Two firms produce a homogeneous product for a certain market

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Two firms produce a homogeneous product for a certain market. Firm 1 produces Q₁ and Firm 2 produces Q₂. The two firms are price takers, and the market price is P = 15. The total costs of producing Q₁ and Q₂, respectively, are

C₁ = .1 Q₁²+ 5 Q₁ - .1 Q₁ Q_2. (total costs borne by Firm 1)

C₂ = .2 Q₂² + Q₂ + .1 Q₂ Q_1. (total costs borne by Firm 2)

a).Which firm is a source of positive externalities, and which is a source of negative externalities, if any? (Careful!) Explain briefly.

b.)Suppose that each firm chooses its own output so as to maximize its own profits, taking the output of the other firm as given. (No remedial action is taken against the externalities.) Calculate the levels of output that each firm will choose.

c.)How would you characterize (conceptually label) the solution you have obtained in part b? Explain briefly.

d.)Suppose that the two firms merge (thus internalizing the externalities), and that their objective is to maximize joint profits. Calculate the new levels of Q₁ and Q₂ that would be chosen.

e.)Compare the values of Q₁ and Q₂ in parts b and d, using as intuition your answer in part a. If there are no additional distortions in the market system, will total social welfare be higher under the assumptions of part b or those of part d? Explain.