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- How can a monopolist identify the profit-maximizing level of output if it knows its total revenue and total cost curves?What is the usual shape of a total revenue curve for a monopolist? Why?Draw a monopolists demand curve, marginal revenue, and marginal cost curves. Identify the monopolists profit-maximizing output level. Now, think about a slightly higher level of output (sayQ0+1). According to the graph, is there any consumer willing to pay more than the marginal cost of that new level of output? If so, what does this mean?
- 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?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?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.
- 1. A monopolist has a cost function given by C(y)=y² and faces a demand curve given by P(y) 120-y. %3D (a) What is the profit maximising 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 maximise 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 maximising level of output? Explain your derivation and comment on the impact on output.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.3. Suppose the inverse demand function is linear: p(q) = 24-q The monopolist's cost %3D function is c(g)-0.5g*. Assume the monopolist must charge a uniform price. (a) Find the optimum monopoly price and quantity. Also calculate the deadweight loss. (b) Suppose the governmet can levy a lump-sum tax T (i.e., a fixed amount indepen- dent of produetion) and an excise tax t per unit of production on the monopolist. These taxes can be negative, in which case they are subsidies. The proceeds of these taxes can be transferred to consumers. The monopolist is always free to quit the market, in which case she does not have to pay any taxes. The government wants to maximize the ensumer welfare: Pind the optimum vaues of t and
- Suppose a monopolist faces a market demand curve given by P = 50 - Q. Marginal cost is initially equal to zero and constant. a. (5) Calculate the profit maximizing price and quantity. Use the Lerner index to calculate the price elasticity of demand at this point. What is the amount of deadweight loss associated with this monopoly2. Think about a monopolist, the market (inverse) demand function is: P = 30-2Q, his cost function is: C(Q) = 5+ Q?, a. What is the monopolist's optimal quantity and price? b. What is the monopolist's highest profit? %3D. 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.