The merger creates a synergy which reduces the marginal

Question

Question 1 -

Review the handout on Cournot mergers with asymmetric marginal costs and three firms. This question will get you to work through that example with numbers.

Suppose that inverse demand is P(q) = 100 - q₁ - q₂ - q₃. The constant pre-merger marginal costs of the firms are c₁ = 20; c₂ = 22 and c₃ = 20 and there are no fixed costs. Assume that these marginal costs are such that all three firms have positive output in equilibrium.

(a) Suppose that firm 1 plans to merge with firm 2. What are their pre-merger profits?

(b) The merger creates a synergy which reduces the marginal cost of the combined firm to a new lower level of 15. The industry now moves to a two firm Cournot equilibrium. Firm 3 has the same marginal cost as before the merger. Compute post-merger profits. Is the merger profitable?

(c) The merging parties employ an economic consultant who claims that the synergy (reducing the merged firm's marginal cost to 15) is so big that the merger will increase consumer surplus.

(i) Is this correct?

(ii) Find how big the synergy has to be to increase consumer surplus (i.e., find the values of the marginal cost of the merged firm which would make this true).

(d) Another consultant argues that the synergy (reducing the merged firm's marginal cost to 15) is so big that the merger will increase total welfare.

(i) Is this correct?

(ii) Find how big the synergy has to be to increase total welfare (i.e., find the values of the marginal cost of the merged firm which would make this true). [HINT: to do this part of the question you need to use the quadratic formula]

(iii) Describe the various ways in which the synergy affects total welfare.

Question 2 -

Consider an N firm symmetric Cournot model where aggregate inverse demand is P = 100 - 2Q, where Q is total output. For this question you can use the formulae for prices, outputs and profits that we used in class.

(a) Suppose that marginal costs are 10. What are profits per firm when there are 5 firms in the industry? What would be the level of per firm fixed costs that would make 5 firms an equilibrium outcome, assuming that firms do not stay in the market when they make losses and that more firms would enter if it was profitable to do so?

(b) Suppose that 2 of the firms merge, and after doing so the four remaining firms play the four firm equilibrium and no new firms enter.

(i) What happens to the combined variable profits of the merging firms?

(ii) And the combined variable profits of the non-merging firms? Explain what has happened.

(iii) While the merger was being proposed, would you expect the merging firms' competitors to be lobbying for or against the merger?

(c) Suppose the 3 non-merging firms remain stuck at their initial outputs (they face binding capacity constraints and costs of adjusting their output). What happens to the profitability of the merger now? Explain.

(d) Suppose that fixed costs are in the range that you found in part (a), and that new entry is possible after the merger has been completed, but before the firms set outputs. Would you expect a merger to lead to entry? How would this affect the profitability of the merger?