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.
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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.
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- 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.Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by P(Q) = ( 300 − Q, if Q < 300) (0, otherwise), where Q = q1 + q2. Firm 1 has a cost function C1(q1) = 40q1, and firm 2 has a cost function C2(q2) = 50q2. Answer the following questions. 1. Assume the game lasts only one period. Compute the equilibrium price, quantities and profits for both firms. 2. If firm 1 becomes the monopolist on this market, what quantities will firm 1 choose to produce? Denote this quantity as QM. 3. One possible strategy is that each firm produces QM 2 . Would the resulting outcome be better for both firms (Pareto improvement)? Explain why this is not the equilibrium in the one period game. 4. Assume this game is infinitely repeated and the interest rate in this economy is r. For what values of r the strategy in (3) is sustainable by using a “Grim Trigger” strategy?Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by 400-Q, if Q< 400 P(Q) = " otherwise where Q = 91 +92. Firm 1 has a cost function C₁ (91) = 40q1, and firm 2 has a cost function C2 (92) = 5092. Answer the following questions. 1) Assume the game lasts only one period. Compute the approximate equilibrium profits for both firms. 2) If firm 1 becomes the monopolist on this market, what quantities will firm 1 choose to produce? Denote this quantity as QM. 3) One possible strategy is that each firm produces. This gives a more Pareto efficient outcome. But given that firm 2 produces this quantity, how much does firm 1 want to produce? 4) Assume this game is infinitely repeated and the interest rate in this economy is r. For what values of r the strategy in (3) is sustainable by using a "Grim Trigger" strategy?
- The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has a cost of production of C1= 15*Q1 and firm 2 has a cost of production of C2=20*Q2 a) Suppose firm 1 and firm 2 compute simultaneously in quantities. What are the Cournot quantities and prices?What are the profits of firm 1 and 2?b) Suppose firm 1 and firm 2 compete simultaneously in prices. What are the Bertrand quantities and prices?What are the profits of firm 1 and 2?Two countries produce oil. The per unit production cost of Country 1 is C1 = $2 and of country 2 it is C2 = $4. The total demand for oil is Q = 40-p where p is the market price of a unit of oil. Each country can only produce either 5 units, 10 units or 15 units. The total production of the two countries in a Nash equilibrium is 10 15 20 25 30Question 3:Suppose the inverse demand for a good is given by P = 50 – 4Q, where Q is the totalquantity supplied by all firms in the market. Suppose each firm in the market has a constantmarginal cost of 18.Q3 a) Assume the market consists of two firms that set their quantities simultaneously.Calculate the duopoly levels of production and the equilibrium price. Q3 b) Now assume firm 1 chooses its production level before firm 2 does. What will be theequilibrium quantities, price and profits in this case?Q3 c) Now instead suppose that the two firms compete over prices rather than quantities.What will be the equilibrium price and profits of firms 1 and 2 in this case? Finally, if firm 1manages to lower its marginal cost to 14, what will be the new equilibrium price, quantitiesand profits?
- Problem 3. Firm 1, Firm 2 and Firm 3 are the only competitors in a market for a good. The price in the market is given by the inverse demand equation P=10 (Q1+Q2+Q3) where Q, is the output of Firm i (i=1,2,3). Firm 1's total cost function is C₁ = 4Q₁+1, Firm 2's total cost function is C₂ = 2Q2 +3, and Firm 3's total cost function is C3 = 3Q3 + 2. Each firm wants to maximize its profits and they simultaneously choose their quantities. Determine a Nash equilibrium in this market.Suppose we have two identical firms A and B, selling identical products. They are the only firms in the market and compete by choosing quantities at the same time. The Market demand curve is given by P=477-Q. The only cost is a constant marginal cost of $16. Suppose Firm A produces a quantity of 66 and Firm B produces a quantity of 49. If Firm A decides to increase its quantity by 1 unit while Firm B continues to produce the same 49 units, what is the Marginal Revenue for Firm A from this extra unit? Enter a number only, no $ sign. Don't forget to include the negative sign if revenue decreases.Two firms compete on price every year. The inverse demand function each firm faces depends on which firm has chosen the lowest price that year. The one that did captures the entire market. If, on the other hand, both prices are the same then they split the market evenly. Consumers round up prices to the nearest integer. For the firm with the lowest price p, demand is given by: q = 24-2p: Marginal costs are constant and equal to $4 for both firms. a. Define the Normal form of the stage game and determine the Nash Equilibria, the Cooperative Equilibrium and the Optimal Deviation from cooperation. b. For the once repeated (2 stages) game, determine if a Nash Equilibrium exists that improves on simply playing the (better) Nash Equilibrium of the stage game twice c. For the infinitely repeated game, determine what the interest rate would have to be to prevent the firms from cooperating. d*. Determine the relation between the interest rate and the number of punishment periods in a…
- consider a market with inverse demand P(Q) = 10 − Q and two firms with cost curves C1(q1) = 2q1 and C2(q2) = 2q2 (that is, they have the same marginal costs and no fixed costs). They compete by choosing quantities. Suppose that Firm 1 chooses quantity first and is able to credibly commit to this choice. Then firm 2 choose its quantity after observing firm 1’s quantity. In the SPNE of this game, what is the price faced by consumers?- p = 3- p = 4- p = 5- p = 6- p = 7Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively isConsider two firms that produce the same product and sell it in a market with the following demand function: d(p) = max{0, 12 − p}, where p ≥ 0 is the unit price of the good. Suppose that, for technological reasons, firm 1 can produce either 4 units of output at the total cost of 10, or 6 units at the total cost of 15. Similarly, firm 2 can produce either 3 units of output at the total cost of 8, or 4 units at the total cost of 10. Assume that the firms make their production decisions simultaneously. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game. Now assume that firm 1 makes its decision first. Firm 2 decides how much to produce after it observes firm 1’s output. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game.
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