Question

In: Economics

Suppose that two identical firms produce widgets and that they are the only firms in the...

Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by

C1 = 60 Q1

and

C2 = 60 Q2

where Q1 is the output of Firm 1 and Q2 is the output of Firm 2. Price is determined by the following demand curve:

P= 2100 − Q where Q=Q1+Q2

Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium. (For all of the following, enter a numeric response rounded to two decimal places.)

When competing, each firm will produce ___ units of output.

In turn, each firm will earn profit of ___.

Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm's profit.

Each firm will produce ___ units of output.

In turn, each firm will earn profit of ___.

Suppose Firm 1 were the only firm in the industry. How would market output and Firm 1's profit differ from that found in above?

Firm 1 would produce ___ units of output.

Firm 1's would earn profit of ___.

Returning to the duopoly above, suppose Firm 1 abides by the agreement but Firm 2 cheats by increasing production. How many widgets will firm produce? What will be each firm's profits?

Firm 2 would cheat by producing ___ units of output.

As a consequence, Firm 1 would earn profit of ___.

Firm 2 would earn profit of ___.

Solutions

Expert Solution

P=2100-Q1-Q2

MR1=2100-2Q1-Q2

MC1=60

MR1=Mc1

2100-2Q1-q2=60

Q1=1020-0.5Q2 { best response function of firm 1}

By symmetry,.

Q2=1020-0.5Q1{ best response function of firm 2}

Q2=1020-0.5(1020-0.5Q2}

Q2=510/0.75=680( each firm Production in cournot equilibrium}

Q=680+680=1360

P=2100-1360=740

Profit of each firm=(740-60)*680=462,400

Cartel,

They will act as monopoly,

P=2100-Q

MR=2100-2Q

MC=60

2100-2q=60

Q=2040/2=1020

q1=Q2=1020/2=510

P=2100-1020=1080

Profit of Each firm=(1080-60)*510=520,200

Monopoly,

Q=1020

P=1080

Profit of firm 1=(1080-60)*1020=1,040,400

Cheating,

q2=1020-0.5Q1

Q2=1020-0.5*510=765

Q=510+765=1275

P=825

Profit of firm 1=(825-60)*510=390,150

Profit of firm 2=(825-60)*765=585,225


Related Solutions

Suppose that two identical firms produce widgets and that they are the only firms in the...
Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by C1=60Q1 and C2=60Q2 where Q1 is the output of Firm 1 and Q2 is the output of Firm 2. Price is determined by the following demand curve: P=2700−Q where Q=Q1+Q2 Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium. (For all of the following, enter a numeric response rounded to two decimal places.) When...
Suppose that two identical firms are selling a product and that they are the only firms...
Suppose that two identical firms are selling a product and that they are the only firms in the market. Total costs are Ci = 20Qi for each firm. The market demand curve is P = 80 – 0.5Q where Q = Q1 + Q2. The Cournot model describes the competition in this market. Using the above information, complete the below statements, a.)If these two firms collude, their combined output is equal to b.)If these two firms collude, each firm’s output...
Suppose there are two firms operating in a market. The firms produce identical products, and the...
Suppose there are two firms operating in a market. The firms produce identical products, and the total cost for each firm is given by C = 10qi, i = 1,2, where qi is the quantity of output produced by firm i. Therefore the marginal cost for each firm is constant at MC = 10. Also, the market demand is given by P = 106 –2Q, where Q= q1 + q2 is the total industry output. The following formulas will be...
Suppose there are two firms that produce an identical product. The demand curve for their product...
Suppose there are two firms that produce an identical product. The demand curve for their product is represented by P=60-2Q, where Q is the total quantity produced by the two firms. The marginal cost of production is zero and there are no fixed costs. A. Refer to Scenario: Oligopoly. Suppose both firms choose their individual quantities q1 (firm 1) and q2 (firm 2) simultaneously and independently (so Q = q1 + q2). What is the unique Nash equilibrium price? B....
Suppose there are two firms, Firm A and Firm B that produce identical products in a...
Suppose there are two firms, Firm A and Firm B that produce identical products in a duopoly. Firm A has a constant marginal cost of production, MCA = 10 and Firm B has a constant marginal cost, MCB = 14. The market demand curve for the the product is given by P = 42 − 0.004Q where Q = (QA + QB). (a) Suppose that Firm A has a first-mover advantage. That is, Firm A is able to choose output...
Suppose we have two identical firms A and B, selling identical products. They are the only...
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=200-Q. The only cost is a constant marginal cost of $17. Suppose Firm A produces a quantity of 50 and Firm B produces a quantity of 50. If Firm A decides to increase its quantity by 1 unit while Firm B continues to produce...
Two identical firms compete in a Bertrand duopoly. The firms produce identical products at the same...
Two identical firms compete in a Bertrand duopoly. The firms produce identical products at the same constant marginal cost of MC = $10. There are 2000 identical consumers, each with the same reservation price of $30 for a single unit of the product (and $0 for any additional units). Under all of the standard assumptions made for the Bertrand model, the equilibrium prices would be Group of answer choices $10 for both firms $30 for both firms $50 for both...
Consider an industry that consists of two firms, Alpha and Beta, that produce identical products. Suppose...
Consider an industry that consists of two firms, Alpha and Beta, that produce identical products. Suppose that Alpha seeks to preempt Beta by making its capacity decision a year before Beta’s. Thus, by the time Beta makes its decision, it will have observed Alpha’s choice and must adjust its decision making accordingly. We will assume that each firm always produces at full capacity. Thus, expansion of capacity entails a trade-off. The firm may achieve a larger share of the market,...
Suppose the natural gas industry consisted of only two firms. Let these firms have identical cost...
Suppose the natural gas industry consisted of only two firms. Let these firms have identical cost functions, C(q) = 40q. Assume the demand curve for the industry is given by P = 100 − Q and that each firm expects the other to behave as a Cournot competitor. a) Calculate the Cournot-Nash equilibrium for each firm, assuming that each chooses the output level that maximizes its profits when taking its rival’s output as given. What are the profits of each...
Suppose there are only two firms in the market, firm 1 and firm 2. They produce...
Suppose there are only two firms in the market, firm 1 and firm 2. They produce identical products. Firm 1 has a constant marginal cost where AC1 =MC1 =20, and firm 2 has a constant marginal cost AC2 =MC2 =8. The market demand function is given by Q = 100 - 0.5P. a) Find the Cournot Nash Equilibrium price and quantity, write down the profits for each firm. (Use "q1" to represent output level for firm 1, and "profit1" to...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT