Suppose that the monopolist is able to charge different prices in the two markets. The inverse demand curve in market 1 is p,=207-0.9q1. The inverse demand curve in market 2 is p2=226-0.7q2. The firm's total cost function is C(q,+q2)=(qj+q2)?. What is the firm's optimal choice of q,?
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![Suppose that the monopolist is able to charge different prices in the two markets. The inverse demand curve in market 1 is p,=207-0.9q1. The inverse
demand curve in market 2 is p2=226-0.7q2. The firm's total cost function is C(q,+q2)=(qj+q2)².
What is the firm's optimal choice of q,?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ea8991-afd7-4b2f-b26b-ea403f10fe15%2Fb6e4aa2a-4f6f-4b3a-89b6-7da80c41f12a%2Fk48vdl6_processed.png&w=3840&q=75)
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- A monopolist is deciding how to allocate output between two geographically separated markets. The demand curve for the firm's output in each market is: P1 = 4,000 - 100Q1 P2 = 2,000 - 50Q2 Where P1 and P2 are the prices of the product in each market and Q1 and Q2 are the amounts sold in each market. The firm's marginal cost curve is: MC = 25Q where Q is the firm's entire output (Q = Q1 + Q2) a) how many units should the firm sell in each market? (Keep Q1 and Q2 in decimal form) b) What price should it charge in the first market? (Use Q1 in decimal form) c) What price should it charge in the second market? ( Use Q2 in decimal form)Acme is a monopolist for a good with inverse demand P = 4000 – 6Q, where P is the price in dollars and Q is the amount sold. Acme's variable costs are TVC(Q) = 4Q². With these functions, the marginal revenue is MR(Q) = 4000 – 12Q and marginal cost is MC(Q) = 8Q. a) If Acme has no fixed costs, what is its profit maximizing price? b) If Acme has non-sunk fixed costs of $700,000, is it worth operating or should they shut down?Consider a monopoly market with demand curve Q(P) = . Suppose that producing a good costs $1 per unit and the firm must produce at least 1 unit by law. (1) What is the elasticity of demand? (2) How much would the monopolistic firm produce?
- A monopolist sells in two markets. The inverse demand curve in market 1 is p1 = 200 – y1. The inverse demand curve in market 2 is p2 = 400 – %D y2. The firm's total cost function is c(y1 + y2) = (y1 + y2) 2. The firm is able to price discriminate between the two markets. What are the optimal prices?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.A different industry has a Demand curve given by Q = 100 p − 1 2 Assume that a monopolist supplies this industry. The cost function of this monopolist is c(Q)=2*Q. What is the price the monopolist charges? What is the quantity the monopolist sells?
- A firm is originally operating as a single-price monopolist that faces a market demand curve P(Q) = 198 –0 and total cost curve equal to TC (q) = 10, 500 + 32Q, with constant MC equal to MC(Q) = 32 for all units produced. Part (a): How much output does the firm produce and at what price is each unit sold for? Part (b): Calculate the firm's profit. The firm now realizes there are actually two distinct groups of consumers that purchase their product, with the following demand functions: P(q1) = 242 – qı P(q2) = 176 – 92 Their total and marginal cost curves have not changed. If the firm wanted to successfully practice third-degree price discrimination: Part (c): How many units of output would they sell to group 1 and how much will each consumer in group 1 pay? Part (d): How many units of output would they sell to group 2 and how much will each consumer in group 2 pay? Part (e): How much profit is earned by the firm when they practice third-degree price discrimination? Part (f): How much…Consider a market for cars with just one firm. The firm has a linear cost functionC(q) = 2q. The market inverse demand function is P(Q) = 9 − Q, where Q is thetotal quantity produced. Since initially there is just one firm, q = Q.(a) Set up the maximisation problem for the monopolist and determine the optimalprice and quantity of cars produced. How much profit does the firm make?A monopolist's inverse demand function is estimated as P= 400 - 2Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC₁(Q1) = 7Q₁, 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 Q₁ + Q₂ = Q.) MR(Q) = 400 $ 7Q₁- b. Determine the profit-maximizing level of output for each facility. Instructions: Round your response to two decimal places. Output for facility 1: 14 Output for facility 2: 50 c. Determine the profit-maximizing price. Instructions: Round your response to the nearest penny (two decimal places). 272 x 4 Q2
- The demand function for a monopolist is given by: P1 = 1,250 – 3.5Q and the cost function is given by C(Q) = 1,200 +1.5Q + 0.8Q. This firm, Otsuka, is a pharmaceutical holding a patent on a depression treatment, Rexulti. However, the patent expired, and a generic treatment is offered in the market. Now, the new market price is P=$400. Based on this information, determine the following: (Use no decimals in final answers). %3D a. The optimal Q with the pattent is: $ b. The optimal P with the pattent is: $ c. The optimal profits with the pattent is: $ d. The optimal Q with the generic treatment is: $ e. The optimal P with the generic treatment is: $ f. The optimal profits with the generic treatment is: $ g. In this which of the statement is correct? (A, B, C, or D). A. The lost of the patent changed the market condition from monopoly to oligopoly. B. The lost of the patent changed the market condition from PCM to monopoly. C. The lost of the patent changed the market conditions from…Albert and Johny are the only sellers of Motorbikes in Ireland. The inverse market demand function for motorbikes is P(Y)= 200- 2Y . Both firms have the same total cost function: T(C)= 12Y and the same marginal cost: M(C)=12. Suppose now that the two firms decide to act like a single monopolist. What will the total quantity of Motorbikes sold in the market be and what will the equilibrium price be? Represent the profit maximisation problem on a graph and indicate the price and quantity at the equilibrium. Calculate the total profit made by the two firms when they act like a monopoly. Compare it with the total profit they were making in the Stackelberg oligopoly. For the two firms to be willing to agree to act as a monopoly, how should they split the quantity to produce between them? We assume that if they do not agree to act like a monopoly, then the market structure is the Stackelberg oligopoly studied above. We further assume that no money transfer is possible between the two…A (classic) monopolist faces a demand curve given by Q(P) = 100 – 0.25P and a continuously divisible product in a factory with cost function TC(Q) = 3.5Q^2 + 100Q + 600.a: Calculate the inverse demand curve P(Q), total revenue curve TR(Q), marginal revenue curveMR(Q), and marginal cost curve MC(Q).b: Carefully write out this firm’s profit maximization problem, using the particulars of thisproblem.c: Give the marginal condition (equation) that characterizes the solution to this problem. Solvethis condition for the firm’s optimal quantity Q*.d: Calculate the optimal price.e: Calculate the firm’s maximized profit.f: On a graph with quantity on the horizontal axis, neatly plot the marginal revenue curve andmarginal cost curve. Show Q* on your graph.g: Label areas on your graph using a, b, c, etc. and indicate the areas that correspond to totalrevenue, variable cost, and producer surplus at Q*.h: Calculate the firm’s producer surplus at Q*
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