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Consider a Cournot Duopoly model. The inverse demand for their products is given by
P = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given by
TCi = 2Qi, for i = 1, 2.
(a) In the Cournot model, what does each firm choose?
(b) What is the timing of each firm’s decision?
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could you show the work for solving (1) and (2) in part A at the end?
- Consider a Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given byT Ci = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?(c) Find the Nash equilibrium quantities (Q∗1, Q∗2)?(d) What is the equilibrium price? Just help with c and d here pleaseSuppose we have the "classic" Cournot duopoly model, with a linear demand curve P = a - bQ And two firms which are identical, each with total costs TC(q) = c + dq. (a) What is the market price in the Cournot equilibrium and what profit is earned by an individual firm?(b) Compare individual quantity, market quantity, market price, individual profits and consumer surplus ( show it in a graph) to the outcomes of this market were a monopoly. Comment on your results. Show all the steps of the calculationIn a Cournot duopoly model, the market demand curve is given by P 100 - yI - y2- !! where y, is the amount of output firm 1 produces and y2 is firm 2's level of output. The cost function of firm 1 is c(y1) 75 +8y1. The cost function of firm 2 is c(y2) = 100 +12y2. %3D The reaction function of firm 1 is y1 = -0.5y2- The reaction function of firm 2 is y2 = -0.5y1- In the Cournot equilibrium, firm 2 produces units of output and makes a producer surplus of $
- Consider a Cournot Oligopoly. One firm has costs C1(Q1) = 12Q1 while the other firm’s cost function is C2(Q2) = 10Q2. The demand for both firms’ products Q=Q1 +Q2 isQD(P)=200−2P. (a) Determine the equilibrium price P, the market shares s1, s2, and the quantities Q1, Q2 produced by both firms. (b) Suppose more firms with the lower cost technology, i.e., with cost function Ci(Qi) = 10Qi enter the market. How many firms with this technology must be in the market such that firm 1’s profit becomes negative. In other words, suppose there is one firm with the high costs, and n firms with the low costs. At what level n will profits of the high-cost firm be negative?Consider two firms that compete according to the Cournot model. Inverse demand is P (Q) = 16 − Q. Their cost functions are C (q1) = 2q1 and C (q2) = 6q2 (a) Solve for Nash equilibrium quantities of each firm (b) Suppose firm 2 becomes more inefficient and its cost function changes to C (q2) = xq2 where x > 6. How large must x be to cause firm 2 to not want to produce anything in equilibrium?Consider a Duopoly model, in which two firms decide a quantity sequentially. For the convenience, let's say Firm 1 is a dominant firm and Firm 2 is a follower. The market demand is given by P=110 - 5Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=7Qi, i=1, 2. Each firm maximizes its profit by choosing the quantity. In this Stackelberg equilibrium, Firm 1 will sell how many units.
- Consider a Duopoly model, in which two firms decide a quantity sequentially. For the convenience, let's say Firm 1 is a dominant firm and Firm 2 is a follower. The market demand is given by P=110 - 5Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=7Qi, i=1, 2. Each firm maximizes its profit by choosing the quantity. In this Stackelberg equilibrium, Firm 1 will sell __________ units.Consider Firm A and Firm B, each with cost functions C(qA) = 5qA, and C(qB) = 5qB, The inverse market demand is given by p = 30 − Q, where Q = qA + qB represents the total quantity demanded in the market. a) Suppose the firms compete in a Cournot oligopoly model. What are the quantities supplied by each firm and their profits? b) Now let Firm A be the first-mover. If the firms compete in a Stackelberg oligopoly model, what are the quantities supplied by each firm and their profits? c) How can you interpret the difference in profits between parts (a) and (b)? In other words, if you were Firm A, which scenario would you prefer, and what might this say in general?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)
- 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.The marginal cost of a product is fixed at MC = 20. The demand for the product is Q = 100 - 2P. (a) Now consider a Cournot model with two firms that are choosing quantities simultaneously. What is the best reply (best response) function for each firm? What is theNash equilibrium? What is the total surplus? (b)What do you expect the total surplus would be with three firms? Why? (You do not need to calculate an exact value. You can say ”total surplus is at least 100”, or ”total surplus is at most 80”)Two 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?