92) = 275-9₁ −92 and each firm has a marginal cost of $35 per unit. A ut of the market et, the resulting equilibrium will be the Nash-Stackelberg equilibrium. Ca 's profits in this equilibrium. (Enter your responses rounded to two decir 60.00
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- Consider a Duopoly model, in which two firms decide a quantity sequentially. For the convenience, let's say Firm 1 is a dominant firm and Firm 2 is a follower. The market demand is given by P=110 - 5Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=7Qi, i=1, 2. Each firm maximizes its profit by choosing the quantity. In this Stackelberg equilibrium, Firm 1 will sell how many units.A homogenous-good duopoly faces an inverse market demand function of p = 150 − Q. Assume that both firms face the same constant marginal cost, MC1 = MC2 = 30. Calculate the output of each firm, the market output, and the market price in a Nash-Cournot equilibrium Re-solve part (a) assuming that the marginal cost of firm 1 falls to MC1 =20 Explain what will happen to each firm’s output, the market output, and the market price if the two firms can collude (e.g., form a cartel)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?
- Kafue Water and Sewerage Company and Lusaka Water and Sewerage Company are duopolistic firms operating under the Cournot model. The two companies are both supplying Water to Chilanga District whose total demand is given by a linear demand function Q = 720 – 2P = 3q1 + 3q2, where q1 represents water output by Kafue Water, and q2 is water output by Lusaka Water and Sewerage Company. Assume that: Each firm has no production costs Each firm has to decide how much water to supply to the market Given the above information, determine The profit-maximizing output, price, and level of profit for the two companies. The individual level of outputs q1 and q2, as well as the revenue for which the two companies are maximizing profits. Interpret your results in (i) and (ii)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?The market demand curve faced by Stackelerg duopolies is: Qd = 12,000 - 5P where Qd is the market quantity demanded and P is the commodity's price in dollars. Firm A's marginal cost is: MCa = 0.08qa where MCa is Firm A's marginal cost in dollars and qa is the quantity of output produced by Firm A. Firm B's marginal cost equation is: MCb = 0.1qb where MCb is Firm B's marginal cost in dollars and qb is the quantity of output produced by Firm B. Because of Firm A's lower marginal cost, Firm B has conceded the power to move first to Firm A. a. Given Firm B will move second, what is the equation for Firm B's reaction function with qb expressed as a function of qa? b. Given Firm A can move first, what quantity of output will Firm A produce? c. What quantity of output will firm B produce? What price will be established for the commodity?
- There are two firms A and B. Firms compete in a Cournot Duopoly in Karhide. They set quantities qA and qB. Inverse demand is P(qA + qB) = 18 − qA − qB and costs are C(q) = 3 ∗ q for both firms. Firm B is a domestic firm (in Karhide,) and firm A is a foreign firm (from Orgoreyn.) The government of Karhide engages in a strategic trade intervention by giving firm B a per unit subsidy of s. (That is, when firm B produces and sells qB units, firm B receives a payment of s ∗ qB from the government.) (d) Solve for the equilibrium outputs (q∗A, q∗b).(e) Solve for the equilibrium price.(f) Solve for firm B profits.Suppose that two Japanese companies, Hitachi and Toshiba, are the sole producers (i.e., duopolists) of a microprocessor chip used in a number of different brands of personal computers. Assume that total demand for the chips is fixed and that each firm charges the same price for the chips. Each firm’s market share and profits are a function of the magnitude of the promotional campaign used to promote its version of the chip. Also assume that only two strategies are available to each firm: a limited promotional campaign (budget) and an extensive promotional campaign (budget). If the two firms engage in a limited promotional campaign, each firm will earn a quarterly profit of $14 million. If the two firms undertake an extensive promotional campaign, each firm will earn a quarterly profit of $11 million. With this strategy combination, market share and total sales will be the same as for a limited promotional campaign, but promotional costs will be higher and hence profits will be lower.…A duopoly faces an inverse market demand of P(Q) = 240−Q.Firm 1 has a constant marginal cost of MC1 (q1) = $10.Firm 2's constant marginal cost is MC2 (q2) = $20.Assume fixed costs are negligible for both firms. Calculate the output of each firm, market output, and price if there is (A) a collusive equilibrium or (B) a Cournot equilibrium. (A) Collusive equilibrium (Enter your responses rounded to two decimal places) The collusive equilibrium occurs where q1 equals ?and q2 equals ? Market output is ? The collusive equilibrium price is ? (B) Cournot equilibrium (Enter your responses using rounded to two decimal places) The Nash-Cournot equilibrium occurs where q1 equals ? and q2 equals ? Market output is ? The equilibrium occurs at a price of ?
- Two firms compete by choosing price. Their demand functions are: Q1 = 20 -P1 +P2 and Q2 = 20 - P1 + P2 where P1 and P2 are the prices charged by each firm, respectively, and Q1 and Q2 are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted and earn infinite profits. Marginal costs are zero.a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) {15 Marks}b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? {10 Marks}c. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same…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 duopoly where firms compete for market share by setting prices. The firms produce differentiated products and face the following demand functions where q is output and P is the price in dollars. q1 = 100 – 2P1 + 2P2 Demand Function for Firm 1 q2 = 120 – 4P2 + P1 Demand Function for Firm 2 Suppose that firm 1 is able to produce output at a constant marginal cost of $30 and that firm 2 is able to produce output at a constant marginal cost of $20. Both firms operate with no fixed costs. Derive the best response function for firm 1. Derive the best response function for firm 2.