Gillette (firm 1) and Schick (firm 2) are the only two firms in the market for disposable razors

The market demand is

P = 95 - q1 - q2

Marginal Cost of firm 1 is

MC1 = 5

Hence, Total Cost of firm 1 is

C1 = 5.q1

Marginal Cost of firm 2 is

MC2 = 5

Hence, Total Cost of firm 2 is

C2 = 5.q2

? Under Cournot Duopoly,

• For firm 1,

Total Revenue is

R1 = P.q1 = (95 - q1 - q2).q1

or, R1 = 95.q1 - q1^?????2 - q1.q2

Marginal Revenue is

MR1 = dR1/dq1

or, MR1 = 95 - 2.q1 - q2

At profit maximization,

MR1 = MC1

or, 95 - 2.q1 - q2 = 5

or, q1 = 45 - 0.5.q2.........RF1

This is reaction function of firm 1.

• Similarly for firm 2,

Total Revenue is

R2 = P.q2 = (95 - q1 - q2).q2

or, R2 = 95.q2 - q1.q2 - q2^?????2

Marginal Revenue is

MR2 = dR2/dq2

or, MR2 = 95 - q1 - 2.q2

At profit maximization,

MR2 = MC2

or, 95 - q1 - 2.q2 = 5

or, q2 = 45 - 0.5.q1...........RF2

This is reaction function of firm 2.

Now, solving RF1 and RF2 reaction functions we get,

q1* = 30 and q2* = 30

Each firm will supply an output of 30 units.

Putting q1* = q2* = 30 in the market demand curve we get,

P* = 95 - q1* - q2* = 95 - 30 - 30

or, P* = $35

Market-clearing price will be $35.

Hence, the profit of each firm is

π = R - C

or, π = P.q - 5.q

or, π = 35×30 - 5×30

or, π = $900

Profit of each firm will be $900.

? Now, if firm 1 is the Stackelberg leader, them it will put reaction function of firm 2 (RF2) in his profit maximization problem. Hence,

Firm 1's Total Revenue is

R1 = P.q1

or, R1 = (95 - q1 - q2).q1

Putting q2 = 45 - 0.5.q1 we get,

R1 = (95 - q1 - 45 + 0.5.q1).q1

or, R1 = (50 - 0.5.q1).q1

or, R1 = 50.q1 - 0.5²

Hence, Marginal Revenue is

MR1 = dR1/dq1

or, MR1 = 50 - q1

At profit maximization,

MR1 = MC1

or, 50 - q1 = 5

or, q1° = 45

Firm 1 will supply an output of 45 units.

Putting q1° = 45 in RF2 we get,

q2° = 45 - 0.5.q1° = 45 - 0.5×45

or, q2° = 22.5

Firm 2 will supply an output of 22.5 units.

Putting q1° = 45 and q2° = 22.5 in the market demand curve we get,

P° = 95 - q1° - q2° = 95 - 45 - 22.5

or, P° = $27.5

The market-clearing price will be $27.5.