Firm 1 and Firm 2 are Stackelberg competitors. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions: Firm 1: C₁(Q1) = 4Q1 Firm 2: C₂(Q2) = 4Q2 The market demand is QD=42-0.5P
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- QUESTION 7 Firm 1 and Firm 2 are Stackelberg competitors. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions: Firm 1: C₁(Q1) = 4Q1 Firm 2: C2(Q2) = 4Q2 The market demand is QD = 46-0.5P Compute the SPE of this game. In equilibrium, Firm 1 produces Q₁= ✓, Firm 2 produces Q2= ✓, and the price is P=Suppose that Firm 1 and Firm 2 are Stackelberg competitors in the market for popsicles. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions such that MC = 4. Market demand for popsicles is given by QD = 38 – 0.5P. Use this information to answer questions #1 and #2. 1. How many popsicles will Firm 1 produce in the SPE of this game? a. 91 6 b. q1 = 9 12 91 d. 91 с. 18 e. q1 = 36 %3D 2. If these firms were Cournot competitors, then compared to the outcome in #1 (Hint: No calculations necessary.) a. Firm 1 would earn more profit, and Firm 2 would earn less profit. b. Firm 1 would earn less profit, and firm 2 would earn more profit. c. Both firms would earn less profit. d. Both firms would earn more profit. The firms' profits would be the same, but industry-wide profit would be lower.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?
- 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 questionIn a given market the demand for a homogenous product is given by p(q) = 120 – 5Q. The market has two firms, firm 1 has a marginal cost cı 5 and firm 2 has a marginal cost c2 = : 10. (i) Assume that the firms compete in a Cournot game. Compute the price in equilibrium, quantity produced by each firm and deadweight loss generated in this market.1. 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.
- The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has a cost of production of C1= 15*Q1 and firm 2 has a cost of production of C2=20*Q2 a) Suppose that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantityfirm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What arethe profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?Suppose two Bertrand competitors, F1 and F2, make identical products for a market with inverse demand P = 600 – 0.5Q. Both firms have the same costs Ci = 20qi, and each firm has sufficient capacity to supply the entire market. a. What prices will the firms choose? How much might each produce and what profit would they make? Is the result a Nash equilibrium? Explain. b. Suppose F1 improves its efficiency, reducing its cost to C1 = 16q1. What will happen in this market? Explain. c. Assume now that the firms have their original identical costs, but that F1 has only 100 units of capacity and F2 has only 200 units of capacity. What prices will the firms choose now? Explain why neither firm will want to decrease its price at the equilibrium you identify. Why would neither firm want to increase its price? Prove this for F1.QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)
- Consider 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?1. Consider two firms producing hats, A and B. The demand functions are as follows: qĄ(Pa, PB) = 592 – 8pA + 4pB and qB (PA, PB) = 400 – 8pg + 4pA Firm 1 has constant marginal cost c prices, i.e. the game's joint strategy space is {(pa, PB) E R² | Pa > 0,Pp > 0}. 10 per hat and firm 2 has c2 = 7. The firms decide on 1.1. What is the nature of the relationship between the hats produced by A and the hats produced by B? [No calculations required.] 1.2. Write down payoff functions for the two firms. 1.3. Derive best-response functions for the two firms.2 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)?
