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Consider a Bertrand duopoly. Market
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- Consider a Bertrand duopoly where market demand is P(Q)=107-5Q. Each firm faces a marginal cost $18 and no fixed cost. what is one market price that can occur in a Nash equilibrium?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?Consider a Bertrand duopoly where market demand is P(Q)=5-9Q. Each firm faces a marginal cost $2 and no fixed cost. How much is the dead weight loss in a Nash equilibrium?
- Consider a duopoly where firms compete in prices and firms do not have any capacity constraints. Market demand is P(Q)=45-4Q, and each firm faces a marginal cost of $9 per unit. How much is each firm's total variable cost if firms equally divide the market at Nash 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?Consider a Cournot duopoly. The market demand function is P = 180 – 2(q₂ + q₂), where P is the market price, q₂ is the output produced by Firm 1 and q₂ is the output produced by Firm 2. The two firms have a constant marginal cost c = 30. What is the total output in this market? Round your answer to the nearest integer (e.g. 50)
- Two firms - firm 1 and firm 2 - share a market for a specific product. Both have zero marginal cost. They compete in the manner of Bertrand and the market demand for the product is given by: q = 20 − min{p1, p2}. 1. What are the equilibrium prices and profits? 2. Suppose the two firms have signed a collusion contract, that is, they agree to set the same price and share the market equally. What is the price they would set and what would be their profits? For the following parts, suppose the Bertrand game is played for infinitely many times with discount factor for both firms δ ∈ [0, 1). 3. Let both players adopt the following strategy: start with collusion; maintain the collusive price as long as no one has ever deviated before; otherwise set the Bertrand price. What is the minimum value of δ for which this is a SPNE. 4. Suppose the policy maker has imposed a price floor p = 4, that is, neither firm is allowed to set a price below $4. How does your answer to part 3 change? Is it now…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.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.…
- 10Two firms produce differentiated products. The demand for each firm’s product is as follows: Demand for Firm 1: q1 = 20 – 2p1 + p2 Demand for Firm 2: q2 = 20 – 2p2 + p1 Both firms have the same cost function: c(q) = 5q. Firms compete by simultaneously and independently choosing their prices and then supplying enough to meet the demand they receive. Please compute the Nash equilibrium prices for these firms.Consider 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?Consider the following oligopolistic market. In the first stage, Firm 1 chooses quantity q. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose q2 and q1, respectively. Market demand is given by p(O) = 100 – Q, and Q = q1 + 42 + 41. Firm 1's costs are c, (41) = 34, firm 2's costs are cz(4,) = 34; and firm 3's costs are cs(qs) = 3q,. Starting from the end of the game, you can express Firm 2's best response function in terms of q and q3, and you can similarly express Firm 3's best response function in terms of qi and q2. Using these, answer the following questions. a) If Firm 1 chooses q1 = 9, what quantity will Firm 2 choose? b) If Firm 1 chooses qi = 100, what quantity will Firm 2 choose? c) in the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity? d) In the subgame perfect Nash equilibrium of this game, firm 2 and firm 3 each produce what quantity?
