Consider an industry with two identical firms (denoted firm 1 and 2) producing a homogenous good. Firms compete in quantities. Firm 1 has a constant marginal cost of 20. Firm 2 has a constant marginal cost of 80. Demand in the industry is given by D(p) = 380 - p. Let q1 and q2 denote the quantities of firm 1 and 2, respectively. Derive the Nash equilibrium in quantities. What is the total production in this industry?
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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.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 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.
- The market demand function is Each firm has a marginal cost of m = $0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. The Stackelberg-Nash equilibrium quantities are The Stackelberg-Nash equilibrium price is Profits for the firms are and 92 p = $ π2 $ = Q=7,000 1,000p. 91 and units units. (Enter your responses as whole numbers.) (Enter your response rounded to two decimal places.) π₁ = $ (Enter your responses rounded to two decimal places.)Consider two firms that produce the same good and competesetting 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 costfunction for each of the firms is c(qi) = cqi, where 0 < c < 1 and qiis the quantity offered by the firm i = 1, 2. Find the Nash equilibriumoutput choices of the firms, as well as the total output and the price, andcalculate the output and the welfare loss compared to the competitiveoutcome. How would the answer change if the firms compete settingprices? What can we conclude about the relationship between competitionand the number of firms?Jane 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
- 10Two firms produce differentiated products. The demand for each firm’s product is as follows: Demand for Firm 1: q1 = 20 – 2p1 + p2 Demand for Firm 2: q2 = 20 – 2p2 + p1 Both firms have the same cost function: c(q) = 5q. Firms compete by simultaneously and independently choosing their prices and then supplying enough to meet the demand they receive. Please compute the Nash equilibrium prices for these firms.The demand for a product is Q = a - P/2. If there are 4 firms in an industry and marginal cost is MC = 20, then the price in Nash equilibrium is P = 56. What is a?Consider a market for crude oil production. There are two firms in the market. The marginal cost of firm 1 is 20, while that of firm 2 is 20. The marginal cost is assumed to be constant. The inverse demand for crude oil is P(Q)=200-Q, where Q is the total production in the market. These two firms are engaging in Cournot competition. Find the production quantity of firm 1 in Nash equilibrium. If necessary, round off two decimal places and answer up to one decimal place.
- 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?The market demand function is Q=10,000-1,000p. Each firm has a marginal cost of m=$0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. Compare your solution to the Cournot-Nash equilibrium. The Stackelberg-Nash equilibrium quantities are: q1=___________ units and q2=____________units The Stackelberg-Nash equilibrium price is: p=$_____________ Profits for the firms are profit1=$_______________ and profit2=$_______________ The Cournot-Nash equilibrium quantities are: q1=______________units and q2=______________units The Cournot-Nash equilibrium price is: p=$______________ Profits for the firms are profit1=$_____________ and profit2=$_______________Two firms, A and B, sell the same good X in a market with total demand Q = 100 – P. The two firms compete on quantities and decides how much to produce simultaneously. Firm A cost function is C(qA) = 40qA. Firm B cost function is C(qB) = 60qB. 1. Find the best reply functions of both firms and represent them in a graph. 2. Find the quantity produced by each firm in a Nash equilibrium. 3. Find the firms and consumers surplus. 4. Compare the surplus of firms found above with the surplus arising when both firm cooperate to sustain a monopoly outcome. 5. Assume now that A and B compete as in a Stackelberg model. A chooses first and B chooses after observing the choice of A. Find equilibrium quantities produced by each firm and the market equilibrium price.