A monopolist’s demand function is given by D(p) = 90 − 2p. This monopolist is facing a cost function, C(y) = (1/2)y2 + 600. a) Is this a natural monopoly? Explain. b)How can government regulate this monopolist to produce the efficient amount of products?
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6..A monopolist’s demand function is given by D(p) = 90 − 2p. This monopolist is facing a cost function, C(y) = (1/2)y2 + 600.
a) Is this a natural
b)How can government regulate this monopolist to produce the efficient amount of products?
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- 2. A monopolist’s demand function is given by D(p) = 90 − 2p. This monopolist is facing a cost function, C(y) = (1/2)y2 + 600. (a) Is this a natural monopoly? Explain. (b) How can government regulate this monopolist to produce the efficient amount of products?5. A monopolist with cost function c(Q)=faces an inverse demand function given by P(Q)= √Q' (a) Find the elasticity of demand with respect to price. (b) Assuming that the monopolist uses MR = MC pricing rule, find his profit maximizing price, p", and output level, q". (c) Find the marginal cost at q" and calculate the Lerner index. (d) Does the monopolist's market power depend on his cost curve? In particu- lar, does it depend on a? Is your answer surprising?2. Suppose the cost function for a monopoly is given by TC =F+c.q where TC is the total cost, F is the fixed cost and q is the output of the firm. The demand function for the monopoly is given by q = A-bP where A > 0 and b > 0. Find out the profit maximizing price, quantity, and profit for the monopoly. Also find out the expression for the marginal revenue of the monopoly as well as the elasticity of demand facing the monopoly.
- 7. A monopoly firm faces a demand curve given by 2(P) = 40 – 2p. The firm has constant MC=$12. (A) Find the firm's marginal revenue and use this to find the firm's profit-maximizing output and price. Draw a diagram. Hint: first figure out how express the firm's total revenue in terms of Q. Then if you know calculus, take the derivative of this expression with respect to Q to find marginal revenue. If you don't know calculus, recall that for a linear demand curve, (1) the slope of the marginal revenue curve is twice (in absolute value) the slope of the demand curve; and (2) the marginal revenue curve intersects the vertical (price) axis at the same point as the demand curve; and (3) the marginal revenue curve hits the quantity axis at half the distance of the demand curve. (B) Find the price elasticity of demand at the profit-maximizing output and price. Is demand elastic?1. The inverse demand function for a monopolist's product is given by P=21-2Q. What is the maximum price per unit a monopolist can charge to be able to sell 6 units? What is marginal revenue when Q=6? Show your solution 2. Suppose the inverse demand function for a Meralco's service is given by P= 83 -2Q and the cost function is C=12 + 2Q. Required: Compute the profit-maximizing price, quantity and maximum profits.1.) You are the manager of a monopoly, and your demand and cost functions are given by P = 200 − 2Q and C(Q) = 1,400 + 2Q2, respectively. a. What price-quantity combination maximizes your firm's profits? b. Calculate the maximum profits. c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price-quantity combination? 2.) Determine the profit-maximizing output and price, and discuss its implications, if: 1. You are a monopolistically competitive firm and the inverse demand is P = 100 - Q and your cost is C(Q) = 125 + 4Q2 2. You are a monopoly and the inverse demand is P = 200 - Q and your cost is C(Q) = 150 + 4Q2 3.) Suppose the inverse demand function for two Cournot duopolists is given by P = 10 - (Q1 + Q2) and their costs are zero. A. What is each firm's marginal revenue and reaction functions? B. Determine the Cournot equilibrium outputs and equilibrium price. What is the implication of this model?
- 1. A monopolist's marginal cost function is given by: MC = 4q+ 20 where q is the quantity of good the monopolist produces. Fixed costs are 20, and the demand equation for the good produced is p+4q = 40, where p and q are price and quantity, respectively. - Find expressions for total revenue and for profit, as functions of q. Determine the value of q which maximises the profit. 2. Suppose the numbers x, y and z satisfy the following equations, where a is some number: x+y+z= 5-a 2x+y = 7-a x-y-2z = 0. Use a matrix method to determine the values of x, y and z, in terms of a. For what values of a will x, y and z all be positive? 3. Suppose that a is a positive number and that the function f is given by: f(x, y) = y¹ - 8a²y² +13. A monopolist faces a demand curve of P = 120 – 2q and has a production function given by f (L, K) = L'/4K¼. Input prices are w = 1 and r = 4. (a) Calculate the monopolist's (long-run) marginal cost as a function of the quantity it produces. (b) Draw a diagram illustrating the monopolist's problem. Identify each of the following on the diagram and calculate its numeric value: (i) monopolist's profit-maximizing quantity, (ii) price charged, (iii) monopolist's profit, (iv) consumer surplus, (v) producer surplus, and (vi) deadweight loss. Two notes: (1) the area of a triangle is base * height, (2) if you are getting really messy answers here, you may have made a mistake in part (a). (c) The government is concerned about the monopoly and decides to impose a price ceiling. Illustrate the efficient price ceiling on your diagram. i. Illustrate and calculate the price ceiling that will result in an efficient outcome. ii. Compute consumer and producer surplus at the efficient outcome. iii.…1. The market demand for monopoly firm is P=300-4Q and the total cost is C(Q)=50Q+Q?+100. a) How many products this firm should produce in order to maximize its profit and at what price? Calculate profit. Show the profit area on a graph. b) Calculate the consumer, producer surplus and the deadweight loss. c) What will happen to the deadweight loss if the demand increases by 10 units and the demand curve shifts to the right? Calculate the profit with new demand function.
- 1. A monopolist with cost function c(Q) = faces an inverse demand function given by P(Q) = (a) Find the elasticity of demand with respect to price. (b) Assuming that the monopolist uses MR = MC pricing rule, find his profit maximizing price, p", and output level, q™. (c) Find the marginal cost at q" and calculate the Lerner index. (d) Does the monopolist's market power depend on his cost curve? In particu- lar, does it depend on a? Is your answer surprising?19. Firm A is monopolist in x market, and it consumes one unit of y in order to produce one unit of x. It costs 5 + py TL to produce one unit of x. (py is the price of product y.) y is produced by a monopolist, B, and it costs 5 TL to produce one unitf of y. The demand for x is defined by px = 50-qx (px product price, qx quantity demanded). a) Assume that px is set by Firm A and py is set by Firm B. What would be the equilibrium prices for products x and y? Calculate Firm A and B's profits. b) Assume that Firms A and B merge together. What would be the equilibrium prices for products x and y? Calculate the profits of the new firm. c) Would the merger between A and B increase the consumer surplus? Why (not)?8. Amonopolist has a cost function C(q) =– The monopolist faces a market demand curve given by q = 10 – p. a. Find marginal cost. b. Calculate the profit-maximizing price-quantity combination for the monopolist. Also calculate the monopolist's profits. c. What output level would be produced by this industry under perfect competition? d. Calculate the consumer surplus obtained in case (c). Show that this exceeds the sum of monopolist's profits and the consumer surplus received in case (b). What is the value of the deadweight loss from the monopolization? Hint: The area of a triangle is 0.5 * base * height.
