Final answer:
The optimal quantity for a Cournot duopolist firm is determined by equating marginal revenue to marginal cost.
Step-by-step explanation:
The optimal quantity for a Cournot duopolist firm is determined by finding the quantity at which marginal revenue (MR) equals marginal cost (MC). In this case, since the firms operate at zero marginal cost, their marginal cost is zero. The market demand curve is given by p = a - bq, so the inverse demand function is q = (a - p) / b.
To calculate MR, we take the derivative of the inverse demand function with respect to q and multiply it by q. Equating MR to zero, we can solve for the optimal quantity.