Two businesses are located near each other and there are externalities from each firm's production on the other firm. The firms have the following total cost functions C₁ = 40g4092 +400 C₂ = 30q2 + 10q₁ + 109192 + 400 where firm 1 produces q₁ and firm 2 produces 92. These two firms operate in perfectly com- petitive markets where the prices for their outputs are p₁ = 800 and p2 = 1000 respectively. (a) Write down the profit function for firm 1 and determine the profit maximizing level of output. (2) (b) Write down the profit function for firm 2 and determine the profit maximizing level of output. (2) (c) Determine the socially optimal levels of output by maximizing the profit of a merged firm. (3) (d) Explain why the outputs in (c) are different from the outputs chosen in (a) and (b).
