Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by if Q< 400 400-Q, P(Q) {40 " otherwise = 40q1, and firm 2 has a cost function where Q = 91 +92. Firm 1 has a cost function C₁ (91) C2 (92) = 5092. Answer the following questions. =
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- 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”)Suppose that there are only two firms in a market in which demand is given by p = 64 - Q, where Q is the total production of the two firms. Each firm can choose either a low level of output, qL = 15, or a high level of output, qH = 20. The unit cost of production for both firms is $4. Write down the normal-form representation of the game in which the strategic variable for each firm is the quantity of output and the firms make their choices simultaneously. Find the pure strategy Nash equilibrium of this game (quantities produced and market price).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?
- An industry consists of two firms, firm 1 and firm 2. The demand function for the product of each firmsis given by q1 = 720 - 3p1 + 2p2 and q2 = 720 - 3p2 + 2p1. We assume for simplicity that the totalcost of production is zero:TC1 =TC2 =0. a) Are these two products substitutes or complements? Assuming that firms compete over prices, find theprice best-response functions for firm 1 and fin 2. Draw a diagram that shows the BRFs and theequilibrium. Are prices strategic substitutes or complements? Find the Bertrand Nash equilibrium inprices and outputs. Obtain the profits of each firm. b) Show that the duopolists have incentives to collude. Find their joint profit-maximizing price, output, andprofit: find each firm's price. output and protit. Is collusion a Nash equilibrium? If not, what is the optimaldefection for each firm? Show this game in a 2X2 matrix form. What does this imply about the Nashequilibrium or the stability of their collusive agreement? Is it a Prisoner's Dilemma…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.The total cost for a product-testing firm is C(q)=70 + 20q2 q= number of products tested Price of a product = average cost Each corporation purchases one product test per year from a product-testing firm in the same city. All other inputs are ubiquitous. Suppose five corporations are initially distributed uniformly, with one corporation in each city (A,B,C,D,E). Is the initial distribution a Nash Equilibrium? Demonstrate it is not by finding how much one corporation would pay if they deviate and move to another city? What is the average price of having two tests conducted? (Which is the price that the corporation would pay if they "live" in a city where two tests are conducted) The average price of moving and thus, having two tests is: $_____
- Suppose that there are two firms producing a homogenous product and let the market demand besiven by Q(P) = 120 -P/2 . For simplicity assume that each fir operates with zero total cost. a) Assuming that firms compete over quantities, find the price best-response functions of firms 1 and2. Draw a diagram that shows the BRFs and the equilibrium, Are outputs strategic substitutes orcomplements? Find each firm's Cournot equilibrium output, price, profit, and total surplus. DefineNash equilibrium and argue that it is indeed a Nash equilibrium. b) Show that the duopolists have incentives to collude, Find their joint profit-maximizing price, output,and profit: find each firm's output and profit. Is collusion a Nash equilibrium? If not, what is theoptimal defection for each firm? Show this game in a 2X2 matrix form. What does this imply aboutthe Nash equilibrium or the stability of their collusive agreement? Is it a Prisoner's Dilemma Type? c) Suppose now that fims play the above game in…Which of the following is true for Firm 1? Peach strictly dominates Apple. Banana strictly dominates Apple. Banana strictly dominates Grapes. Grapes strictly dominates Apple. Which of the following is true for Firm 2? Blue strictly dominates Purple. Green strictly dominates Blue. Green strictly dominates Pink. Pink strictly dominates Blue. Which of the following is the IEDS (Iterated Elimination of Dominated Strategies) outcome of the game? (Apple, Pink) (Banana, Green) (Peach, Pink) (Banana, Pink) True or False: The outcome (Peach, Pink) is Pareto Efficient. True or False: (Banana, Purple) is a Nash Equilibrium.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?
- Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedulein this market is: p Qd180 150155 175130 200Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever itneeds to be to sell the total output in the market.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your workdetermining the profits in each box in the matrix.(b) Determine the Nash equilibrium of this game.(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreementbe?(d) Explain how the government might respond to such an agreement and why.Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedulein this market is:p Qd180 150155 175130 200Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever itneeds to be to sell the total output in the market.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your workdetermining the profits in each box in the matrix.(b) Determine the Nash equilibrium of this game.(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreementbe?(d) Explain how the government might respond to such an agreement and whyGiven that If Alfonso's marginal cost is $6, their best-response function is, Pa=(Pb+30)/2 and If Bernice’s marginal cost is $12, their best-response function is, Pb=(Pa+36)/2, Find the equilibrium prices for the case in which Alfonso's marginal cost is $6 and Bernice's marginal cost is $12.