 ) such that the budget constraint is given by