Slutsky Equation and Intertemporal Choice. Suppose that the preference ordering of an individual can be represented by the utility function U(c1; c2) = c1c2 where ct is consumption in period t, t = 1, 2. Their endowment is m1 and m2. The interest rate at which they can borrow and lend is r.
(a) Find the demand functions for c1 and c2.
(b) Show that the Hicksian demand functions for c1 and c2 are
(c) Find the optimal consumption bundle if m1 = 100, m2 = 88, and r = :1. Is the consumer a borrower or a lender? How much do they
borrow or lend per period?
(d) Find the optimal consumption bundle if m1 = 100, m2 = 88, and r = :2. Is the consumer a borrower or a lender? How much do they borrow or lend per period?
(e) Break up the change in consumption of good 1 from the increase in the interest rate into (i) the substitution effect; (ii) the ordinary income effect; and (iii) the endowment income effect. [Hint: To find the ordinary income effect, you have to hold money income constant and find the optimal consumption bundle at the new interest rate. The money income at a given interest rate is the numerator in the Marshallian demand functions. This is the future value of the endowment at the old interest rate.]