Question

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 the same 50 units, what is the Marginal Revenue for Firm A from this extra unit? Enter a number only, no $ sign.

Answer 1

Demand is given by :

P = 200 - Q where Q = Q_A + Q_B, Q_A = quantity produced by Firm A and Q_B = quantity produced by Firm B

Initially Q_A = 50 and Q_B = 50

=> P = 200 - Q = 200 - (Q_A + Q_B) = 200 - (50 + 50) = 100

Total Revenue = Price*Quantity.

So, when Firm A produces 50 units its revenue = P*Q_A = 100*50 = 5000

Now, Firm A increases production by 1 unit and thus firm A now produces 51 units and Firm B still produces 50 units. So, Q_A = 51 and Q_B = 50

=> P = 200 - Q = 200 - (Q_A + Q_B) = 200 - (51 + 50) = 99

Total Revenue = Price*Quantity.

So, when Firm A produces 51 units its revenue = P*Q_A = 99*51 = 5049

Marginal Revenue is the additional Revenue received when it increases production by 1 unit.

Here, when Firm A increases production from 50 to 51, Revenue increases from 5000 to 5049.

So, Marginal revenue for firm A from this extra unit = 5049 - 5000 = 49

Hence, Marginal revenue for firm A from this extra unit = 49