need help exercise

Two individuals are interested in buying a product produced by a monopolist. From the past sales data, the monopolist knows that they are either of type-1 customer with demand of p (qi) - 16 - qor of type-2 customer with demand of Pa (92) -11 - qa. The monopolist's cost function is given by c (Q) - 1Q", where Q - 91 + 41. It is assumed that the monopolist employs a linear pricing scheme lie., set a per-unit price). The aggregate demand of the two Individuals is given by 16 0 1053 P(2) 12 - 10 1035 a) If the monopolist cannot prevent arbitrage between two individuals, what price should the monopolist charge in order to maximize its profits? What are the resulting profits in this case? b) If the monopolist can prevent arbitrage between them, what price should the monopolist charge for each type of consumer? What are the resulting (total) profits? Suppose now that new production technology allows the monopolist to produce at a constant marginal cost of A, In order to build a new customer base, the monopolist decided to lower the price to 8 per unit. For the current two types of customers, it set the two-part tariff schedules, 7) = F + pg. where i = 1, 2. c) Determine the optimal two two-part tariff schedules that are incentive compatible with each type of customer