and for Firm 2 is P₂ = 100-92-0.5q₁. marginal cost of m= $1 per unit. Solve for the Nash-Cournot equilibrium quantities. ilibrium quantities are Onses rounded to two decimal places.) 91 = 92 units units.
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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 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. possibiWhat is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q= 1,800 - 1,000p. and each firm's marginal cost is $0.28 per unit? The Cournot-Nash equilibrium occurs where q, equals and 92 equals (Enter numenic responses using real numbers rounded to two decimai places.) Furthermore, the equilibrium occurs at a price of $ (Round your answer to the nearest penny.)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 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.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 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 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 AThe 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=$_______________
- If firm 1 and firm 2 are the oligopolistic firms in bottled spring water production in Nomansland. The market demand is given by ? = 5000 −20?, Qd is the number of kilolitres demanded per month while P is the price of kilolitres of bottled water. The marginal cost of a kilolitre of bottled water is R10.How do I Find the Cournot equilibrium quantities and price? and how do I Find the Cournot profits and the monopolist profits?Suppose that identical duopoly firms have constant marginal costs of $20 per unit. Firm 1 faces a 110-2p1 + P2, where q1 is Firm 1's output, p1 is Firm 1's price, and p2 is Firm 2's price. Similarly, the demand Firm 2 faces is 92 110-2p2 + p1. What is Firm 1's profit demand function of 9₁ under the Nash-Bertrand equilibrium, assuming no fixed costs? = =1 Consider a duopoly with firm 1 and firm 2. Their cost functions are 2q₁ and cq2, respectively, where 2 < c < 10. The market demand function is p=10-Q, where Q=q₁+9₂. (a) Assume that the two firms play the Bertrand price game. Find the firms' price choices in the Bertrand equilibrium. (b) Assume that the two firms play the Cournot quantity game. Find the firms' quantity choices in the Cournot equilibrium.