2. Monopoly: Consider a monopolist with a marginal cost of production c = 8 who faces a demand curve D(p) = 42 - p/4. (a) What is the marginal revenue function of the monopolist? (b) What is the monopoly price? (c) At the monopoly price, what is the value of the Lerner Index?
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- What is the usual shape of a total revenue curve for a monopolist? Why?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 has a cost function given by C(y)=y² +12 and faces a demand curve given by P(y) = 24-y. (a) What is the profit maximising level of output and price charged by the monopolist? Show your calculations. (b) If you impose a lump sum tax of £100 on this monopolist, what would be the impact on output? Explain your calculations and your result. (c) If you wanted to price regulate this monopolist so as to maximise consumer plus producer surplus, what price ceiling would you impose? 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 would its profit maximising level of output be? Explain your derivation and comment on the impact on output.
- 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.…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 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)=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 firm encounters a demand function Qd = 60–0.5P and MC = AC = $20 (a) If the market is a competitive market, find the firm's equilibrium quantity, price and profit. (b) If the firm is a monopolist, find the firm's equilibrium quantity, price and profit. (c) Suppose being a monopolist, this firm can discriminate the market. Compute quantity, price, profit, consumer surplus, and deadweight loss in the secondary market. (d) Compute the price elasticity of demand at equilibrium price in the original market.
- 1. A monopolist has a cost function given by C(y)=y² and faces a demand curve given by P(y) 120-y. %3D (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.3. Consider a monopolist who faces the following demand: Demand: P= 100 – 10Q MC= 50+20 a) Find the price quantity combination that maximizes profit for the monopolist. b) Is the firm making positive, negative or zero profits? (100,100) Kareem chooses (60, 105) (500, 400) Saleem chooses Kareem chooses (50,420) 4. Calculate the SPNE/SPNES for the game stated above.2. Consider a monopolist with constant marginal cost MC(Q) = 1 facing two con- sumers. Consumer 1 has demand function Q? = 5-P while consumer 2 has Q = 10 – 2P. (a) Suppose the monopolist acts competitively and uses P = MC pricing strat- egy. Find the resulting equilibrium price and quantity. Find the consumer, producer, and aggregate surplus. (b) Suppose the monopolist uses MR = MC pricing strategy. Find the result- ing equilibrium price and quantity. Find the effect on consumer, producer, and aggregate surplus. (c) Suppose the monopolist uses 1st degree price discrimination. Find the resulting equilibrium prices and quantities. Find the consumer, producer, and aggregate surplus.
