Question

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 ___.

Answer 1

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