What is the homogeneous-good dupopoly's Nash-Cournot equilibrium if the market demand function is Q = 300 - 1200p, and each firm's marginal cost is $0.22 per unit?
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What is the homogeneous-good dupopoly's Nash-Cournot equilibrium if the
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- Consider a market for crude oil production. There are two firms in the market. The marginal cost of firm 1 is 20, while that of firm 2 is 20. The marginal cost is assumed to be constant. The inverse demand for crude oil is P(Q)=200-Q, where Q is the total production in the market. These two firms are engaging in Cournot competition. Find the production quantity of firm 1 in Nash equilibrium. If necessary, round off two decimal places and answer up to one decimal place.Two dairy farmers produce milk for a local town with local milk demand given by Q=100-1/3P(P denotes price measured in Rands, Q denotes the quantity measured in liters). Both farmers have the same cost function given by TC=150+2q (where q denotes output). (a) Determine the reaction function of each farmer.(b) Find the Cournot-Nash equilibrium.(c) Calculate profits for each farmerConsider 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?
- Three electricity generating firms are competing in the market with the inverse demand given by P(Q) = 20 – Q. All firms have constant marginal costs. Firm 1’s marginal cost is MC = 5; it has a capacity constraint of K1 = 5 units. Firm 2’s marginal cost is MC = 8; it has a capacity constraint of K2 = 2.5 units. Firm 3’s marginal cost is MC = 10; it has a capacity constraint of K3 = 2.5 units. A. The three firms compete in the style of Cournot. Please compute the Nash equilibrium quantities. Also compute the price in the Nash equilibrium. B. Which of these firms would have produced a larger quantity if it had a larger capacity?Consider a "Betrand price competition model" between two profit maximizing widget producers say A and B. The marginal cost of producing a widget is 4 for each producer. Each widget producer has a capacity constraint to produce only 5 widgets. There are 8 identical individuals who demand 1 widget only, and individuals value each widget at 6. If the firms are maximizing profits, then which of the following statement is true: a) Firm A and Firm B will charge 4 b) Firm A and Firm B will charge 6 c) Firm A and Firm B will charge greater than or equal to 5 d) None of the options are correct. Explain clearly.Consider a market structure comprising two identical firms (A and B), each with the cost function given by: Ci = 30Qi , where Qi for i = {A, B} is output produced by each firm. Market demand is given by: P = 210 − 1.5Q, where Q = QA + QB (i) Find Cournot equilibrium. (ii) What will be the outcome if the firms decide to collude? Compare it with the results under the Cournot equilibrium.
- Consider two firms that produce the same good and compete setting quantities. The firms face a linear demand curve given by P (Q) = 1 − Q, where the Q is the total quantity offered by the firms. The cost function for each of the firms is c(qi) = cqi, where 0 < c < 1 and qi is the quantity offered by the firm i = 1,2. Find the Nash equilibrium output choices of the firms, as well as the total output and the price, and calculate the output and the welfare loss compared to the competitive outcome. How would the answer change if the firms compete setting prices? What can we conclude about the relationship between competition and the number of firms?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?Carl and Simon are the only sellers of pumpkins at the market, where the total demand function for pumpkins is q =3 ,200−1,600p. The total number of pumpkins sold at the market is q = qC + qS, where qC is the number that Carl sells, qS is the number that Simon sells. The cost of producing pumpkins for each farmer is $.50 per pumpkin; the fixed costs are zero. .a. Find the Cournot equilibrium price and quantities. .b. Find the Bertrand equilibrium price and quantities. . .c. Suppose now that every spring the snow thaws off of Carl’s pumpkin field a week before it thaws off of Simon’s. Therefore, Carl can plant his pumpkins one week earlier than Simon while predicting Simon’s choice based on the previous year information. Simon observes Carl’s choice and chooses how much pumpkin to plant. Find the new equilibrium price and quantities. .d. Compare the quantities and prices in parts a, b, and c. Rank these outcomes according to Pareto efficiency.
- Consider two firms that produce the same good and competesetting quantities. The firms face a linear demand curve given by P(Q) =1 − Q, where the Q is the total quantity offered by the firms. The costfunction for each of the firms is c(qi) = cqi, where 0 < c < 1 and qiis the quantity offered by the firm i = 1, 2. Find the Nash equilibriumoutput choices of the firms, as well as the total output and the price, andcalculate the output and the welfare loss compared to the competitiveoutcome. How would the answer change if the firms compete settingprices? What can we conclude about the relationship between competitionand the number of firms?In a Bertrand duopoly with homogenous goods and symmetric and identical constant marginal costfunctions the Nash equilibrium has:.Assume that there are two identical firms serving a market in which the inverse demandfunction is given byP =100-2Q. The marginal costs of each firm are $10 per unit.Calculate the Cournot equilibrium outputs for each firm, the product price, and the profitsof each firm.
