In a Bertrand competition with differentiated goods where firms set the prices sequentially, we have the following demand functions:
q1 is quantity of goods demanded for firm 1 q2 is quantity of goods demanded for firm 2 p1 and p2 are prices of goods for firm 1 and firm 2.
q1 = 16 - 2*p1 + p2 q2 = 16 - 2*p2 + p1
The marginal cost is 4. No fixed costs.
The profit function for firm 1 is: TR1 = p1*(16 - 2*p1 + p2) - (16 - 2*p1 + p2)*4
The profit function for firm 2 is: TR2 = p2*(16 - 2*p2 + p1) - (16 - 2*p2 + p1)*4
Firm 1 sets the price first, firm 2 sets the price after. It's a squential game.
How can I write the strategies of firm 2?
Isn't it just S(p1) = 6 + 1/4*p1 ?
How is p1 = p2 = 8 a Nash equilibrium?