Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of 9₁ =70-2p₁ + 1P2, where 91 is Firm 1's output, p₁ is Firm 1's price, and p2 is Firm 2's price. Similarly, the demand Firm 2 faces is 92 z =70 − 2p2 +1P1. Solve for the Bertrand equilibrium. In equilibrium, p₁ equals $ and P2 equals $ (Enter numeric responses using integers.)
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- 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…What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q=4,000-1,000p, and Firm l's and Firm 2's variable cost functions are V (q1) = 0.22qlandV (q2) = 0.22q2 , respectively. Select one alternative: Both firms produce 1300 units of outpuit. Both firms produce 1280 units of output. Both firms produce 1240 units of output. Both firms produce 1260 units of output.Three firms sell identical products in a market with inverse demand given by P(Q) = 540 - 4Q, where Q=q1+ q2 + q3, i.e., the sum of all quantities produced by all three firms. Each firm has a constant marginal cost of production MC = 23 and no fixed cost. Firm 1 chooses q1 first. Firms 2 and 3 simultaneously choose q2 and q3 after observing q1. Calculate the subgame perfect equilibrium profit of firm 1. Round your answer to 2 decimal places.
- Three firms sell identical products in a market with inverse demand given by P(Q) = 590 - 4Q, where Q = q1 + q2 + q3, i.e., the sum of all quantities produced by all three firms. Each firm has a constant marginal cost of production MC = 18 and no fixed cost. Firm 1 chooses q1 first. Firms 2 and 3 simultaneously choose q2 and q3 after observing q1. Calculate the subgame perfect equilibrium profit of firm 2.Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of q1 = 70 – 2p1 + 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 = 70 – 2p2 + 1p1- Solve for the Bertrand equilibrium. In equilibrium, p1 equals $ and P2 equals $ (Enter numeric responses using integers.)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 + 1p1. Solve for the Bertrand equilibrium. In equilibrium, p, equals $ and p2 equals $. (Enter numeric responses using integers.)
- Consider two firms that provide a differentiated product, which they produce at the same constant marginal cost, MC = 3. The demand function for Firm 1 is q1 = 10 - p1-0.5p2 and for Firm 2 is q2 = 20 - p2 - 0.5p1, where p1 is Firm 1's price and p2 is Firm 2's price. What are the Nash-Bertrand equilibrium prices and quantities? If the two firms merged, what would be the new equilibrium prices and quantities, and how would they compare to the pre-merger prices?Two firms compete by choosing price. Their demand functions are and Q₂ =20+P₁-P2₁ 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. 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.) Each firm will charge a price of $1. (Enter a numeric response rounded to two decimal places.) Each firm will produce units of output. In turn, each firm will earn profit of $ Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will each sell, and what will be profits?…Suppose that there are two firms operating in the market of laptops, the first firm supplies quantity qi and the second firm supplies q2. The inverse demand function for laptops is P(q1 +q2)=2,000-2(q₁ +q2). The marginal costs are constant and equal to $400. a. b. c. Find the Cournot equilibrium outputs and price. Find the Bertrand equilibrium outputs and price. Suppose that the first firm is the leader choosing the output first, and the second firm is the follower choosing the output after observing the firm firm's choice. Find the new equilibrium output and price and compare them with those in parts a and b. Which of the equilibria is socially preferable?
- Two firms compete in selling homogeneous goods. They choose their output levels q1 and q2 simultaneously and face demand curve P=80-6Q, where Q=q1+q2. The total cost function of firm 1 is C1=8q1 and the total cost function of firm 2 is C2=32q2+2/3. a) Find and draw the reaction curves of the two firms. b) Compute equilibrium quantities, price and profits. Suppose now that firm 2, thanks to a technological innovation, becomes more efficient. The new total cost function of firm 2 is C2=8q2 c) Compute the new equilibrium quantities, price and profits.Two firms compete by choosing price. Their demand functions are Q, = 200 - P, +P2 and Q2 = 200 + P, - P2, where P, and P, are the prices charged by each firm, respectively, and Q, and Q, 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. 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.) Each firm will charge a price of $ . (Enter a numeric response rounded to two decimal places.)Consider two firms that produce the same good and compete setting quantities. The firms face a linear demand curve given by P (Q) = 1 − Q, where the Q is the total quantity offered by the firms. The cost function for each of the firms is c(qi) = cqi, where 0 < c < 1 and qi is the quantity offered by the firm i = 1,2. Find the Nash equilibrium output choices of the firms, as well as the total output and the price, and calculate the output and the welfare loss compared to the competitive outcome. How would the answer change if the firms compete setting prices? What can we conclude about the relationship between competition and the number of firms?