There are two firms that engage with a Cournot competition with the inverse demand curve given by P=1000-5Q. Suppose the two firms have constant marginal costs $5 and $10.
a). Write down the profit function for each firm
b). Firm 2 produces 10 units, what is the quantity for firm 1 that maximizes it profit?
c). Firm 1 produces 15 units, what is the quantity for firm 2 that maximizes its profit?
d). Please find the Nash equilibrium.
e). What is the price at the Nash equilibrium? Profits?