The firms in a duopoly produce differentiated products. The inverse demand for Firm 1 is P₁ = 82-9₁-0.592 The inverse demand for Firm 2 is P₂=40-92-0.591-
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- The firms in a duopoly produce differentiated products. The inverse demand for Firm 1 is The inverse demand for Firm 2 is and P₁ = 52-9₁-0.592. Each firm has a marginal cost of m= $1 per unit. Solve for the Nash-Cournot equilibrium quantities. The Cournot equilibrium quantities are (Enter your responses rounded to two decimal places.) P₂ = 100-92-0.5q1₁. 91 = units 92 units. =The firms in a duopoly produce differentiated products. The inverse demand for Firm 1 is The inverse demand for Firm 2 is P₂=70-02-0.501- Each firm has a marginal cost of m=$1 per unit. Solve for the Nash-Coumot equilibrium quantities. The Cournot equilibrium quantities are and P₁-52-91-0.592 (Enter your responses rounded to two decimal places.) 4₁ = units 92 units. possibiConsider a duopolistic market in which the two identical firms compete by selecting their quantities. The inverse market demand is P(Q) = 210−Q and each firm has a marginal cost of $15 per unit. Assume that fixed costs are negligible for both firms. Cournot Model Determine the Nash-Cournot equilibrium for this market.(Enter your responses rounded to two decimal places.) Firm 1's quantity: q1= ? units. Firm 2's quantity: q2 = ? units. Market price: P= ? Stackelberg Model Determine the Nash-Stackelberg equilibrium for this market, assuming that Firm 1 is the Stackelberg leader. (Enter your responses rounded to two decimal places.) Firm 1's quantity: q1 = ? units Firm 2s quantity: q2 = ? units. Market price: P = ?
- 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.Suppose that two firms produce mountain spring water and the market demand for mountain spring water is given as follows: P = 125 - 91 - 92 Firm 1 and Firm 2 have a MC = 5 a) Find the Cournot-Nash equilibrium price and quantity of each firm. b) Assume now that firm 1 becomes the Stackelberg leader. What will be the market price, output by each firm? Compared to part a, who gains? c) If Firm 1 chooses a quantity, then Firm 2 chooses a quantity (having observed Firm 1's quantity), then Firm 1 has an opportunity to revise its quantity (having observed Firm 2's quantity), then payoffs are determined, does either firm stand to gain relative to the case of simultaneous quantity choice? Why or why not? (hint: there is no need to do any calculation here)Duopoly and menu costs. (This is adapted from CaminaI 1987.) Consider two firms producing imperfect substitutes. Both firms can produce at zero marginal cost. The demand for the good produced by firm i is given by Now suppose that both firms enter the period with price p., which is the Nash equilibrium price for some value of a, a·. They know b and c. They each observe the value of a for the period, and each firm must independently quote a price for the period. If it wants to quote a price different from p*, it must pay a cost k. Otherwise, it pays nothing. Once prices are quoted, demand is allocated, demand determines produdion, and profits are realized. (b) Compute the set of values of a (around a*) for which not to adjust prices is a Nash equilibrium. (c) Compute the set of values of a (around a*) for which to adjust prices is a Nash equilibrium. (d) Check that all equilibria are symmetric and therefore that there are no other equilibria than the ones computed above.…
- Consider a Cournot duopoly with the inverse demand P = 200−2Q. Firm 1 and 2 compete by simultaneously choosing their quantities. Both firms have constant marginal and average cost MC = AC = 20. A) Find each firm’s best response function. Plot the best response functions (label the x-axes as ?1 and y-axes as ?2 ). B) Find the Cournot-Nash equilibrium quantities, profits and market price. Illustrate the equilibrium point on your graph in part ADuopoly quantity-setting firms face the market demand p= 90 -Q. Each firm has a marginal cost of $15 per unit. What is the Cournot equilibrium? The Cournot equilibrium quantities for Firm 1 (9,) and Firm 2 (42) are 91 units and units. (Enter numeric responses using real numbers rounded to two decimal places.) The Cournot equilibrium price is What is the Stackelberg equilibrium when Firm 1 moves first? The Stackelberg equilibrium quantities when Firm 1 moves first are 91 = units and 92 = units. %3D The Stackelberg equilibrium price isConsider 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 firms produce and sell differentiated products that are substitutes for each other. Their demand curves are Firm 1: Q, = 40 - 3P,+ P2 Firm 2: Q, = 40 - 3P2+ P, Both firms have constant marginal costs of $3.10 per unit. Both firms set their own price and take their competitor's price as fixed. Use the Nash equilibrium concept to determine the equilibrium set of prices. Since the firms are identical, they will set the same prices and produce the same quantities. In equilibrium, each firm will charge a price of $ and produce units of output. (Enter your responses rounded to two decimal places.)Consider a Cournot duopoly with the inverse demand P = 200 − 2Q. Firm 1 and 2 compete by simultaneously choosing their quantities. Both firms have constant marginal and average cost MC = AC = 20. A) Find each firm’s best response function. Plot the best response functions (label the x-axes as ?1 and y-axes as ?2 ). B) Find the Cournot-Nash equilibrium quantities, profits and market price. Illustrate the equilibrium point on your graph in part (A). C) Suppose instead that firm 1 had MC = AC = 20, but firm 2’s MC = 8. What is the Cournot-Nash equilibrium outputs and profits now? How would this affect your answers to part (B)? ExplainExercise 6.7. Suppose two identical companies produce wood stoves and they are the only ones on the market. Its costs are given by: C1 (q1 )=200q1 and C2 (q2) = 200q2. And the inverse market demand curve is: P=2000-2Q, where Q =q1 + q2 Get the Cournot-Nash equilibrium. Calculate the profits of each company. Show graphically. Suppose that the two companies form a cartel to maximize joint profits. How many stoves will you produce? Calculate the profits of each company. Represent graphically. Managers now note that explicit agreements to collude are illegal. Each company must decide on its own whether to produce the amount of Cournot or that of the cartel.
