Answered: Suppose that a monopolist faces the…

Suppose that a monopolist faces the market demand Q(p)=200-5p. Then its marginal revenue function MR(q) is? MR(q)-200-10q O MR(q)=40-0.2q MR(q)-40-0.4q MR(q)-200-5q MR(q)-40-5q

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter23: Monopoly

Section23.3: Perfect Competition And Monopoly

Problem 1ST

See similar textbooks

Similar questions

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?
Suppose a nonlinear price discriminating monopolist faces an inverse demand curve: P = 110-Q, and can set three prices depending on the quantity a consumer purchases. The firm's profit is: π = P₁ Q₁ + P₂ (Q₂ −Q₁) + P3 (Q3 − Q₂) - mQ3, where p₁ is the high price charged on the first units Q₁ (first block) and P2 is a lower price charged on the next (Q₂ -Q₁) units and p3 is the lowest price charged on the (Q3 - Q₂) remaining units. Q3 is the total number of units actually purchased, and m = 75 is the firm's constant marginal and average cost. Using calculus, determine the profit-maximizing values for P₁, P2, and p3, and the firm's profits. The profit-maximizing value for (round your answers to the nearest penny) P₁ P₂ = $ P3 = $ The firm's profit is $ 9 and
A monopolist discriminates the price of its product among two groups as follows: Q1 = 100 - p1 (demand of customers in group 1) Q2 = 120 - 0.5p2 (demand of customers in group 2) TC = 2000 + ( Q1 + Q2)2 (total cost of production) a) Find the optimal sales to the first, Q1 * , and to the second, Q2 * , group. b) Find prices to be charged to the first, p1 * , and to the second, p2 * , group. c) Find the profit of this firm. d) Show that the group with more elastic demand gets lower price.
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?
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?
A monopolist's inverse demand function is estimated as P=100-2Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC₁(Q)=4Q₁, and the marginal cost of producing at facility 2 is MC₂(0₂)=202. a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall that Q+Q₂ = Q.) MR(Q)=-91-9₂ b. Determine the profit-maximizing level of output for each facility. Instructions: Round your response to two decimal places. Output for facility 1:[ Output for facility 2:[ c. Determine the profit-maximizing price. Instructions: Round your response to the nearest penny (two decimal places).
Suppose a monopolist has the following cost function C(Q) = 40Q (with marginal cost MC = 40). Suppose it faces market demand of P = 100 - Q.< (a) Sketch market demand, marginal revenues, and marginal costs. Be neat.< (b) What is the monopolist's optimal level of output, price, and profits? Show your work.< (c) What is the deadweight loss (DWL) associated with the monopoly output? Show your work and explain why the DWL arises.< (d) (Cournot Competition) Now suppose we added a second firm that has identical costs to the monopolist. Show that the resulting Cournot Equilibrium has each firm producing output of 60 units. That is, show that, if the other firm sells 60 units, then the best a firm can do is also sell 60 units. (e) What are total profits under Cournot Competition compared to the Monopoly case? Why do they differ? (f) What happens to the deadweight loss under Cournot Competition relative to the Monopoly case? Explain why this happens.<
A monopolist has discovered that the inverse demand function of a person with income Y for the monopolist’s product is P = 0.002Y-Q where P is the price, Y the income, and Q is the output. The monopolist can observe the incomes of its consumers and hence vary its price accordingly. The monopolist has a total cost function C(Q) = 100Q. A. Calculate the profit maximising price as a function of the consumer’s income Y carefully explaining all the steps in the derivation of the formula. B. A monopolist has a constant marginal cost of £2 per unit and no fixed costs. He faces two separate markets in the United States and in the UK. The goods sold in one market are never resold in the other. He sets one price P1 for the US market and another price P2 for the UK market (both measured in £). The demand in the United States is given by Q1=7,000-700P1 and the demand in the UK is given by Q2=1,200-200P1. Calculate the profit maximising output produced and price charged in each country by the…
There is a firm who is monopolist. Suppose that there are 20,000 potential customers with valuations uniformly distributed between £0 and £1000. A customer will purchase the products if her valuation is more than the firm's price. a) How many quantity will the firm sell if it sets a single price of £550? b) Write an equation for the firm's demand curve. c) If marginal cost is £100, what is the profit-maximizing price and quantity? What is consumer surplus and total welfare? Suppose that the firm can perfectly price discriminate. a) What is the profit-maximizing quantity now? b) What is consumer surplus and total welfare
= 240 + 0.5Q², and face 4. A monopolist has the cost function TC(Q) market demand P = 45 – Q. (a) Find the monopoly equilibrium price and output. Find the monopolist's profit.
Suppose a monopolist faces two markets withdemand curves given by D1(p1) = 200 − p1D2(p2) = 100 − 2p2Assume that the monopolist’s cost function is c(y) = y2 1. What is the optimal prices for the monopolist if it can charge different prices in these markets?2. What is the optimal price if the monopolist must charge the same price in each market?3. How much total consumers’ surplus changes between the two separate prices and the sameprice cases?
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. %24