(i) A monopolist faces the following demand and total cost functions: Q= 65 - 1/2P TC= Q(to the 2nd power) + 10Q + 50

(a) find out the profit maximizing output and price of the monopolist. find out the resulting profit.

(b) Suppose the government imposes an excise tax of $30 on the production and sale of the product. find out the resulting optimal profit maximizing output and price for the monopolist. Also determine the level of profit.

(c) If the government's objective is to generate the maximum possible tax revenue from the monopolist, what excise tax rate should the government impose on the monopolist? find out the resulting optimal output, and price of the monopolist as well as government's tax revenue.

(ii) Two firms produce differentiated products and set prices to maximize their individual profits. Demand functions for the firms are given by

Q1 = 64 - 4P1 + 2P2
Q2 = 50 - 5P2 + P1

where P1, P2, Q1, Q2, refer to prices and outputs of firms 1 and 2
respectively. Firm 1's marginal cost is $5 while firm 2's marginal cost is $4. Each firm has a fixed cost of $50. Assuming that the two firms decide on prices independently and simultaneously, find out the best response function of each firm in terms of prices. find out the resulting equilibrium price quantity combination for each firm. Illustrate your answer with a suitable graph. Also find out optimal profits of each firm.