1. Consider a price competition with differentiated products with N = {D, H} and pi € S₁ = [0, +∞) for each i N. Let firm i's demand be D; (pi, Pj) 100 - 2p; + p; and firm i's cost function be C; (qi) = c;q; such that cp = 10 and CH = 30. Find a Nash equilibrium of this game. =
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- Consider the following game. Firm 1, the leader, selects an output ?1, after which firm 2, the follower, observes the choice of ?1 and then selects its own output ?2. The resulting price is one satisfying the industry demand curve ? = 200 − ?. Both firms have zero fixed costs and a constant marginal cost of 60. Determine the equilibrium output of each firm in the leader-follower game. What are firm 1’s profits in the equilibrium?(Cournot competition with different marginal costs) Our best estimate for total marketdemand in a given market is P 1000-2Q. Two firms (1 and 2) are competing in this market in quantities, choosing Q1 and Q2 simultaneously. Firm 1 has marginalcost equal to c1 = 100 and Firm 2 produces at marginal cost c2 = 200. (a) Write down the profits of both firms and and their best response functions. (b) Find the Cournot - Nash equilibrium in quantities, and calculate equilibrium profits for both firms. (c) Suppose that each firm has the option, at a previous stage, to invest in an R&D project that will reduce its marginal cost of production by 50% if successful. What is the value of this innovation to each firm? Given that R&D costs and successprobabilities are equal, which one has greater incentives to invest in R&D ? You can think in terms of per - period profits to set aside timing issues.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…
- 1. Consider an industry with inverse demand given by p = 8 – q, where p is the price, and q is the quantity. There is one incumbent firm and one potential entrant. In the first stage of the game, the incumbent chooses its quantity qi. In the second stage, the potential entrant observes qi and chooses its quantity Ce. The potential entrant can also decide not to enter the market. The production technology of both firms are represented by the cost function C = 2q. To enter industry implies a fixed entry cost of F. (a) Find the equilibrium of the game, assuming that the potential entrant enters the industry. What are the profits of firms? (b) Assume that entry is not blockaded. For which values of F does the incumbent firm prefer to deter entry? (c) For which values of F, entry blockaded?Three firms compete in the style of Cournot. All firms have a constant returns to scale technology: There are no fixed cost and each firm's marginal cost is constant. The market demand is given by Q(P) = 9 - P. Firm 1's marginal cost is MC1 = 1, firm 2's marginal cost is MC2 = 2. Let MC3 be the marginal cost of Firm 3. Which of the below is a necessary condition so that q > 0 for all three firms in a Nash equilibrium? a. MC3 < 1 b. MC3 < 4 c. MC3 < 3 d. MC3 > 1 e. MC3 < 2consider 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 = 7
- The market demand function is Q=10,000-1,000p. Each firm has a marginal cost of m=$0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. Compare your solution to the Cournot-Nash equilibrium. The Stackelberg-Nash equilibrium quantities are: q1=___________ units and q2=____________units The Stackelberg-Nash equilibrium price is: p=$_____________ Profits for the firms are profit1=$_______________ and profit2=$_______________ The Cournot-Nash equilibrium quantities are: q1=______________units and q2=______________units The Cournot-Nash equilibrium price is: p=$______________ Profits for the firms are profit1=$_____________ and profit2=$_______________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?Title 1. Two firms have costs of AC 1 = MC 1 = 20 and AC 2 = MC 2 = 16 respectively. Market demand is Q =. Description 1. Two firms have costs of AC1 = MC1 = 20 and AC2 = MC2 = 16 respectively. Market demand is Q = 1000 − 40P. a. Suppose irms practice Bertrand competition, that is, setting prices for their identical products simultaneously. Compute the Nash equilibrium prices. (To avoid technical problems in this question, assume that if irms both have the same price, then the low-cost irm makes all the sales.) b. Compute irm output, irm proit and market output. c. Is total welfare maximised in the Nash equilibrium? If not, suggest an outcome that would maximise total welfare, and compute the deadweight loss in the Nash equilibrium compared with your outcome.
- Consider the following model of Cournot competition with fixed cost. There are two identical firms, and the inverse demand function is given byP(q1,q2) = 19−(q1 +q2). Firms have constant marginal cost, but any firm operating in this market (that is, qi > 0) must pay a license fee F . In particular, firm i’s cost function is ( attached below ) a) Derive the firms’ best response functions. (b) For what values of F, if any, will there be a symmetric (pure) Nash equilibrium in which firms produce a positive quantity? What is the Nash equilibrium in that case? (c) For what values of F, if any, will both firms shutting down be the symmetric (pure) Nash equilibrium?Consider the payoff matrix below representing two firms engaged in Bertrand Competition. Firm A is player 1 and Firm B is player 2. High price Low price High price 10, 12 -1, 13 Low price 12, 2 0, 3 What is Firm A's dominant strategy? Question 14Answer a. High price b. Low price c. Firm A does not have a dominant strategyPlease no written by hand 1. Suppose the automobile manufacturing industry has two firms, General Motors and Ford. Assume that the market demand function is Q = 1,000 − p, and each firm’s marginal cost and average cost are $40. a. What is the marginal revenue for General Motors? Assume, ??? represent residual demand for General Motors and ?? represents residual demand for Ford. b. What is the best response function for General Motors and Ford? c. What is the Nash-Cournot equilibrium in this market? d. Graph the best response curves for both General Motors and Ford, placing the quantity produced by General Motors (???) in the x-axis. Label intercepts and Nash-Cournot equilibrium.
