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Your monopoly company exhibits the following costs:

TC=60+6Q+Q2 & MC=6+2Q

And the following market demand and marginal revenue functions:

Qd=598-P; MR=598-2Q

a)Find the profit maximizing level of output for the monopoly

b) At what price does the monopolist sell its good?

c)What are the monopolist profits

d)Is there any dead weight loss in the market? 

 

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Anne Gillian Duero
Anne Gillian DueroLv10
28 Sep 2019

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Related questions

Harry Smith owns a metal-producing company that is an unregulated monopoly. After considerable experimentation and research, total cost and marginal cost curves are: TC = 100 + 60Q + Q2 MC = 60 + 2Q where MC is marginal cost (in dollars) and Q is output. The demand and marginal revenue curves for the product are P = 100 Q MR = 100 2Q where P is the product price (in dollars) and Q is output.

a. If Smith wants to maximize profit, what output should he choose?

b. What price should he charge and what are his profits?

The demand curve that a monopoly faces is QD = 787 - 8P.

Rearranging this yields the inverse demand curve P = 787/8 - QD/8.

The marginal revenue curve is MR = P = 787/8 - 2QD/8.

There are no fixed costs for the monopoly and marginal cost is constant so marginal and average cost are equal.

AC = MC = 8

What is the dead weight loss due to the monopoly?

ROUND TO THE NEAREST CENT

Suppose a monopolist faces a demand curve for its output of P = 300−Q. This means that the marginal revenue curve of the monopolist is M R = 300 − 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?

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