Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces a demand function of 9, = 100 - 2p, + 1p2. where q, is Firm 1's output, p, is Firm 1's price, and p, is Firm 2's price. Similarly, the demand Firm 2 faces is 92 = 100 - 2p2 + 1p,. Solve for the Bertrand equilibrium. In equilibrium, p, equals $ 44 and p2 equals $ 44. (Enter numeric responses using integers.) At these prices, q1 equals and q2 equals The total quantity supplied is.
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- 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 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 __________ units.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.
- 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 a Bertrand duopoly. Both firms produce an identical good at the same constant marginal cost of $0.80. Demand is given by Q=100−P. If the two firms charge the same price, they share market demand equally. The firms are located in Singapore, where the smallest currency denomination is $0.05. The firms thus can only choose prices in increments of $0.05. a) Suppose that both firms choose the same price, P. What is the profit of a firm as a function of P? b) Now suppose that one firm unilaterally deviates from the arrangement in (a) by charging a price $0.05 lower than P. What is that firm’s profit as a function of P? c) A Nash equilibrium occurs when no firm has an incentive to deviate by lowering its price. Using your answers in (a) and (b), set up an inequality that characterizes the Nash equilibrium. Then solve for the Nash equilibria in this game. (Hint: there are three equilibria)Consider a Bertrand duopoly. Market demand is P(Q)=41-3Q, and each firm faces a marginal cost of $4 per unit. How much is the sum of firms' total revenue in the 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?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…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 ?
- 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?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)Consider duopoly model with firm 1 and firm 2. Firms have constant marginal costs, c_1 = c_2 = 10. Demand functions are given by equations: Q_1= (7*100) - 2*P_1 + P_2 Q_2 = (7*100) + P_1 - 2*P_ 2 Note that * signifies the multiplication sign. Firms play a simultaneous moves game where each store chooses its own price. Find each firms’ best response functions. Draw the best response functions of each firm. Label the graph properly. Is this a game of strategic substitutes or strategic complements? Why? Find the pure-strategy Nash equilibrium of the game. Find the profits each firm receives.