. (i) A monopolist faces the following demand and total cost functions: Q = 65 %
ID: 1178274 • Letter: #
Question
. (i) A monopolist faces the following demand and total cost functions:
Q = 65 %u2013 1/2P
TC = Q^2 + 10Q + 50
(a) Calculate the profit maximizing output and price of the monopolist. Calculate the resulting profit.
(b) Suppose the government imposes an excise tax of $30 on the production and sale of the product. Calculate the resulting optimal profit maximizing output and price for the monopolist. Also determine the level of profit.
(c) If the government%u2019s objective is to generate the maximum possible tax revenue from the monopolist, what excise tax rate should the government impose on the monopolist? Calculate the resulting optimal output, and price of the monopolist as well as government%u2019s 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%u20134P1 +2P2
Q2 =50%u20135P2 +P1
where P1, P2, Q1, Q2, refer to prices and outputs of firms 1 and 2 respectively. Firm 1%u2019s marginal cost is $5 while firm 2%u2019s marginal cost is $4. Each firm has a fixed cost of $50.
Assuming that the two firms decide on prices independently and simultaneously, calculate the best response function of each firm in terms of prices. Calculate the resulting equilibrium price quantity combination for each firm. Illustrate your answer with a suitable graph. Also calculate optimal profits of each firm.
Explanation / Answer
The monopolist will produce at MR = MC
TR = P*Q = 100Q - 2Q^2
MR = TR' = 100 - 4Q
MC = TC' = 20
20 = 100 - 4Q
4Q = 80
Q = 20
solve for P in the Demand Eq
P = 60
The monopolist will not sell at the "highest price", it will set price to maximize profits.
@ P = 60, Q = 20 TR = 1200; TC = 500; Profit = 700
@ P = 80, Q = 10 TR = 800; TC = 300; Profit = 500
If the monopolist increases price, quanity demanded decreases, and profit decreases.
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