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) [6 points] What are the utility-maximizing levels of raisin consumption xP and xS for Mrs. Parker and Mr. Smith, respectively? b) [12 points] 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.]