Question

Marvin has a Cobb-Douglas utility function, U(q1, q2) = q 0.5 1 q 0.5 2 , his income is Y = $100, and, initially, he faces prices of p1 = 1 and p2 = 2.

(a) Derive Marvin’s uncompensated demand functions for the two goods, D1(Y, p1, p2) and D2(Y, p1, p2).

(b) Derive Marvin’s compensated demand functions for each good, H1(U, p ¯ 1, p2) and H2(U, p ¯ 1, p2).

(c) Suppose p1 increases to 2. Calculate the change in his consumer surplus.

(d) For the same change in p1 (i.e. increase from 1 to 2), use the expenditure function to calculate Marvin’s compensating variation (CV) and equivalent variation (EV).