In the previous problem, suppose that A is a much more efficient shopper than B so that A is able to get twice as much consumption goods as B can for every dollar that he spends. Let a be the amount of consumption goods that A gets and b the amount that B gets. We will measure consumption goods so that one unit of consumption goods costs $1 for A and $2 for B. Thus the parent’s budget constraint is a + 2b = 1, 000.
(a) If the mother’s utility function is U(a, b) = a + b, which child will get more money? A.
(b) If the mother’s utility function is U(a, b) = a × b, which child will get more money? ______________________ Which child will get to consume more? ____________
(c) If the mother’s utility function is U(a, b) = −1/a – 1/b , which child will get more money?
____________ Which child will get to consume more? ____________
(d) If the mother’s utility function is U(a, b) = max{a, b}, which child will get more money? ______________ Which child will get to consume more? ______________
(e) If the mother’s utility function is U(a, b) = min{a, b}, which child will get more money? ___________ Which child will get to consume more? _________________