3. A consumer buys only two goods, 21 and 22. Initially, the prices are (P1, P2) = (1, 2) and the consumer chooses (21, 22) = (5,5). Later, the prices change to (P1, P2) = (4,2). At these new prices the consumer chooses (x1, x2) = (10,4). (a) Compute the income of the consumer at the two price vectors. (10 Points) (b) Are these choices consistent with utility maximization? (10 Points) (c) Can you state whether the consumer prefers bundle (x1, x2) = (5,5) or bundle (x1, x2) = (10,4)? (10 Points) 3. A consumer buys only two goods, 21 and 22. Initially, the prices are (P1, P2) = (1, 2) and the consumer chooses (21, 22) = (5,5). Later, the prices change to (P1, P2) = (4,2). At these new prices the consumer chooses (x1, x2) = (10,4). (a) Compute the income of the consumer at the two price vectors. (10 Points) (b) Are these choices consistent with utility maximization? (10 Points) (c) Can you state whether the consumer prefers bundle (x1, x2) = (5,5) or bundle (x1, x2) = (10,4)? (10 Points)