Consider a market with the following kinked inverse demand P=20-3g for q ≤ 3 and P=14-g for q>3. A monopolist in this market has marginal costs of m. Ⓒa. The monopolist will not produce q = 3 for any value of m. Ob. The monopolist will produce q=3 if m= 8. Oc. The monopolist will produce q=3 if 82 m 2 2. Od. The monopolist will produce q=3 if m= 2.
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- A monopolist hires you to design its pricing policy. After month of doing market research you realize that the own-price elasticity is not the same for different groups of consumers in the market. (a) If group (a) has an own-price elasticity of 2.16 and group (b) 1.26. Assuming that the firm can directly observe an indicator of belonging to groups (a) and (b), what degree of price-discrimination can the monopolist implement? which group will end up paying more? (b) Will producer's surplus increase or decrease with price discrimination? what about consumer surplus? (consider single pricing vs price discrimination) (c) If a you get hold of a magic crystal ball that tells you the exact willingness to pay of each consumer. What type of price discrimination can the monopolist use to maximize profits? is this strategy “efficient” from the point of view of total surplus? are consumers better-off or worse-off? (Hint: A graph can greatly clarify this part.)A monopolist w11ishes to maximize total revenue. She produces two outputs, (x1, x2) and faces the following demands for her products, X1 = 20 – 2p1, and X2 = 20 – 4p2 Where p1 and p2 are, respectively, the prices of the two goods. To produce one unit of x1 the monopolist must use one unit of land and one unit of capital. And, to produce one unit of x2 requires two units of land and one unit of capital. The firm has available 10 units of land and 6 units of capital. Specify the firm’s short-run maximization problem. Set up the Kuhn-Tucker conditions for maximization (you do not need to solve). Assume that the solution is x*1 = 5 1/3 (i.e. 16/3) and x*2 = 2/3. Explain which constraints are binding and whether the Lagrange multipliers are positive or zero and what they mean.2. A monopolist has two specific demanders with demand equations: qA = 10 – p and qB = 10 – 2p. This monopolist implements an optimal two-part tariff pricing scheme, under which demanders pay a fixed feea for the right to consume the good and a uniform price p for each unit consumed. The monopolist chooses a and p to maximize profits. This monopolist produces at constant average and marginal costs of AC = MC = 2. The monopolist’s profits are __________ and the average price paid by demander B is _________.
- A monopolist has two types of customers. There are 100 of Type A, who will each pay up to $10 for a single unit of the good, and 50 of Type B, who will each pay up to $8. Neither is willing to purchase additional units at any price. If it must charge a uniform price, find that price. a. Assume that spending $80 on advertising will attract 100 more Type B customers. Should the monopolist advertise? If so, what will happen to price?Consider a monopolist who produces perishable (non durable good) in two periods. The cost of production of one unit is c = 1/4. In both periods the monopolist faces a unit mass of costumers of two types θH = 1 and θL = 1/2. Each consumer needs only one unit of the good and gets a utility θ from buying it. Fraction of each type in the population is µ = 1/2. The discount factor is δ > 1/2. Suppose the monopolist cannot price discriminate between new and returning customers, what would be his prices and profits in the two periods? Suppose now the monopolist got a technology that allows him to track costumers, so that at period 2 he can distinguish new and returning customers, i.e. in period 2 he can charge price pN to a new customer and price pR to a returning customer. As in the class, assume there is not commitment to What would be the monopolists prices and profits in this case? What is the monopolist’s gain from the ability to price discriminate, explain the intuition behind…Consider a monopolist who is selling his blockbuster drug in two markets where one market is much larger than the other. Suppose the demand in the two markets is given by q1 = 30 − p1 and q2 = 3 − p2 (quantity is measured in millions of complete dosages and price is in your favorite currency) and the marginal cost of production and distribution is roughly the same and equal to 1 per unit (c=1). This problem asks you to compare equilibrium outcomes (prices, quantities, profits, consumer surplus, and consumer surplus per unit of output) when the monopolist can price discriminate across the two markets versus when it must set a uniform price. It then asks you to comment on some recent policy proposals. For each market separately, set up and solve the monopolist’s profit-maximizing problem. Specifically, write down/compute the following. Inverse demand and the profit functions. Equilibrium prices (), quantities () and profits () Consumer surplus () and consumer surplus per unit of…
- A telephone company has isolated three distinct demands for its services:Weekdays: Q1=90-0.5P1Holidays: Q2=35-0.25P2Nights: Q3=30-0.2P3TC=25+20Q WHERE Q=Q1+Q2+Q3Show that as a discriminatory monopolist this company will maximize profits by charging the highest price in the market where the price elasticity of demand is lowest, by finding a) the profit maximizing level of outputb)the profit maximizing price and c) the price elasticity of demand in each marketUse Cramer's rule for solving simultaneous equations and the Hessian for the second order conditionsThere are two types of consumers in Melbourne: students and non-students. The student population is 10, and each student's demand of printing paper is Qs, = 1-p, for p<1. The non-student population is 40, and each non-student's demand of printing paper is Qa =3-p. for p <3. Suppose OfficeMax is the only seller of printing paper in Melboume Assume zero production cost. The monopolist OfficeMax claims that the student discount improves social welfare. Is it true? Explain why it is (not) true.Consider a monopolist operating the underground in Europacity with a total cost curve given by c(x) = 15 + 5x. The monopolist sets two prices: a high price ph and a low price pl. everyone is eligible for the high price, but only by taking the tube outside the peak hours is anyone eligible for the discount price. Suppose that the only o¤-peak travelers are those who are not willing to buy the ticket at ph. a. If the monopolist faces the inverse demand curve given by p(x) = 20 - 5x, what are the profit maximizing values of ph and pl? b. How much economic profit does the monopolist take? c. How much profit would be made if the same price were charged to all buyers (no price discrimination)? Discuss the difference from part b.
- Suppose there are two classes of buyers in a market served by a monopolist. At this point the two classes are lumped together and the monopolist is currently producing the profit maximizing quantity based upon being a single price monopolist. Suppose that the monopolist perceives that its relevant market demand curve is given by the equation P = (40/3) –(2/3)Q and its MC = ATC = 4.Suppose this monopolist acts as a single price monopolist. Calculate the monopolist’s price, quantity, and profit given the above information.. Let the demand curve for a monopolist’s product be P = 100 – 2Qd and the marginal cost of production be constant at MC = 10. Suppose that the firm considers moving from a uniform pricing strategy to a two-block tariff where the first block provides 15 units at a price of P1 = $70 and the second block provides an additional 15 units at a price of P2 = $40. How much does the monopolist’s profit rise with this scheme?Exercise A.6 A monopolist facing the demand curve Q = 42 – 0.6P operates with constant average and marginal costs equal to 20. a) Calculate the quantity, price and profit obtained by the monopolist. Represent graphically. (b) What quantity, what price and what benefit will you get if you can apply first-degree price discrimination? Calculate the consumer surplus and represent graphically. c) The monopolist warns that he can separate consumers into two distinct groups with demands Q1 = 12 - 0.1P1 and Q2 = 30 - 0.5P2. Calculate the quantities, the prices you will set in each market, and the profit you will make. Represent graphically.