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 ???????? = 1,2,3. The firms produce with constant marginal costs given by ????1 = 1, ????2 = 1 and ????3 = 0. Fixed costs are zero for all firms. The inverse demand function in the market is given by ???? = 3 − ????, where ???? is the price of the product and ???? is total output, i.e., ???? =????1 + ????2 + ????3.
a) Compute the equilibrium quantities of the firms, the total equilibrium quantity, the equilibrium price, as well as the corresponding consumer surplus. (Mark 1.0)
b) 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?
c) 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 ???? = 1/2. Should this merger be allowed or prohibited by the competition authority, under the “consumer surplus” standard? Explain your answer.
[Marking scheme: economic intuition 30%, use of appropriate arguments 30%, correct application 20%, overall presentation 20%].