Solve for the Nash-Bertrand equilibrium for the firms described in Question 5.5 if Firm 1's marginal cost is \(\$ 30\) per unit and Firm 2's marginal cost is \(\$ 10\) per unit.

Data From Question 5.5:-

Suppose that identical duopoly firms have constant marginal costs of \(\$ 10\) per unit. Firm 1 faces a demand function of \(q_{1}=100-2 p_{1}+p_{2}\), where \(q_{1}\) is Firm 1's output, \(p_{1}\) is Firm 1's price, and \(p_{2}\) is Firm 2's price. Similarly, the demand Firm 2 faces is \(q_{2}=100-2 p_{2}+p_{1}\). Solve for the NashBertrand equilibrium.