A monopolist has a cost function of c(x) = x so that its marginal cost is constant at $1 per unit. It faces the following demand curve: D(P) = { 100/p 100/p if p > 20 if p ≤ 20 A. What is the profit-maximizing choice of output/price for the monopolist? Graphically represent the monopoly market. B. If the government sets a price ceiling on the monopolist in order to force it to act as a competitor, what price should the government set? C. What output would the monopolist produce if forced to behave as a competitor? D. Based on the information in parts A-C, find the consumer-, producer-, and social surpluses before and after the government intervention.
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- 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.…A monopolist faces a market demand curve given by Q(p) = 70 – p. Its total costs are described by TC(Q) = 3ố0 Q³ – 5Q + 250. 1 a) Derive the monopoly price, quantity, and profits. b) Calculate Lerner Index under the monopoly equilibrium. c) Now suppose the government sets the maximum price at $40. What output level and price level will the monopolist choose to maximize profits? What is the deadweight loss? d) Suppose the government sets the maximum price at $30. What output level and price level will the monopolist choose to maximize profits? What is the deadweight loss?The following graph gives the demand (D) curve for water services in the fictional town of Streamship Springs. The graph also shows the marginal revenue (MR) curve, the marginal cost (MC) curve, and the average total cost (ATC) curve for the local water company, a natural monopolist. On the following graph, use the black point (plus symbol) to indicate the profit-maximizing price and quantity for this natural monopolist. ? PRICE (Dollars per hundred cubic feet) 40 36 32 28 24 20 16 12 8 4 0 +↓ 0 + 1 MR 8 3 4 5 6 7 QUANTITY (Hundreds of cubic feet) True 2 ATC False 9 10 D Which of the following statements are true about this natural monopoly? Check all that apply. Monopoly Outcome In order for a monopoly to exist in this case, the government must have intervened and created it. The water company is experiencing diseconomies of scale. The water company is experiencing economies of scale. The water company must own a scarce resource. True or False: Without government regulation, natural…
- The following graph gives the demand (D) curve for water services in the fictional town of Streamship Springs. The graph also shows the marginal revenue (MR) curve, the marginal cost (MC) curve, and the average total cost (ATC) curve for the local water company, a natural monopolist. On the following graph, use the black point (plus symbol) to indicate the profit-maximizing price and quantity for this natural monopolist. ? PRICE (Dollars per hundred cubic feet) 40 36 32 28 24 20 16 12 4 0 0 1 2 3 5 6 7 8 QUANTITY (Hundreds of cubic feet) MR 4 True ATC MC O False 9 10 D The water company is experiencing economies of scale. Which of the following statements are true about this natural monopoly? Check all that apply. + Monopoly Outcome The water company must own a scarce resource. It is more efficient on the cost side for one producer to exist in this market rather than a large number of producers. In order for a monopoly to exist in this case, the government must have intervened and…Marginal Analysis II Question 3 Assume that a monopolist faces a demand curve for its product given by: p=100−1qp=100-1q Further assume that the firm's cost function is: TC=470+9qTC=470+9q Using calculus and formulas (don't just build a table in a spreadsheet as in the previous lesson) to find a solution, what is the profit (rounded to the nearest integer) for the firm at the optimal price and quantity? Round the optimal quantity to the nearest hundredth before computing the optimal price, which you should then round to the nearest cent. Note: Non-integer quantities may make sense when each unit of q represents a bundle of many individual items. Hint 1: Define a formula for Total Revenue using the demand curve equation. Then take the derivative of the Total Revenue and Total Cost formulas to compute the Marginal Revenue and Marginal Cost formulas, respectively. Use these Marginal Revenue and Marginal Cost formulas to perform a marginal analysis. Hint 2: When computing the total…A monopolist has a single customer with the demand curve P=20-Q. (So this customer will buy different quantities at different prices.) Suppose the monopolist’s marginal cost is MC=0. (And assume FC=0 to keep things simple.) The monopolist uses “standard” pricing, i.e., it sets a single price for all units that the customer buys. The graph below shows the demand curve and MC curve. Solve graphically for the price & quantity that will maximize profit for the monopolist. Shade the areas on your graph that represent consumer surplus and the monopolist’s profit.
- The following graph shows the demand (D) for cable services in the imaginary town of Utilityburg. The graph also shows the marginal revenue (MR) curve, the marginal cost (MC) curve, and the average total cost (ATC) curve for the local cable company, a natural monopolist. On the following graph, use the black point (plus symbol) to indicate the profit-maximizing price and quantity for this natural monopolist. (? 100 90 Monopoly Outcome 80 70 60 50 40 ATC 30 MC 20 10 MR D 2 6 8 10 12 14 16 18 20 QUANTITY (Number of subscriptions) Which of the following statements are true about this natural monopoly? Check all that apply. O In order for a monopoly to exist in this case, the government must have intervened and created it. O The cable company is experiencing diseconomies of scale. O The cable company is experiencing economies of scale. O It is more efficient on the cost side for one producer to exist in this market rather than a large number of producers. True or False: Without government…the supply curve is given Qs= P and the demand curve is given by Qd = P QD = 12 -. 5P Q and mariginal cost is zero 1. there was a monopoly, with the same supply curve. Given the option between selling 6,000, 8,000 and 10,000, which would the monopolist choose? What will the consumer surplus be? 2. Graphically represent the effects of an increase in demand.a) Find and highlight the consumer surplus in the monopoly in the diagram.b) Draw a possible marginal cost curve for the monopolist into the diagram that is consistentwith all the other curves that are already given. c) Based on the marginal cost curve that you constructed in part (b), find and highlight themonopolist’s total costs at the monopoly price in the diagram. d) Briefly (200 words max) explain the shape of the marginal revenue curve as compared tothe demand curve in the diagram.
- d) If a price ceiling of $17.50 is imposed by the government on the monopolist, estimate (based on the graph) the quantity that the monopolist will produce. In this case, does the price ceiling in a monopoly improve economic efficiency or not? e) Supposed that instead of a regular monopoly, the graph above pertains to a natural monopoly, what change must be made to the graph to depict a natural monopoly?Assume that the market for coal is a monopoly market. We have the following: ?(?) = ?? − ?? ????? ? > ? ??(?) = ?? ? − ?? ? + ?? + ??? a. Find the monopolist price and quantity. b. What is the value of Profit (or loss) at monopolist equilibrium price and quantity? c. What is the value of dead weight loss (DWL) at monopolist price and quantity?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.