Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces a demand function of q, = 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 q, = 100 - 2p, + 1p,. Solve for the Bertrand equilibrium. In equilibrium, p, equals $ and p2 equals $. (Enter numeric responses using integers.)
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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.
- Solve for the Bertrand equilibrium for the firms described in Problem 32 if both firms have a marginal cost of $0 per unit. Problem 32 Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of where is Firm 1’s output, is Firm 1’s price, and is Firm 2’s price. Similarly, the demand Firm 2 faces is Solve for the Bertrand equilibrium. CConsider 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)
- 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 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?In the duopoly market where two firm exist, the demand curve is given as follows. P=120-y (y is the total market output) Firm1 has a marginal cost of 10 and Firm 2 has a marginal cost of 20. 1. Determine the Firm1’s reaction function and the Firm2’s reaction function. 2. What is the output of each firm in the Cournot equilibrium? 3. Firm1 is Stackelberg leader, Firm2 is Stackelberg follower. How much should the leader produce in order to maximize profits? I don't know the answer of number 2 and 3. some says number 2 answer is both 60 but some also says that its each 60 and 40 units. Also, for number 3, some says its maximize profit is 140 but some says 80. I don't know what the correct answer is. please show me the correct answer and correct explanantion.
- 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)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?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.