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A firm with market power faces the demand function q=4000-40p. The firm's total cost function is TC(q)=10q+.001q^2+1000.

a. If the firm behaves as a single price monopoly, identify the firm's optional price and output level.

b. Demonstrate that the single price monopolist's profit maximizing choice of price and output also maximizes producer surpulus.

c. Identify the output level that would maximize total surplus.

d. Identify the output level that a perfect price discriminating monopolist would produce.

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Joshua Stredder
Joshua StredderLv10
28 Sep 2019

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Related questions

A Monopoly firm faces the following demand curve: P=200-0.5Q Where Q is the output and P is the price in dollars. The firm's total cost function is given by TC=20,000 + 40Q

1. What is the level of production?

2. What is the price monopolist should charge?

3. What is the level of profit?

Suppose a monopolist faces a demand curve for its output of P = 300รขยˆย’Q. This means that the marginal revenue curve of the monopolist is M R = 300 รขยˆย’ 2Q. Assume that the marginal cost of production is constant and equal to $40.

a) Write down an expression for the monopolists profit, as a function of the quantity of output it produces.

b) If the monopolist must charge the same price for all units of output that it sells (that is, if the monopolist is a single price monopolist), what level of output will maximise the monopolists profit? What price will the monopolist charge? What is its level of profit?

c) If this were a competitive market instead of a monopoly, what level of output would be produced and what price would be charged? What is the level of profit for firms if it were perfectly competitive?

d) Draw a diagram of demand, marginal revenue, and marginal cost that illustrates your answer to part b). From this work out consumer surplus and producer surplus.

e) Draw the same diagram but for your answer to c), the case of the competitive market. From this work out consumer surplus and producer surplus. How much deadweight loss is there from the monopoly? Why?

Suppose a monopoly with a cost function of C(Q) = 4Q2 - 6Q + 200 faces a market demand of QD = 2,388 - 2P. A) Calculate the firm's total revenue, marginal revenue, and marginal cost. B) Calculate the profit-maximizing output and price. C) Over what range of prices is the demand for repairs inelastic? D) Why will the firm not produce a quantity at which the market demand is inelastic? E) Graph the demand, marginal revenue, and marginal cost curves for Wally's. On the graph, label the profit-maximizing level of output, price, consumer surplus, and deadweight loss.

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