SOLVE THE FOLLOWING PROBLEM UNDER THE COURNOT DUOPOLY AND THE STACKELBERG DUOPOLY.

Let q₁ and q₂be the quantities of a homogeneous product produced by firms 1 and 2, respectively.

Let P(Q)=800-Q be the market price (the inverse demand equation)

Where: Q=q₁+q₂

Let C(q_i)=200q_ifor all i=1,2

Players: Company 1 and company 2.

Strategies: S_i=[0,) for all i=1,2

₁(q₁,q₂)= P(Q)*q₁-cq₁

The following is sought to establish the Nash equilibrium:

₁(q₁*,q₂*)> ₁(q₁*,q₂*) (1)

Equation (1) forms a Nash equilibrium for each firm if q_i^* is a solution of: