Molly has a Cobb-Douglas utility function U (c1, c2) = ca1 c1−a2, where 0 < a < 1 and where c1 and c2 are her consumptions in periods 1 and 2 respectively. We saw earlier that if utility has the form u(x1, x2) = xa1 x1−a 2 and the budget constraint is of the “standard” form p1x1+p2x2 = m, then the demand functions for the goods are x1 = am/p1 and x2 = (1 − a) m/p2.
(a) Suppose that Molly’s income is m1 in period 1 and m2 in period 2. Write down her budget constraint in terms of present values.
(b) We want to compare this budget constraint to one of the standard form. In terms of Molly’s budget constraint, what is p1? _____. What is p2? _____. What is m? _______.
(c) If a = .2, solve for Molly’s demand functions for consumption in each period as a function of m1, m2, and r. Her demand function for consumption in period 1 is c1 =______. Her demand function for consumption in period 2 is c2 = ___________.
(d) An increase in the interest rate will _______ her period-1 consumption. It will _______ her period 2 consumption and ________ her savings in period 1.