Consider the price function y²-5Y+26, 0≤Y ≤ 10 Y≥ 10 P(Y) = where y₁ denotes the output of firm 1 and y2 denotes the output of firm 2 such that Y = y₁ + y2. Suppose that the total cost to each firm is given by TC;(yi) = 2y; for i = 1, 2. Use Cournot's Duopoly Model to find outputs y₁ and y2, profits ₁ and 72, and price P.
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- Consider the Cournot competition between two firms with different marginal costs. For firm 1, let the cost function be: C1(q1)-3*q1 For firm 2, let the cost function be: C2(q2)-6*q2 The inverse demand function is: P(Q)=12-Q, where Q=q1+q2 In this game, write down the profit functions for firm 1 and firm 2 (as functions of q1 and q2). Then, find the Nash equilibrium quantities for firm 1 and firm 2. In the NE, which firm produces more: the one with the low or the high marginal cost? Note: To get credit, you need to show your calculations and explain your answer.consider a market with inverse demand P(Q) = 10 − Q and two firms with cost curves C1(q1) = 2q1 and C2(q2) = 2q2 (that is, they have the same marginal costs and no fixed costs). They compete by choosing quantities. Suppose that Firm 1 chooses quantity first and is able to credibly commit to this choice. Then firm 2 choose its quantity after observing firm 1’s quantity. In the SPNE of this game, what is the price faced by consumers?- p = 3- p = 4- p = 5- p = 6- p = 7Two firms sells an identical product. The demand function for each firm is given: Q = 20 - P, where Q = q1 + q2 is the market demand and P is the price. The cost function for reach firm is given: TCi = 10 + 2qi for i = 1, 2. a) If these two firms collude and they want to maximize their combined profit, how much are the market equilibrium quantity and price? b) If these two firms decide their production simultaneously, how much does each firm produce? What is the market equilibrium price? c) If Firm 1 is a leader who decides the production level first and Firm 2 is a follower, how much does each firm produce? What is the market equilibrium price?
- The inverse market demand curve for salmon is given by P(Y) = 100 – 2Y, and the total cost function for any firm in the industry is given by TC(y) = 4y. a. Suppose that two Cournot firms operated in the market. What would be the reaction function for Firm 1 and the reaction function of Firm 2? (Notes: The marginal cost is not zero). If the firms were operating at the Cournot equilibrium point, what would the industry output and price be? b. For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graphConsider a market that only includes two large firms. The (inverse) market demand is P = 100 – Q. 3q2. Firm 1 has a cost function of C, = 2q1, and firm 2 has a cost function of C2 Use a Cournot model to calculate the Nash equilibrium outputs q, and q2 of the two firms. and 92 (a) Give each firm's profit as a function of (b) Compute the Nash equilibrium q, and q2.Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively is
- Suppose we have two identical firms A and B, selling identical products. They are the only firms in the market and compete by choosing quantities at the same time. The Market demand curve is given by P=477-Q. The only cost is a constant marginal cost of $16. Suppose Firm A produces a quantity of 66 and Firm B produces a quantity of 49. If Firm A decides to increase its quantity by 1 unit while Firm B continues to produce the same 49 units, what is the Marginal Revenue for Firm A from this extra unit? Enter a number only, no $ sign. Don't forget to include the negative sign if revenue decreases.In the domestic airline market, where companies compete on the number of seats they make available in the market measured in millions (x), the inverse of the demand for seats is pd(x) = 40 - 4x.Assume that there are 2 airlines: LON and Pacific Airlines. The marginal cost per seat of both airlines is 10:(a) Determine the market equilibrium (quantity produced by each firm, market price and profits). Graph(b) Assume that LON and Aerolineas del Pacifico collude and act as a monopoly. Calculate the number of seats (x) and the selling price.(c) What is the efficient number of seats that should be made available to consumers, and at what price would each seat be sold?Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 - Q where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2’s marginal cost to $15. Firm 1’s marginal cost remains constant at zero. TRUE-FALSE: Is the following statement true of false? ”As a result, the market price will rise to the monopoly level.” Solve for the Cournot equilibrium and write a convincing explanation of your answer.
- There are two firms that are producing identical goods in a market characterized by the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1's and Firm 2's output, q₁+q2. Each firm's marginal cost is constant at 12, and fixed cost are 0. Answer the following question, assuming that the firms are Cournot competitors. a. Calculate each firm's reaction function and illustrate them graphically (15 points) b. How much output does each firm produce? (12.5 points) c. What is the market price? (7.5 points) d. How much profit does each firm earn? What is the industry profit? (10 points)suppose there are two firms that compete in prices, say firms 1 and 2, but that the firms produce differentiated products. Suppose that the demand for firm 1 is q1(p1,p2)=10-2p1+p2 and the demand for firm 2 is q2(p2,p1)=10-2p2+p1. Also, assume that firm 1 has a constant marginal cost of c1 = 2 and firm 2 has a constant marginal cost of c2 = 3. i. Solve for the Bertrand equilibrium in prices. ii. Now, suppose firms 1 and 2 merge and firm 1 will operate both firms and they will split the resulting profits equally. Will both firms agree to this merger or do they prefer the Bertrand outcome?What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q=4,000-1,000p, and Firm l's and Firm 2's variable cost functions are V (q1) = 0.22qlandV (q2) = 0.22q2 , respectively. Select one alternative: Both firms produce 1300 units of outpuit. Both firms produce 1280 units of output. Both firms produce 1240 units of output. Both firms produce 1260 units of output.