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Firm Gamma is the monopolist of a particular market. Gamma's cost function is C= 100+1.5q^2
The demand for Gamma’s output is Q^D= 525 - 0.5p
Gamma chooses quantity Q* that maximizes its profit. Firm Gamma produces Q*= units of output and charges a price p*=.
Firm Gamma’s profit is Profit=.
In this market, the Lerner Index of Market Power is L=.
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- A monopolist faces the following market demand function: D(P) = 100 – P and has total costs equal to TC(Q) = 100 + 100 Show that the monopolist's cost function is subadditive for all relevant levels of demand (for all Q< 100). (Hint: Let EN Qi = Q be a way to split up the total production of quantity Q in N different firms. You can then use the fact that the minimum of EN Q? is reached at Qi = 8.)BYOB is a monopolist in beer production and distribution in the imaginary economy of Hopsville. Suppose that BYOB cannot price discriminate; that is, it sells its beer at the same price per can to all customers. The following graph shows the marginal cost (MC), marginal revenue (MR), average total cost (ATC), and demand (D) for beer in this market. Place the black point (plus symbol) on the graph to indicate the profit-maximizing price and quantity for BYOB. IF BYOB is making a profit, use the green rectangle (triangie symbols) to shade in the area representing its profit. On the other hand, if BYOB is suffering a loss, use the purple rectangle (diamond symbols) to shade in the area representing its loss. 4.00 3.50 Monopoly Outoome 3.00 ATC 2.50 Profit 2.00 1.50 Los MC 1.00 0.50 MR 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 QUANTITY (Thousands of cans of beer) PRICE (Dollars per can)Consider a monopolistic market with demand function: P = 36 – 0.5Q The monopolist’s marginal cost (MC) and total cost (TC) function are: MC = $2 TC = 4 + 2Q How much total economic profit does the monopolist earn?
- Suppose a monopolist faces two groups of consumers. Group 1 has a demand given by P1=50−2Q1�1=50−2�1 and MR1=50−4Q1��1=50−4�1. Group 2 has a demand given by P2=40−Q2�2=40−�2 and MR2=40−2Q2��2=40−2�2. The monopolist faces a constant marginal cost equal to MC=10��=10.If the monopolist is allowed to engage in 3rd degree price discrimination, how many units of output will the monopolist sell? Question 12Answer a. 25 b. 10 c. 15 d. 20Suppose a profit-maximizing monopolist is producing 1100 units of output and is charging a price of $60.00 per unit. If the elasticity of demand for the product is - 3.00, find the marginal cost of the last unit produced. The marginal cost of the last unit produce is $ (Enter your response rounded to two decimal places.) What is the firm's Lerner Index? The firm's Lerner Index is - (Enter your response rounded to two decimal places.) Suppose that the average cost of the last unit produced is $12.00 and the firm's fixed cost is $1000. Find the firm's profit. The firm's profit is $ (Enter your response rounded to two decimal places.)A monopolist faces two markets with demand functions given by q1 = 120 − p1 q2 = 120 − 2p2 The monopolist has no fixed costs of production, and the marginal cost of production is $10. Suppose the monopolist charges the price $80 per unit of output. What is the market demand at this price? Suppose that the monopolist charges different prices per unit of output in the two markets. How much output is produced? What are the prices? What is the monopolist’s profit?
- A monopolist faces two geographically distinct markets, say market 1 is New York and market2 is California. The inverse demand curves in these markets are P1 = 400 – Q1 and P2 = 200 – Q2. Themonopolist’s total cost function is C(Q) = 0.25Q^2 and marginal cost function is MC(Q) = 0.5Q, where Q =Q1 + Q2 is the total quantity that it produces. Your job is to find out how much quantity to sell in eachmarket in order to maximize the monopolist’s profit.a) Carefully express this monopolist’s profit maximization problem.b) State the two equations that characterize the profit-maximizing amounts of Q1 and Q2, given an interiorsolution with positive quantities sold in each market.c) Solve these two equations for Q1* and Q2*.d) Find the prices P1* and P2* that the monopolist should charge in each market.e) Calculate the monopolist’s (maximized) profit.Consider a firm that has one factory, but can sell its product in two observably different markets, engaging in third-degree price discrimination. You may assume that the good produced is continuously divisible (like ethanol). The firm has a monopoly in market 1 and faces market demand curve Q1(P) = 100 – 2P and the firm also sells its product in market 2 which is competitive and has market price P2 = $30. The firm has cost function C(Q) = 0.25Q2 with marginal cost equal to MC(Q) = 0.5Q, where Q = Q1 + Q2 is the total quantity it produces: Q1 is the quantity to be sold in market 1 and Q2 is the quantity to be sold in market 2. a) Write out the firm’s profit maximization problem. b) Give the marginal conditions (equations) that a solution to the profit maximization problem satisfies. c) Solve for the firm’s optimal quantities to sell in each market. d) Give the price that the firm optimally charges in each marketA monopolist faces two markets (think of it as a domestic market and a foreign market). The demand functions of the two markets are respectively: Q 1 =100 - P 1 ; Q 2 =180 - P 2 The cost function of the monopoly firm is: TC = 40Q. Q1: If this firm charges a uniform price, what price should maximize its profit? What is the total profit? Q2: If this firm charges a Third Degree Price Discrimination, what is the equilibrium price for each market in order to maximize profits? And what is the profit of each market and the total profit?
- A movie monopolist sells to college students and other adults. The demand function for students is Q = 1,560 - 100P, and the demand function for other adults is Q = 1,800 - 100P. but who has cost function C(Q) = Q +0.005Q² Marginal cost is MC = 1 + 0.010, where Q=Qs+ QA- Instructions: Round your answers to 2 decimal places as needed. a. What prices will the monopolist set when she can discriminate? Pstudent = $ per ticket. Padult = $ Profit = $ b. What if demand for adults increases to = 2,000 - 100P? Q Pstudent = $ Padult = $ Profit = $ per ticket. O increases. O decreases. per ticket. c. When adult demand increases, the adult price: per ticket. does not change. O decreases. O increases. d. When adult demand increases, the student price: does not change.Topside Tiles, which produces roofing tiles, is a local monopoly. Its inverse demand function is p=140-2Q, and its constant marginal cost is 10. The owner has delegated the decision of how much output to produce to the plant manager. The manager's income, Y, is 5% of revenue: Y=0.05R. Show that a manager who wishes to maximize income, Y, will choose an output that exceeds the profit-maximizing level. Is there a conflict of interest between the owner and manager? Is this situation an agency problem? (Hint: This problem can be solved using a graph, by using calculus, or by using the rule that the MR curve has twice the slope of the demand curve.) The output that maximizes profit is (Enter your response rounded to one decimal place.) units.Firm Gamma is the monopolist of a particular market. Gamma's cost function is C= 3Q2 The demand for Gamma's output is QD = 600 – 0.5p Suppose the government wants to use price control to eliminate the deadweight loss in this market. The government can restore the efficient output level if it introduces a + (select price ceiling or price floor) equal to $ : .
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