Question

Consider a Bertrand duopoly. Market demand is P(Q)=41-3Q, and each firm faces a marginal cost of $6 per unit. What is the sum of both firms' revenue in the Nash equilibrium? Enter a number only, no $ sign.

Answer 1

$70.14

Step-by-step explanation:

The Bertrand duopoly condition (Nash equilibrium condition) be: P =MC

Here, P = 41 - 3Q

P = MC

41 - 3Q = 6

3Q = 41-6

3Q = 35

Q = 35 / 3

Q = 11.6667

Q = 11.67

Total demand (Q) = Q1 + Q2 (Q1 = Firm 1 Output, Q2 = Firm 2 Output)

Q = Q1 + Q2

11.67 = Q1 + Q2

So price be: P = MC ==> P = 6

Sum of both firm revenue = (Price)*Total quantity)

= $6 * (Q)

= $6 * (Q1 + Q2)

= $6 * (11.69)

= $70.14

So therefore, the sum of both firms' revenue in the Nash equilibrium is 70.14