Monopolist’s Profit-maximizing Level of Output Assignment Help
1.A monopolist faces a demand curve P=210 −4Q and initially faces a constant marginal cost MC = 10.
a) Calculate the profit-maximizing monopoly quantity and compute the monopolist’s total revenue at the optimal price.
b) Suppose that the monopolist’s marginal cost increases to MC = 20. Verify that the monopolist’s total revenue goes down.
c) Suppose that all firms in a perfectly competitive equilibrium had a constant marginal cost MC = 10. Find the long-run perfectly competitive industry price and quantity.
d) Suppose that all firms’ marginal costs increased to MC = 20. Verify that the increase in marginal cost causes total industry revenue to go up.
2.Suppose that an industry is characterized as follows:
|C = 100 + 2q2||each firm”s total cost function|
|MC=4q||firm”s marginal cost function|
|P = 90 – 2Q||industry demand curve|
|MR= 90-4Q||industry marginal revenue curve|
a. If there is only one firm in the industry, find the monopoly price, quantity, and level of profit.
b. Find the price, quantity, and level of profit if the industry is competitive.
c. Graphically illustrate the demand curve, marginal revenue curve, marginal cost curve, and average cost curve. Identify the difference between the profit level of the monopoly and the profit level of the competitive industry in two different ways. Verify that the two are numerically equivalent.
3.Suppose a monopolist faces the following demand curve:
P = 596 – 6Q.Marginal cost of production is constant and equal to $20, and there are no fixed costs.
a)What is the monopolist’s profit-maximizing level of output?
b)What price will the profit-maximizing monopolist charge?
c)How much profit will the monopolist make if she maximizes her profit?
d)What would be the value of consumer surplus if the market were perfectly competitive?
e)What is the value of the deadweight loss when the market is a monopoly?
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4.You are given the following information about the costs of a perfectly competitive firm.
You are hired to determine the profit-maximizing quantity of the firm for different market prices. Complete the table below.
|Market Price||Profit-maximizing level of output||Total Revenue||Total Cost||Profit|
5.Suppose that demand for rollerblades is given by D(p) = A – p. The cost function for all firms is C(y) = wy2 + f , where f is a fixed set-up cost. The marginal cost of production is MC(y) = 2wy. Assume that the industry is perfectly competitive.
(a) Find a competitive firm’s supply function. If there are n firms in the industry, what is industry supply?
(b) If there are n firms in the industry, find expressions for the competitive equilibrium price and quantity. What is the equation for how much each firm produces? What is the equation for the profit of each firm? [Hint: Your answer should be 4 algebraic equations that express the endogenous variables (price, quantity, firm supply, and firm profit) as a function of the exogenous variables (A, n, f , and w).]
(c) Suppose A = 100, w = $4, f = $100, and n = 2. Using the equations you derived in part (b), what is the equilibrium price and quantity? Firm supply and profits? Using two diagrams, graph this competitive equilibrium. In one diagram illustrate the market equilibrium. In the second, show the equilibrium position of a representative firm. On this second diagram make sure you indicate the profit-maximizing output of a firm as well as the profit earned.
(d) Is the equilibrium you found in part (c) a short-run or long-run equilibrium? Why? If the industry is not in long-run equilibrium, explain the adjustment process that will occur.
(e) For the parameter values given in part(c),find the long-run competitive equilibrium.On the two diagrams from part(c),indicate the long-run equilibrium. What is the long-run equilibrium number of firms?
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