Consider two quantity-setting firms that produce a homogenous good and choose their quantities simultaneously. The inverse demand function for the good is given by P = a - q₁ - q₂, where q₁ and q₂ are the outputs of firms 1 and 2 respectively. The cost functions of the two firms are C₁ (q₁) = c₁q₁ and C₂ (q₂) = c₂q₂, where c₁ < a and c₂ < (a + c₁) / 2.

1. Compute the Nash equilibrium of the game. What are the market shares of the two firms?

2. Given your answer to (1), compute the equilibrium profits, consumer surplus, and social welfare.

3. Prove that if c₂ decreases slightly, then social welfare increases if the market share of firm 2 exceeds 1 / 6, but decreases if the market share of firm 2 is less than 1 / 6. Give an economic interpretation of this finding.