Assume that there are two consumers of raisins. Mr. Smith has a utility function uS(x) = 10 + x - x 2 , while Mrs. Parker has a utility function uP(x) = 10 + x - 2x2 , where x is the amount of raisins each purchase and consume. Initially, they purchase x = 0, therefore their utilities are uS(x) = uP(x) = 10. Farmer Gordon, the monopoly producer of raisins, cannot distinguish between Mr. Smith and Mrs. Parker. But he can sell different sized bundles and charge different prices for them.

a) What are the utility-maximizing levels of raisin consumption xP and xS for Mrs. Parker and Mr. Smith, respectively?

b) Supposing Farmer Gordon offers bundles of size xp and xS (the amounts you found in part (a)). What are the prices (PP; PS) that he should charge so that (i) Mr. Smith consumes the xS - sized bundle at price PS and (ii) Mrs. Parker consumes the xP - sized bundle at price PP? [Hint: calculate the utility gain after purchase of xp and xS compared with when x = 0.]