Answer each of the following questions as either true or false. For a statement to be "true," it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer "false." You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram)
(a) (4) Sean derives utility from watching soccer games s and consuming a composite utility bundle b according to the function U(qs, qb) = 4√qs+qb. The composite bundle costs $1, Sean pays $4per game to stream sporting events, and he spends $50 per week on these goods. True or false: Sean will watch more than 4 games when he consumes the utility-maximizing bundle.
(b) (4) True or false: if two goods, x and y, are perfect substitutes, then a utility-maximizing consumer is always willing to exchange between them in a 1:1 ratio
(c) (4) True or false: The utility functionsU1(a, b) =a2b3,U2(a, b) = 2ln(a) + 3ln(b) andU3(a, b) =ab2all represent the same set of preferences.
(d) (4) The Cookie Monster has marginal rate of substitution for cookies (c) and milk (m) of M RS=MUcMUm=3qm4qc. Cookies currently cost $3 and milk costs $15. True or false: if the Cookie Monster is currently consuming 15 cookies and 5 glasses of milk, he could increase his utility by buying more cookies and less milk.