Question

Consider two companies A and Bsharing a market by producing identical goods (or highly substitutable goods). Company A’s marginal cost is MC=20and company B’s marginal cost is MC=10. Market demand is known to be P=100-0.001Q.

1. Find profit maximizing level of Q_Aand Q_Bunder oligopoly setting.
2. Determine the market price.
3. Determine the revenue of company A and B.
4. Determine the profit of company A and B.
5. Find collusive level of profit maximizing output for A and B(Under collusion A and B share the same MC=10and share the market equally).
6. Using a simple game theory method, show that the collusive outcome is not sustainable. Be sure to construct a 2x2 matrix with correct payoffs.

Answer 1

Since the companies are operating in a perfectly oligopolistic market as the goods are highly substitutable, and under oligopoly situation firm will operate until their Marginal Revenue is equal to Marginal Cost and Total Quantity Q= Q_a+Q_b, So Inverse Demand Function will be P= 100-0.001(Q_a+Q_b)

a. Profit maximizing level of output

Finding Marginal Revenue(MR) Curve

Marginal Curve has slope which is twice of Inverse Demand function (P=100-0.001Q)

So MR = 100 - .002Q

For firm A, MR = MC

(100-0.001Q_b)-0.002Q_a= 20

Q_a= 40000 - 0.5Q_b

and for Firm B, MR=MC

(100-0.001Q_a)-0.002Q_b=10

Q_b= 45000 - 0.5Qa

Solving above two equations

40000 - 0.5Q_b = 90000 - 2Q_b​

1.5Q_b = 50000

Q_b= 33333.33

Putting Value of Q_b in above equation

Q_a=40000-0.5(33333.33)

Q_a= 23333.33

b. The Market Price Will be

P = 100 - 0.001(33333.33 +23333.33)

P = 100 - 56.66

P = 43.34

c. Revenue Of Company A = P*Q_a = 43.34*23333.33 = 1011266.52

Revenue Of Company B = P*Q_b = 43.34*33333.33 = 1444666.52

d. Profit of Company A and B

The Price is 43.34

and MC for Company A = 20 , So profit = 43.34-20 = 23.34, Total Profit = 23.34*23333.33 = 544599.92

MC for Company B = 10 , So profit = 43.34-10 = 33.34, Total Profit = 23.34*33333.33 = 777999.92

Note - The Above Calculation is done using Cournot Model