A consumer has Cobb-Douglas utility function u(x1, x2) = x1x2 over two goods x1 and x2. The vector of unit prices is p = (p1, p2) and the consumer's income is I > 0.

(a) Formulate the consumer's utility maximization problem, solve it to obtain his Marshallian demand function x1(p, I) for good 1 and x2(p, I) for good 2, and examine the second order condition.

(b) Suppose that sellers of the first good offer the following promotion: if the consumer buys x1 amount of the first good, he gets an amount x1 of the second good at no extra charge, where > 0 is a fixed parameter. The unit prices of the two goods and the income of the consumer are unchanged. Obtain the consumer's new Marshallian demand function x 0 1 (p, I, ) for good 1, which results from the promotional offer.

1 (c) Find the indirect utility function v(p, I, ).