IVE POSTED THIS QUESTION BEFORE AND I GOT THE SAME ANSWER! PLS DO NOT GIVE THE SAME ANSWER AGAIN!

Three firms, labeled 1, 2 and 3, compete in a homogeneous-good market by selecting production quantities. The quantity of firm i is denoted by q_i = 1,2,3. The firms produce with constant marginal costs given by c₁ = 1, c₂ = 1 and c₃ = 0. Fixed costs are zero for all firms. The inverse demand function in the market is given by P= 3 Q, where P is the price of the product and Q is total output, i.e., Q =q₁ + q₂ + q₃.

a) Consider the possibility of a merger between firms 1 and 2. Compute the market equilibrium under this scenario. Should such a merger be allowed or prohibited by the competition authority, under the consumer surplus standard? Explain your answer.

b) Consider again the possibility of a merger between firms 1 and 2. Assume now that the two firms merge also their R&D labs. As a result, efficiency gains are created. In particular, the merged entity produces its quantity at a lower marginal cost, given by c = 1/2. Should this merger be allowed or prohibited by the competition authority, under the consumer surplus standard? Explain your answer.