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.]