Consider two firms, referred to as firms 1 and 2, who compete in a market by choosing quantities produced and face the following inverse demand: P(Q)= 10-20 Each firm has a marginal cost of production of $4.00. Suppose these firms collude by agreeing to produce quantities to maximize their joint profits. Firm 1 sticks to the agreement, but firm 2 does not. If firm 2 can secretly change its produced quantity, how much would it produce?
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- Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each earn as profit? How does the price compare to the marginal cost? Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each…Suppose that two clothing manufacturers, Lands’ End and L.L. Bean, are deciding what price to charge for very similar field coats. The cost of producing these coats is $100. The coats are very close substitutes, so customers flock to the seller that offers the lowest price. If both firms offer identical prices, each receives half the customers. For simplicity, assume that the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices (Lands’ Ends Profit, LL Bean’s Profit) is attached in the payoff matrix below: a.) What is the Nash equilibrium and expected profits to LL Bean and Lands’ End of this game? b.) Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a priceof $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while Lands End has a1/3 chance of choosing each strategy. What’s the expected payoff to LL Bean? c.) Suppose that in hopes of raising…Consider Firm A and Firm B, each with cost functions C(qA) = 5qA, and C(qB) = 5qB, The inverse market demand is given by p = 30 − Q, where Q = qA + qB represents the total quantity demanded in the market. a) Suppose the firms compete in a Cournot oligopoly model. What are the quantities supplied by each firm and their profits? b) Now let Firm A be the first-mover. If the firms compete in a Stackelberg oligopoly model, what are the quantities supplied by each firm and their profits? c) How can you interpret the difference in profits between parts (a) and (b)? In other words, if you were Firm A, which scenario would you prefer, and what might this say in general?
- How would the Cournot equilibrium change in the airline example if American's marginal cost were $90 and United's were $180? The demand the duopoly quantity-setting firms face is Q=339−p with an inverse demand function of p=339−1qA −1qU where qA is the quantity produced by American and qU is the quantity produced by United. The Cournot-Nash equilibrium occurs where qA equals ? enter your response here and qU equals? enter your response here. (enter numeric responses using integers) Furthermore, the equilibrium occurs at a price of ? (round your answer to the nearest penny)Why can Q-learning sustain collusion? a. Because collusion maximizes firms' profit. b. Because collusion is the Nash equilibrium of the pricing game, even if it is played only once. c. Because the algorithm takes into account future profits, and learn that price cutting today will lead to price war tomorrow. d. Because firms use the algorithm to communicate with each other and sustain collusion. 21 Suppose a platform tries to recommend the best movie to Ann and Ben. Movie 1's quality is uniformly distributed from 0 to 1. Movie 2's quality is uniformly distributed from 0.5 to 1. Suppose the platform recommends a movie to Ann and Ben at the same time. What are the expected quality of movie 1 and 2, and which one should it recommend? a. 0.5, 0.5, movie 1. b. 0.75, 0.5, movie 1. c. 0.5, 1, movie 2. d. 0.5, 0.75, movie 2.Suppose that Flashfry and Warmbreeze are the only two firms in a hypothetical market that produce and sell air fryers. The following payoff matrix gives profit scenarios for each company (in millions of dollars), depending on whether it chooses to set a high or low price for fryers. Warmbreeze Pricing High Low Flashfry Pricing High 11, 11 2, 15 Low 15, 2 8, 8 For example, the lower-left cell shows that if Flashfry prices low and Warmbreeze prices high, Flashfry will earn a profit of $15 million, and Warmbreeze will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfry and Warmbreeze are both profit-maximizing firms. If Flashfry prices high, Warmbreeze will make more profit if it chooses a price, and if Flashfry prices low, Warmbreeze will make more profit if it chooses a price. If Warmbreeze prices high, Flashfry will make more profit if it chooses a price, and if Warmbreeze prices low, Flashfry will make more profit if…
- 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?Consider a Cournot Oligopoly. One firm has costs C1(Q1) = 12Q1 while the other firm’s cost function is C2(Q2) = 10Q2. The demand for both firms’ products Q=Q1 +Q2 isQD(P)=200−2P. (a) Determine the equilibrium price P, the market shares s1, s2, and the quantities Q1, Q2 produced by both firms. (b) Suppose more firms with the lower cost technology, i.e., with cost function Ci(Qi) = 10Qi enter the market. How many firms with this technology must be in the market such that firm 1’s profit becomes negative. In other words, suppose there is one firm with the high costs, and n firms with the low costs. At what level n will profits of the high-cost firm be negative?Consider a situation where two firms, 1 and 2, compete by choosing prices simultaneously. Theycan either compete (charge a low price) or cooperate (collude, charging a high price). The firmsplay this competition game repeatedly and indefinitely, using a grim trigger strategy toincentivize cooperation. They use the same interest rate, i, to discount future payoffs. Payoffsare $4,050 when both firms cooperate and $3,600 when they compete. If one firm charge a lowprice while the other charges a high price, the firm charging the low price gets $7,200, and theother gets zero, but now assume there is a 10% chance that aregulatory agency will give both firms a $1,500 fine in each period if they are caught colluding.Find the condition on the interest rate, i , necessary for sustaining the cooperative equilibrium.Which of the following statements is correct?(a) For any i < 1/7 the firms will cooperate.(b) For any i < 1/11 the firms will cooperate.(c) For any i > 1/11 the firms will…
- 2 clothing manufacturers, LE and LL B, are deciding what price to charge for very similar field coats. Cost of producing these coats is $100. The coats are very close substitutes, so customers swarm to the seller that offers the lowest price. If both firms offer the same prices, each receives half of the customers. Assume the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices is shown in the payoff matrix below $103 ($150, $150) ($0, $200) ($0, $120) Lands' End $102 ($200, $0) ($100, $100) ($0, $120) $101. ($120, $0) ($120, $0) ($50, $50) What is the Nash equilibrium and expected profits to LLB and LE of this game? If this was a mixed strategy game in which LLB has a 25% percent chance of choosing a price of $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while LE has a1/3 chance of…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?Two identical firms are engaged in Cournot competition, with cost functionsTCA(QA) = 10 QA and TCB(QB) = 10 QB. The market demand is given by P = 610 –2Q.a) Plot the best response functions and report the Cournot-Nash equilibrium quantities, price and profits.b) What are the prices, quantities, and profits for the firms if they decide to collude and share profits equally? c) Show that firms have an incentive the deviate from the collusive outcome.d) Find the Stackelberg equilibrium if A leads and B follows.e) Show the equilibria in the previous parts on the inverse demand function. Calculate and identify consumer surplus and deadweight loss in each equilibrium..