Question

Consider a duopoly market in which the market demand function is as follows: \( P = 40 - Q \). For the two firms producing with identical marginal costs of 10, the Bertrand-Nash equilibrium price will be:

• A. 40
• B. 10
• C. 20
• D. 30

Hint:

In a Bertrand-Nash equilibrium, firms with identical products and costs set prices equal to their marginal costs.

Answer 1

The Correct Option is B

In a Bertrand-Nash equilibrium with identical products and marginal costs, firms set their prices equal to marginal cost in order to avoid losing customers to the competitor. Since the marginal cost for both firms is 10, the Bertrand-Nash equilibrium price will be 10.
Step 1: The market demand function \( P = 40 - Q \) is given. At equilibrium, the price is set equal to the marginal cost.
Step 2: Since both firms have identical marginal costs of 10, they will both set their price at 10.
Step 3: Conclusion.
Thus, the Bertrand-Nash equilibrium price is 10.
Final Answer: (B) 10