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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
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?
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- 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?Consider the following static game with two firms as the players. Each firm must decide either to upgrade (U) an existing good to a new version; or not upgrade it (N). The decisions are simultaneous. If a firm chooses to upgrade, they have to pay a fixed cost of 7. If they don’t upgrade, there is no fixed cost. The marginal cost is always equal to 3. The demand side of the market is as follows: If neither firm upgrades, each firm sells 2 units at price 4. If both firms upgrade, each firm sells 3 units at price 5. If only one firm upgrades, the one who upgrades sells 5 units at price 5, and the other firm does not sell anything.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. Now consider a modified game, which goes as follows: First, Firm 1 decides whether to enter the market or not. As in the previous question, there is no fixed cost, even if the firm decides to enter. Next, Firm 2 observes Firm 1’s entry choice and decides whether to enter or not.Firm 2 has no fixed cost as well. If no firm enters, the game ends. If only one firm enters, that firm chooses quantity, operating as a monopolist. If both firms enter, then Firm 1 chooses quantity q1. Then, Firm 2 observes Firm 1’s choice of q1 and then chooses q2 (like in the previous question). If a firm does not enter, it gets a payoff of zero. Which of the following statements is consistent with the SPNE of this game? Hint: you don’t need complicated math to solve this problem.(a) Neither firm…
- 1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB). Now assume firm A chooses quantity first. Firm B observes this choice and then chooses its own quantity. d)Firm A has MRA = 150 – 4QA/3. What are the equilibrium QA and QB selected in this game? e)What is the equilibrium price, and how much profit does each firm collect?Consider a market that only includes two large firms. The (inverse) market demand is P = 100 – Q. 3q2. Firm 1 has a cost function of C, = 2q1, and firm 2 has a cost function of C2 Use a Cournot model to calculate the Nash equilibrium outputs q, and q2 of the two firms. and 92 (a) Give each firm's profit as a function of (b) Compute the Nash equilibrium q, and q2.1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.
- Consider two firms with a homogeneous product who face the market demand function p = 2 – q1 – 92, where q; and p are the quantities and price. Their constant marginal costs are given by c= 1. The firms compete in quantities in a simultaneous move game. Use this specific example (not a general case) to show that the Nash equilibrium is not Pareto efficient, and the cooperative solution is not an equilibrium (in the sense that both firms have an incentive to cheat). In your answer, use the fact that the firms are identical. Namely, they produce equal amounts (both in the simultaneous move game and in the cooperative case).Suppose that there are only two firms in a market in which demand is given by p = 64 - Q, where Q is the total production of the two firms. Each firm can choose either a low level of output, qL = 15, or a high level of output, qH = 20. The unit cost of production for both firms is $4. Write down the normal-form representation of the game in which the strategic variable for each firm is the quantity of output and the firms make their choices simultaneously. Find the pure strategy Nash equilibrium of this game (quantities produced and market price).Four firms (A, B, C, and D) play a pricing game (i.e. Bertrand). Each firm (i) may choose any price P; in [0, infinity) with the goal of maximizing its own profit. (Firms do not care directly about their own quantity or others' profits.) Firms A and B have MC = 10, while firms C and D have MC = 20. The firms serve a market with the demand curve Q = 100 - P. All firms produce exactly the same product, so consumers purchase only from the firm with the lowest price. If multiple firms have the same low price, consumers divide their prices evenly among the low-priced firms. If firms choose price simultaneously: A) a price firm A would choose in equilibrium: a price firm B would choose in equilibrium: B) a price firm C would choose in equilibrium: C) a price firm D would choose in equilibrium:
- Two firms produce Bliffs. They compete by simultaneously choosing prices in a single period. The demand for Bliffs is given by P(Q) = 100-2Q where Q is market quantity and P is market price. Firm 1 has costs C1(q1) = 20q1 and Firm 2 has costs C2(q2) = 10q2. Which statement is true? In the Nash equilibrium to the game, both firms play dominated strategies None of the other answers are correct O In the Nash equilibrium to the game, both firms play dominant strategies In the Nash equilibrium to the game, both firms slowly lower prices towards marginal costs O In the Nash equilibrium to the game, both firms set price equal to marginal costTwo 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 30Firm 1 and Firm 2 are Stackelberg competitors. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions: Firm 1: C₁(Q1) = 4Q1 Firm 2: C2(Q2) = 4Q2 The market demand is QD = 42 -0.5P Compute the SPE of this game. In equilibrium, Firm 1 produces Q₁= and the price is P= v, Firm 2 produces Q2=
