Charlotte loves apples and hates bananas. Her utility function is U(a, b) = a b2,

Charlotte loves apples and hates bananas. Her utility function is U(a, b) = a – ¼ b2, where a is the number of apples she consumes and b is the number of bananas she consumes. Wilbur likes both apples and bananas. His utility function is U(a, b) = a + 2√b. Charlotte has an initial endowment of no apples and 8 bananas. Wilbur has an initial endowment of 16 apples and 8 bananas.
(a) On the graph below, mark the initial endowment and label it E. Use red ink to draw the indifference curve for Charlotte that passes through this point. Use blue ink to draw the indifference curve for Wilbur that passes through this point.
(b) If Charlotte hates bananas and Wilbur likes them, how many bananas can Charlotte be consuming at a Pareto optimal allocation? ____________
On the graph above, use black ink to mark the locus of Pareto optimal allocations of apples and bananas between Charlotte and Wilbur.
(c) We know that a competitive equilibrium allocation must be Pareto optimal and the total consumption of each good must equal the total supply, so we know that at a competitive equilibrium, Wilbur must be consuming ___________ bananas. If Wilbur is consuming this number of bananas, his marginal utility for bananas will be __________ and his marginal utility of apples will be __________ If apples are the numeraire, then the only price of bananas at which he will want to consume exactly 16 bananas is __________ In competitive equilibrium, for the Charlotte-Wilbur economy, Wilbur will consume _________ bananas and _________ apples and Charlotte will consume ___________ bananas and _______ apples.