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- 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?I need ans 3 In the next two problems, (1) and (2), consider a monopolist that maximizes profits and charges all consumers the same price. The inverse demand function is P = 100 – Q, where P is the price and Q is output. Calculate the deadweight loss to consumers (if any) and to the monopolist (if any). (1) Marginal cost is always zero. (2) Marginal cost is MC = Q. (3) Assume that every consumer has the inverse demand function P = 10 – Q and that marginal cost is always zero. There are 10 consumers. The monopolist wants to maximize profits by designing a two-part tariff. Calculate the two parts of the tariff, and calculate profits.. Suppose a monopolist producing Q units of output faces the demand curve P = 130 − 4Q. Its total cost when producing Q units of output is T C(Q) = F + 34Q+ 2Q2 , where F is a fixed cost. (a) For what values of F can a profit-maximizing firm charging a uniform price earn at least zero economic profit? (b) For what values of F can a profit-maximizing firm engaging in perfect first-degree price discrimination earn at least zero economic profit.
- 5. There are only two consumers in a city. Consumer A has demand q4 = 10 - p and Consumer B has demand qg = 15 – 3p. The monopolist can tell the two consumers apart. The total cost function of the monopolist is TC = q with q being the total quantity produced. (a) Assume that the laws of the city force the monopolist to use a single price. Find the price that maximizes the monopolist's profit. (b) Assume that the monopolist can use whatever pricing strategy they want. What is the one that maximizes profit?3. 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. A monopolist with zero cost, that is c(q) = 0, faces two consumers whose demand functions are given below. Q1 = 10-P Q2 (a) Suppose the monopolist cannot engage in any price discrimination. Find the firm's optimal pricing strategy. (b) Now, assume that price discrimination is possible. Find the monopolist's optimal first degree price-discrimination strategy. (c) Find the monopolist's optimal second degree price-discrimination strategy.
- 1. A monopolist has a cost function given by C(y)=y? and faces a demand curve given by P(y) = 120-y. %3D (a) What is the profit maximizing level of output and the price that the monopolist will charge? Show your calculations. (b) If you impose a lump sum tax of £100 on this monopolist, what will be the impact on output? Explain your calculations and the intuition behind your result. (c) If you wanted to choose a price ceiling for this monopolist so as to maximize consumer plus producer surplus, what price ceiling should you choose? How much output will the monopolist produce at this price ceiling? Explain your calculations. (d) Suppose that you impose a specific tax of £20 per unit of output. What will be the monopolist's profit maximizing level of output? Explain your derivation and comment on the impact on output.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?Assume inverse demand function for game console in an imaginary country is P=1200-4Q and the total cost function is TC=400+4Q2. Government put $120 of specific tax on production. If the market is competitive what is the incidence of tax on consumer? If the market is monopolist what is the incidence of tax on consumer?
- 1. A Chinese steel producer has identified two markets. The first has a demand of q = 56 - p, the second of q = 24 - p. The cost function is C = 10+q². a) What is the profit maximizing price and output for the monopolist? You can assume that market segmentation is feasible. b)* Suppose now the monopolist's cost increases to C = 10 + 2q². How is your answer in a) affected? Discuss what happenedConsider a monopolist with a demand equation P = 60 - 2Q, where P is the price in dollars and Q is the quantity. The monopolist is able to produce the output with a constant marginal cost of $20 which is equals to the average total cost. Assume that there is no fixed cost. A. If the monopolist practice single pricing, determine the price, quantity, profit, consumer surplus and producer surplus in this market with the aid of a suitable diagram. Appraise the efficiency in this market. B. If the monopolist were to practice perfect price discrimination, determine the quantity, profit, consumer surplus and producer surplus of the monopolist. Appraise the efficiency in this market. C. Consumers and the society are always worse off in a monopolised market compared to a perfectly competitive market. Do you agree? Examine the two (2) market structures and explain with the help of a suitable market diagram.You are the manager of a monopolist. Assume that the demand curve of the firm is linear, and the marginal cost is a fixed constant. a. Graphically illustrate the profit-maximizing output and price set by the monopolistic firm. b. If the government set a tax of $t per unit sold, graphically illustrate how the output and price of the monopolist’s profit maximization will change?
