There are two firms in the market. Denote the price and the quantity of firm j by p¡ and q; , respectively. Those two products are differentiated and the demand system is given by 91 = 100 – 2p1 + P2. 92 = 100 + p1 – 2p2 For simplicity, assume zero production costs, meaning that profit is equal to revenue. Consider the two-stage game in which firm 1 decides the price first and then firm 2 choose its price after observing firm 1's price. If firm 1's price is 24, what is the best response price of firm 2? Report only the value . Answer:
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- 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.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 that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantityfirm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What arethe profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?Problem 3. Consider the following game with three firms. First, firms 1 and 2 si- multancously choose quantities q1 and q2 respectively. After observing firm 1 and 2's quantities, firm 3 chooses its quantity q3. There is no production cost and the inverse demand function is p= 12 – (91 +2 + 93). (a) Compute the SPNE of this game. (b) Give an example of Nash equilibrium s* with s = 4 and s, = 6 , that is not subgame perfect. game theory question
- 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.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 30Consider the following sequential move game: 1. Ifz=0, find any subgame perfect NE. 2. For what values of z will M occur in the subgame perfect equilibrium? 21
- 5) Consider the following sequential move game: M 2,1 1,3 1,3 3,0 2,3 4,1 a) If z=0, find any subgame perfect NE. b) For what values of z will M occur in the subgame perfect equilibrium?Two firms, X and Y, are involved in a price war. The demand equations for each firm are the following: Qx = 52 - 2Px + Py Qy = 52 - 2Py + Px Further, assume the cost of each unit of out is constant at $4. What is the Nash equilibrium of this game? (Use the best response functions in a graph to answer) There is no Nash equilibrium O $24 $20 $22Jane and Sara are competing orange juice salespersons in Amherst. Their stands are next to each other on a street and consumers regard them as identical. The marginal cost of an orange juice is $1. The demand for orange juice every hour is Q = 20 − P where P is the lowest price between the two salespersons. If their prices are equal they split demand equally. a. If they set prices simultaneously (prices can be any real number), what is the Nash equilibrium price? b. If, against what we have assumed in class, orange juice salespersons have to charge prices in whole dollars ($1, $2, $3, etc), what are the Nash equilibrium prices? c. Assuming whole dollar pricing, if Jane sets her price before Sara, what price would she charge? Answer all 3 parts
- Suppose OPEC has only two producers, Saudi Arabia and Nigeria, Saudi Arabia has far more oil reserves and is the lower-cost producer compared to Nigeria. The payoff matrix in the table to the right shows the profits earned per day by each country. "Low output" corresponds to producing the OPEC assigned quota and "high output" corresponds to producing the maximum capacity beyond the assigned quota Which of the following statements is true? OA. The Nash equilibrium is a cooperative equilibrium. OB. The Nash equilibrium is a noncooperative, dominant strategy equilibrium OC. The Nash equilibrium is a collusive equilibrium. D. There is no Nash equilibrium in this game because each party. pursues its dominant strategy. Low output Nigeria High output Low output Nigeria earns $20 million Saudi Arabia Nigeria earns $30 million Saudi Arabia earns $100 million Saudi Arabia earns $80 million High output Nigeria earns $12 million Saudi Arabia earns $75 million Nigeria earns $20 million Saudi Arabia…QUESTION 10 Suppose there are two firms that produce an identical product. The demand curve for the product is given by P = 62 - Q where Q is the total quantity produced by the two firms. Both firms choose their individual quantities qı20 and q22 0 simultaneously. Each firm has a marginal cost of 37. What is the market price when both firms produce the quantities in the unique Nash equilibrium? Give your answer as a number to two decimal places.1. Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs: Firm B - low output 300, 250 Firm B - high output 200, 100 Firm A - low output Firm A - high output 200, 75 75, 100 a. Draw a tree (extensive form) of this game.