Consider a market with linear inverse demand P = a- Q, where Q = q1 + q2 + q3.

Firms 1 and 2 are private firms. Each one's objective is to maximize its own profit. They have zero fixed cost and zero variable cost.

Firm 3 is a public firm, its objective is to maximize Social Surplus. It has zero fixed cost, but constant marginal cost given by c.

Calculate the equilibrium quantities, price, profit and social surplus levels if these firms choose their quantities simultaneously.