(1) What is the quantity the monopolist will produce? (2) What is the quantity supplied to Class 1? What is the quantity supplied to Class2? (3) What is the price for Class 1? What is the price for Class2? (4) What is the monopolistic price if a single price were set for both classes? (5) What is the profit the monopolist would make if a single price were set for both classes? Is the profit bigger or smaller? (Compare with the case in which a monopolist acts as a third degree price discriminator)
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- Question 4. Consider a monopolist facing a demand curve of the form D(p) = 100 – 2p where p is the - unit price. Suppose the monopolist has a constant marginal cost of production of $2 a unit. Bunter was asked to determine the price which would maximize consumer surplus. Here is his solution: Total surplus as a function of price is 50(100 – 2x)dx. The derivative of this with respect to p is -(100-2p). This is maximized by making p as large as possible, i.e., p = 50. Is Bunter correct? If not, what is the error that Bunter has made?4) A monopolist is operating in two separate markets. The inverse demand functions for the two markets are P1 = 52 – 2Q1 and P2 = 64 – 1.5Q2. The monopolist’s total cost function is TC(Q) = 20 + 4(Qı + Q2). The monopolist can price discriminate. What kind of price discrimination is relevant here? What is the profit-maximizing price in each market? What is the monopolist's profit?Q1) Suppose that the inverse demand for a product is represented by the equation P = 50 – Q, where P is the price in Euros and Q is the annual output. Suppose that only one firm produces this product and that the marginal and average cost is €10. Calculate the profit-maximising price for this monopolist. Q2) In autumn, Erling Kagge, who lives alone on an island near the North Pole, puts 50 bags of root vegetables from his harvest into a cave just before a family of polar bears goes in to hibernate. The polar bears do not eat vegetables but would attack Kagge if he approached them. As a result, he is unable to get the vegetables out before the polar bears emerge the following spring. The vegetables spoil at the same rate no matter where he stores them. Which of the following statements best describes this behaviour? A. Kagge’s behaviour is an example of the anchoring effect in action B. Kagge’s behaviour is an example of the framing effect in action C. Kagge’s…
- Problem 08-09 A monopolist's inverse demand function is estimated as P = 150 – 3Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q1, and the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2. a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall that Q + Q2 = Q.) MR(Q): Q2 b. Determine the profit-maximizing level of output for each facility. Output for facility 1: Output for facility 2: c. Determine the profit-maximizing price. %248. A monopolist with cost function c(q) = q faces two consumers whose demand functions are given below. Q₁ = 100-P 50-P Q₂ (a) Suppose the monopolist is a uniform pricing firm (i.e.the monopolist can- not engage in any price discrimination). Find the firm's optimal pricing strategy. Calculate the firm's Lerner index. (b) What is the deadweight loss associated with this pricing strategy, if any? (c) Now, assume that price discrimination is possible. Find the monopolist's optimal second degree price-discrimination strategy. (d) Find the monopolist's optimal third degree price-discrimination strategy.2. Consider a monopolist who has a cost function of c(Q) = 5Q. This monopolist faces two consumers, the first having demand q₁(P₁) = 80 - 2P₁ and the second having demand q₂ (P₂) = 50 - P₂. a) Calculate the profit-maximizing price and then the optimal quantity sold to each consumer under uniform pricing, i.e. the monopolist charges the same price for both consumers. What are the monopolist's profits? b) Suppose now that the monopolist can engage in third degree price discrimination. Find the monopolists profit maximizing prices for consumers 1 and 2 (they should be different), and calculate the monopolist's profits. How do they compare to the profits in part (a)?
- 9. A monopolist produces a good at a constant marginal cost of 4. Suppose the monopolist is able to practice first-degree price discrimination (FDPD). The (in- verse) market demand function for the good is given by P=10-bQ where P is price, Q is quantity and b> 0 is a constant. Let DL(Q) denote the deadweight loss at quantity Q, and let CS(Q) denote the consumer surplus at Q. (a) Under FDPD, the marginal revenue function of the monopolist is the same as the market demand function. Is this true or false? Explain carefully.Question 8 Firm D is a monopolist that faces a market with inverse demand given by: P = 120-4Q Where Q is Firm D's output level. Firm D's total cost function is given by: TC(Q) = 11Q +42 Assuming that Firm D can perfectly (1st degree) price discriminate, what is Firm D's profit maximizing output level, Q*? (Hint: Because Firm D can perfectly price discriminate, its Marginal Revenue function is equivalent to inverse demand).Assume the following for price discriminating monopolist aimed at maximizing profit. Total demand for the product of the monopolist is Q = 50-5P (P = 100-2Q) · Demand in Market one is Q1= 32-0.4P1(P1= 80-2.5Q1) · Demand in Market two is Q2= 18-0.1P2(P2= 180-10Q2) · Cost function is C = 50+40Q (where Q = Q1+ Q2) a. Find equilibrium quantities (Q1and Q2), and equilibrium prices (P1and P2), b. Calculate profit (π), c. Calculate and Interpret elasticities (ε1 and ε2)
- A monopolist serves a market with five potential buyers, each of whom would buy at most one piece of the monopolist's good. Anna would be willing to pay up to £50 for it, Bob up to £70, Chloe up to £90, Dave up to £110 and Elizabeth up to £130. The monopolist's variable cost function is given in below table. [Note: In parts (a) and (b), working outs only need to be shown for at least one result per line of the table.] Quantity 1 Marginal Costs 50 Price Marg. Revenue 2 55 3 60 d) Find the total surplus maximising (i.e., socially optimal) quantity. e) Quantify the Deadweight Loss! 4 65 5 70You are the only seller of Melba sauce in the Albany region. The local demand for jars of Melba sauce and your marginal costs of producing the sauce are as follows: Marginal benefit (demand): P = 50 - 0.5Q Marginal cost (supply): P = 2 + 2Q What quantity of jars of Melba sauce should you optimally produce as a monopolist?A monopolist faces a demand of D(P) = 400−(1/5)P and constant marginal costs: TC(Q) = 1,000Q. (Please solve subparts 4-6) 1. Calculate the optimal price, quantity and total profit of the monopolist. 2. Derive the dead weight loss created by the monopolist and illustrate graphically. 3. Repeat questions 1) and 2) but now assume that the market is perfectly competitive (marginal cost pricing) 4. Take the monopoly case (as in 1) and 2). Now the government imposes a maximum price of $1250. Discuss the (welfare) effects of this measure. 5. Still in the monopoly case, assume that, instead of the maximum price, the government gives producers a per unit subsidy of $1,000. Discuss the welfare effects of this measure. 6. Suppose the market is perfectly competitive—as in 3)— and the government gives producers a per unit subsidy of $1,000. What is the welfare effect of this subsidy? Compare your answer with 5).