Please show the calculations. Thank you.

Shelby loves apples and hates bananas. Her utility function is U(a, b) = a ib2, where a is the number of apples she consumes and b is the number of bananas she consumes. Jonathan likes both apples and bananas. His utility function is U (a, b) = a + 251/2. Shelby has an initial endowment of U apples and 8 bananas. Jonathan has an initial endowment of 16 apples and 8 bananas. (a) On the graph below, with Shelby's origin in the lower left and Jonathan's origin in the upper right, mark the initial endowment and label it E. Use red to draw the indifference curve for Shelby that passes through this point. In blue, draw the indifference curve for Jonathan that passes through this point. (.0 ' 0 I | | 0 4 8 12 16 Bananas (b) On the graph above, use black to mark the locus of Pareto optimal allocations of apples and bananas between Shelby and Jonathan. If Shelby hates bananas and Jonathan likes them, how many bananas can Shelby be consuming at a Pareto optimal allocation? (c) We know that a competitive equilibrium allocation must be Pareto optimal and the total consumption of each good must equal the total supply. For the Shelby-Jonathan economy, how many of each good will the two members consume? (d) If apples are the numeraire, at what price will Jonathan want to consume exactly 16 bananas