Firm A and firm B sell identical Soma to a market that has inverse demand p= 120 – Q where Q is total market supply. Suppose firm A and firm B each has a constant marginal cost of production of ca and cB per unit of Soma respectively (CA < 60, cB 60). The two firms are engaged in a Cournot competition. 1. What are the equilibrium quantities and profits in terms of Ca and cg?
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- Consider a duopoly market with 2 firms. Aggregate demand in this market is given by Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B. Assume the firms compete a la Cournot. What are the equilibrium quantities? What is the total quantity supplied on this market? What is the equilibrium price in this market?Suppose oil production in the Gulf of Mexico was a symmetric horizontal oligopoly in Cournot competition. Assume there are two producers, each with a constant marginal cost of production of $50 per barrel. Let the demand function for oil in the region be D(p) = 12000 – 20p, where demand is measured in barrels per day. (You will need to calculate inverse demand from demand before moving on). What would the perfectly competitive equilibrium price and quantity be? What would be the consumer surplus and producer surplus? Draw each firm’s residual inverse demand curve. Calculate the Cournot-Nash equilibrium price and quantity. What is the total consumer surplus, total producer surplus across the two firms, and deadweight loss?The tables (below) show the willingness to pay by three (competitive) consumers for additional units of some good, and the marginal costs of three (competitive) firms that produce that good. a) Compute the competitive equilibrium quantity and price for this market. Also, compute each consumer's surplus and each firm's profits. b) Now suppose that you have access to the same technology (and competitive input markets) as that of Firm 3. Entering the market (that is, launching a fourth firm) means a fixed (yes, sunk too) cost of $10. Would you decide to enter? (Entry has effects on the market, of course.) c) With the same data, suppose that all three firms merge. That is, now a single corporation controls (and decides on output for) all three firms (now, plants of one single firm). Obtain the output (or, equivalently, the price) that this monopolistic corporation will choose, and evaluate the consequences for the consumers (that is, the effect on the consumer surplus) and for the profits…
- Consider two gas stations in a remote village facing the simple linear market demand Q= 300− 5p but have different marginal costs of production, both constant, such that MCx = 20 and MCy = 101. Measuring the quantities Qx on the horizontal axis and the quantities Qy on the vertical axis, draw the reaction curves for each of the gas stations.2. Based on a Cournot equilibrium, find the profit-maximizing quantities Qxand Qy for the two gas stations.3. Based on your answers to (1) and (2) above, if gas station y decided to produce 175 units, (a) what would be the reaction of gas station x, and (b) how would y, in turn, react to that level of output of x?There are two firms selling differentiated products. Firm A faces the following demand for his product: QA=20-1/2PA+1/4PB Firm B faces the following demand: QB=220-1/2PB+1/4PA PA represents the price set by firm A. PB represents the price set by firm B.Assume that the marginal cost is zero both for firm A and firm B.What are the equilibrium prices of a simultaneous price competition?What would the equilibrium prices be if A is the leader and B is the follower?1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB). Now assume firm A chooses quantity first. Firm B observes this choice and then chooses its own quantity. d)Firm A has MRA = 150 – 4QA/3. What are the equilibrium QA and QB selected in this game? e)What is the equilibrium price, and how much profit does each firm collect?
- Melanie and Oli are competing Pacific halibut fishers. Both have been allocated ITQs that limit their catch to 1,000 tons of Pacific halibut each. Melanie's cost per ton is $20; Oli's cost per ton is $28.Refer to the information given and assume that the market price of Pacific halibut is $40 per ton. If Melanie pays Oli $10 per ton for his ITQs and then catches her new limit of 2,000 tons, their combined profit would be: $28,000. $32,000. $40,000. $54,000.Consider the differentiated goods Bertrand price competition model where firms A and B produce similar goods and sell them at pA and pB. The demand for each firm’s product is given byqA =60−2pA +pB andqB =60–2pB +pA ,and there are NO costs of producing either good (all costs are 0). (a)Calculate the (Bertrand) equilibrium prices and the net profits of each firm (b) Now suppose that -instead of competing to maximize their own individual profits- the firms decide to “collude” and set prices pA and pB to maximize their joint profits (sum of their profits). What would be each firm’s optimal price and net profits? Compare these prices and profits with what you found in (a) (greater/smaller/the same?).Need answer for part b only Zeus and Iron are the only two cement producers in Gotham. The cement they produce is essentially identical. In this market, each firm chooses the output level to produce and the price is determined by aggregate output (Cournot competition). The inverse demand for cement is given by P = 225 − Q/2 . Q is measured in tons and P is in euros. The marginal cost for Zeus is constant at 50 euros/ton. The respective cost for Iron is constant at 40 euros/ton. A technological innovation in the production process allows both firms to reduce marginal cost by 5 euros/ton. a) How much would each firm be willing to pay for the innovation, if it were the only firm to acquire it? b) Consider a situation where firms’ managers, simultaneously and non-cooperatively decide whether to acquire the innovation or not, which costs 900 euros, and then compete in quantities. What is the equilibrium of this game, based on its payoff matrix?
- DuopolyMarket for mechanical pencils can be described by the following demand schedule:Price | Number of pencils demanded$6 | 80$5 | 200$4 | 320$3 | 440$2 | 560$1 | 680$0 | 800The fixed cost is $340, while the variable cost is $0.50.d) If there were two firms on the market and they agreed to cooperate, how much would eachfirm need to produce? Follow the procedure outlined in the lecture and show that the otherfirm would prefer to deviate from the agreement.e) When the firms deviate from the agreement, there is a new optimal level of output. Showwhether the firms have an incentive to deviate from that level?f) If there were two firms on the market, what would be the price and the quantity of pencilstraded if the firms couldn’t cooperate?Consider a market for energy drinks consisting of only one firm. The firm has a linear cost function: C(q)=4q, where q represents quantity produced by the firm. The market inverse demand function is given byr P(Q)=24-2Q, where Q represents total industry output. Based on the given information answer the following. a. Now suppose a second firm enters the market. The second firm has an identical cost function. What will be the Cournot equilibrium output for each firm? b. Whay is the Stackelberg equilibrium output for each firm of firm 2 enters second? How much profit will each firm make in yhe Cournot game? How much in Stackelberg? c. Which type of market do consumers prefer: monopoly, Cournot duopoly or Stackelberg duopoly?Two firms (called firm 1 and firm 2) are the only sellers of a good for which the demand equation is Here, q is the total quantity of the good demanded and p is the price of the good measured in dollars. Neither firm has any fixed costs, and each firm’s marginal cost of producing a unit of goods is $2. Imagine that each firm produces some quantity of goods, and that these goods are sold to consumers at the highest price at which all of the goods can be sold. A Cournot equilibrium in this environment is a pair of outputs (q1, q2) such that, when firm 1 produces q1 units of goods and firm 2 produces q2 units of goods, neither firm can raise its profits by unilaterally changing its output. Find the Cournot equilibrium. Determine whether the price at which the goods are sold exceeds marginal cost.