Three firms compete in the style of Cournot. All firms have a constant returns to scale technology: There are no fixed cost and each firm's marginal cost is constant. The market demand is given by Q(P) = 9 - P. Firm 1's marginal cost is MC1 = 1, firm 2's marginal cost is MC2 = 2. Let MC3 be the marginal cost of Firm 3. Which of the below is a necessary condition so that q > 0 for all three firms in a Nash equilibrium? a. MC3 < 1 b. MC3 < 4 c. MC3 < 3 d. MC3 > 1 e. MC3 < 2
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- Consider the following model of Cournot competition with fixed cost. There are two identical firms, and the inverse demand function is given byP(q1,q2) = 19−(q1 +q2). Firms have constant marginal cost, but any firm operating in this market (that is, qi > 0) must pay a license fee F . In particular, firm i’s cost function is ( attached below ) a) Derive the firms’ best response functions. (b) For what values of F, if any, will there be a symmetric (pure) Nash equilibrium in which firms produce a positive quantity? What is the Nash equilibrium in that case? (c) For what values of F, if any, will both firms shutting down be the symmetric (pure) Nash equilibrium?Consider a market with two firms. Call them firm 1 and firm 2. The demand function describing the market is P = 216 – 0.4Q. Firms are initially identical, with the cost function C(q) = 140 + 40q. Calculate the total profits in the market. Under what conditions, the two firms may succeed to collude? How much would each firm earn if they could collude?Exercise 6.8. Two companies with cost functions C1 (q1 )=5q1 and C2 (q2)= 0.5 q2 ² supply the to the same market. If the inverse market demand function is given by P = 100 - 0,5Q , where Q = q₁ + q₂ , find a) The production level of each firm, the price and the profits if the companies compete according to the Cournot model. (b) The level of production of each undertaking, the price and the profits if the undertakings agree to jointly maximise their profits. Show the results with the help of graphs.
- Consider the following market demand function: Q= 20-2P, where P is the market price. Suppose there are two firms- A,B in the market and they have the same cost function: the per unit cost of producing output is 4. The firms compete by choosing quantities. Find the reaction functions for both the firms if they are maximizing profits. What is the profit maximizing output for each firm and corresponding market price? If there was only one firm in the market how would your answer change?Perrier and Apollinaris. Perrier and Apollinaris are two companies that sell mineral water in Tampa, FL. Each company has a fixed cost of $5,000 per period, regardless whether they sell anything or not. The two companies are competing for the same market and each firm must choose a high price ($2 per bottle) or a low price ($1 per bottle). Here are the rules of the game: At a price of $2, 5,000 bottles can be sold for total revenue of $10,000. At a price of $1, 10,000 bottles can be sold for total revenue of $10,000. If both companies charge the same price, they split the sales evenly between them. If one company charges a higher price, the company with the lower price sells the whole amount and the company with the higher price sells nothing. Payoffs are total profits. In this case, Apollinaris has: no dominant strategy. Perrier has a dominant strategy of P=$1. a dominant strategy of P=$1. Perrier also has a dominant strategy of P=$2. a dominant strategy…Perrier and Apollinaris. Perrier and Apollinaris are two companies that sell mineral water in Tampa, FL. Each company has a fixed cost of $5,000 per period, regardless whether they sell anything or not. The two companies are competing for the same market and each firm must choose a high price ($2 per bottle) or a low price ($1 per bottle). Here are the rules of the game: At a price of $2, 5,000 bottles can be sold for total revenue of $10,000. At a price of $1, 10,000 bottles can be sold for total revenue of $10,000. If both companies charge the same price, they split the sales evenly between them. If one company charges a higher price, the company with the lower price sells the whole amount and the company with the higher price sells nothing. Payoffs are total profits. In this case, the NE is(are): (P=$2, P=$1). (P=$1, P=$2). (P=$2, P=$2). (P=$1, P=$1).
- Two firms sells an identical product. The demand function for each firm is given: Q = 20 - P, where Q = q1 + q2 is the market demand and P is the price. The cost function for reach firm is given: TCi = 10 + 2qi for i = 1, 2. a) If these two firms collude and they want to maximize their combined profit, how much are the market equilibrium quantity and price? b) If these two firms decide their production simultaneously, how much does each firm produce? What is the market equilibrium price? c) If Firm 1 is a leader who decides the production level first and Firm 2 is a follower, how much does each firm produce? What is the market equilibrium price?Q. Three firms operate in a market with a Demand function p = 169 - 2Q. All three firms have identical Cost functions: TC = 1200 - 95q + 2q2.i) Given that the firms are able to collude, what is the equilibrium market price and output?ii) If all of the firms cheat and each increases output by two units, what would be the new equilibrium price and the impact on an individual firm’s profits?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.
- Pizza Hut and Dominoís are considering to open a shop in a new shopping precinct in Burwood. Suppose both charge $10 for a pizza (price competition is ignored here), and the aggregate local demand for pizza at this price is Q: If both Örms open a shop in the shopping precinct, Q is shared equally between the two shops. On the other hand, if there is only one pizza shop in the shopping precinct, the total demand Q goes to that shop. The total cost function for Pizza Hut is TC P(Q) = 5Q + 6000 and the total cost function for Dominos is TCD(Q) = 5Q+ 6000: Each has two strategies: Open a shop or Not, and they make their decisions simultaneously. The payoff is zero for a firm that does not open a shop in the shopping precinct. Suppose Q= 3000: Construct a 2 X 2 payoff matrix for this entry game between Pizza Hut and Dominoís and Önd the NE of the game. Suppose Q = 2000:Construct a 2x2 payoff matrix for this entry game between Pizza Hut and Dominoís and Önd the NE of the game.…There are two firms that are considering entering a new market, and must make their decision without knowing what the other firm has done. Unfortunately the market is only big enough to support one of the two firms. If both firms enter the market then they will each make a loss of £20 million. If only one firm enters the market, that firm will earn a profit of £80 million, and the other firm will just break even. If both firms do not enter the market, then they will just break even as well Based on a maximin strategy, what will be the outcome? (explain the decision step by step)There are two firms that are considering entering a new market, and must make their decision without knowing what the other firm has done. Unfortunately the market is only big enough to support one of the two firms. If both firms enter the market then they will each make a loss of £20 million. If only one firm enters the market, that firm will earn a profit of £80 million, and the other firm will just break even. If both firms do not enter the market, then they will just break even as well Construct the normal form for this game. Construct the extensive form for this game.