Consider a homogeneous good duopoly with linear demand P(q) = 12- q,where q is the total industry output, and constant marginal costs c = 3.

1. Suppose that firms simultaneously set quantities. Determine the equilibrium (price, quantities, profit, welfare).

2. The firms consider to merge although their production costs are not affected. Determine the optimal price and quantity after merger.

3. Is such a merger profitable?

4. What are the welfare effects of such a merger?