1) Obtain the reaction function of the first firm. (2) Find the equilibrium (output and profit of each firm) when two firms simultaneously compete
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There are two firms in the market (duopoly). These two firms are competing
simultaneously. The first firm chooses its output level (x) by predicting the second firm’s
output (y). Let c denote the total cost function c(x) = x and c(y) = y. Also, let’s assume
that the inverse demand function is p(Y) = 7 - Y where Y = x + y. (1) Obtain the reaction
function of the first firm. (2) Find the equilibrium (output and profit of each firm) when
two firms simultaneously compete
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- Problem 3. Consider the following game with three firms. First, firms 1 and 2 si- multancously choose quantities q1 and q2 respectively. After observing firm 1 and 2's quantities, firm 3 chooses its quantity q3. There is no production cost and the inverse demand function is p= 12 – (91 +2 + 93). (a) Compute the SPNE of this game. (b) Give an example of Nash equilibrium s* with s = 4 and s, = 6 , that is not subgame perfect. game theory question1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.Two firms simultaneously decide whether or not to enter a market, and if yes, when to enter a market. The market lasts for 3 periods: starting in period 1 and ending in period 3. A firm that chooses to enter can enter in any of the three periods. Once a firm enters the market in any period it has to stay in the market through period 3. In any period t that the the firm is not in the market, it earns a zero profit. In any period t, if a firm is a monopolist in the market, it makes the profit 10t–24. In any period t if a firm is a duopolist in the market it makes a profit of 71-24. A firm's payoff in the game is the total profit it earns in all the periods it is in the market, or zero if it never enters the market. Is there a Nash equilibrium in which both firms enter the market?
- Consider 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.Consider the following Cournot game with two firms i = 1, 2. The demand function is P(Q) = 100 − Q, with Q = q1 + q2. The production costs for firm i are: C(qi) = 400 + 2qi . Find the nash equilibrium of this game. plz answer correct calculatuon asap plz dont answer by peparConsider a Stackelberg duopoly:There are two firms in an industry with demand Q = 1 − Pd.The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF.Suppose now that the cost function is Ci(qi) = qi2 for i = L, F. (a) Find the subgame perfect equilibrium. (b) Compare the equilibrium you found with the Nash equilibrium if the game was simultaneous (i.e., Cournot competition). Is the Nash equilibrium of the Cournot game also a Nash equilibrium of the sequential game? Why or why not?
- Consider a duopoly market, where two firms sell differentiated prod- ucts, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices pi and p2 simultaneously. The derived demand functions for the two firms are: D1 (p1, P2) and D2 (p1, P2) = + 2, where S > 0 and the parameter t > 0 을 + S + P2-P1 2t 2t measures the degree of product differentiation. Both firms have constant marginal cost c > 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profits of the two firms.Consider Hotelling's model (a street of length one, consumers uniformly distributed along the street, each consumer has a transportation cost equal to 2t, where t is the distance traveled). Suppose there are two gas stations, one located at 1/4 and the other located at 1. (a) Calculate the demand functions for the two firms. (b) If the two gas stations compete in prices and settle at a Nash equilibrium, will they charge the same price for gasoline? (assume that production costs are zero, that is, firms maximize revenue).The market demand function is Each firm has a marginal cost of m = $0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. The Stackelberg-Nash equilibrium quantities are The Stackelberg-Nash equilibrium price is Profits for the firms are and 92 p = $ π2 $ = Q=7,000 1,000p. 91 and units units. (Enter your responses as whole numbers.) (Enter your response rounded to two decimal places.) π₁ = $ (Enter your responses rounded to two decimal places.)
- 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 please2 firms are engaged in Cournot competition; firm A faces the cost curveCA(yA)=40yAand firm Bfaces the cost curveCB(yB)=40yB. The inverse market demand curve isP(y)=100y, whereyrepresents market level of output. a)Define the Cournot game. b)In 1 or 2 sentences explain why a firm has no incentive to deviate from the Cournot Nash equilibrium(holding their opponent’s strategy constant). c)Find the Cournot Nash Equilibrium. d)Now suppose instead of playing their strategies at the same time, firm A moves first and then firm B moves second(sequentialgame).Does firm A earn higher profits in this game or the game in part c)?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. Now consider a modified game, which goes as follows: First, Firm 1 decides whether to enter the market or not. As in the previous question, there is no fixed cost, even if the firm decides to enter. Next, Firm 2 observes Firm 1’s entry choice and decides whether to enter or not.Firm 2 has no fixed cost as well. If no firm enters, the game ends. If only one firm enters, that firm chooses quantity, operating as a monopolist. If both firms enter, then Firm 1 chooses quantity q1. Then, Firm 2 observes Firm 1’s choice of q1 and then chooses q2 (like in the previous question). If a firm does not enter, it gets a payoff of zero. Which of the following statements is consistent with the SPNE of this game? Hint: you don’t need complicated math to solve this problem.(a) Neither firm…