Question 3 Consider a ski resort owner (local monopoly) who cannot identify consumers by their types. There are 2 types of consumers: Low-demand consumers with an inverse demand of p = 12 -Q, and high-demand consumers have an inverse demand of p = 16 -Q. MC per lift ride is again $4. Assume that there are N. high demand consumers and Ni low demand consumers but that the ski resort owner does not know the type of each skier. The monopoly offers a price quantity package designed specifically for each type. F 1PI F 23 P2 Let be the entry fee and unit price combination paid by the low demanders and be the entry fee and unit price combinations paid by the high demanders.\fa) We know that for any price po that the monopoly can charge the low demand type will demand Q1 =12 - PI. (i) Compute Fi for any price pi that the firm charges the low demand type. The high demand type (knowing that the monopoly will extract all consumer surplus) will have an incentive to cheat and select the package designed for the low type. To see the outcome from cheating we can start by (/) either plugging the 12 - pi quantity of the low demand type's package in to their demand curve p =16 -Qz, (approach used in class) or (2) plugging in to p = 16 -Q2 the price pi of the low demand type to get Q? = 16 - p1 (ii) Using approach (2) compute - CS of the high demand type = what the monopoly can charge as entry fee if the high types pay p. = pi and buy Q1 = 16 - pi - the gain to the high demand type from cheating = difference between the entry fee for Q, = 16-p, units and the entry fee charged to the low demand types For any price pa that the monopoly can charge the high demand types as part of the package designed for them, the high types retain the following surplus /(16 - pz) - F2-b) We know that the price-quantity package and the entry fee F2 for the high demand types is incentive compatible with the package offered to the low demand type if takes away the incentive of the high demand types to pretend to be the low demand type (i.e. the monopoly lets them retain the consumer surplus they would get by cheating and pretending to be the low type). Using this definition of incentive compatibility, we can express the surplus retained by the high demand types as a function of pi: 14(16 -p) -F1= 1(16 -p) - W/(12-pi) Compute F, as a function of p, and pz- c) The monopoly's total profit when it offers the high type an incentive compatible package (i.e. serves both types) is It = Ni[(p2 - 4)(16 - p) + Fi] + N[(p1 - 4)(12 - pi) + Fi] Compute the optimal price that the monopoly will charge each type as a function of only N, and N? (Hint: Use calculus tools for x maximization) d) What is the monopoly's profit if it serves only the high type? e) If N /N= 1 will the monopoly serve both types. Show your calculations