Question

You are given the following​ best-response functions for duopoly firms playing a Bertrand​ price-setting game:

p₁ = 25 + 0.5m₁ + 0.25p₂ and p₂=25+0.5m₂+0.25p₁ ​, where m1 and m2 are the marginal costs for firm 1 and firm 2 respectively.
Let m₁ =.............m=..............$10. Solve for the Bertrand equilibrium prices.

Answer 1

To solve for the Bertrand equilibrium prices in a duopoly, substitute the given values of marginal costs into the best-response functions and solve the simultaneous equations.

Step-by-step explanation:

To solve for the Bertrand equilibrium prices, we need to determine the values of p₁ and p₂. We are given the best-response functions p₁ = 25 + 0.5m₁ + 0.25p₂ and p₂ = 25 + 0.5m₂ + 0.25p₁. Substituting the given value of m₁ and m₂, which is $10, into the equations, we get p₁ = 25 + 0.5(10) + 0.25p₂ and p₂ = 25 + 0.5(10) + 0.25p₁. Solving these two simultaneous equations will give us the Bertrand equilibrium prices.