Question

Horizontal Mergers. Consider a market that initially has two firms selling differentiated products and competing in prices. The cost of production of each firm is C(q)=0. Demand for the two goods is given by the following system: q1=420-4p1+p2 q2=420-4p2+p1 The goal of this question is to find by how much the prices of the goods will increase if the firms horizontally merge. To do this, we first derive the equilibrium prices before the merger, and then compare with the optimal prices set by the merged firm.

a) Firm 1’s profit maximization problem is to choose p1 so as to solve: max [p1 (420-4p1+p2)] p1≥0 Derive firm 1’s first order condition (differentiating this profit function with respect to p1).

b) Assuming in equilibrium p1=p2, find the equilibrium prices before the merger.

c) If the firms merge, and continue to sell the same two products, the merged firm chooses both prices choosing p1 and p2 so as maximize problem. Write the profit maximization problem.

d) Find the profit maximizing prices. You may assume that these prices are equal p1=p2.

Answer 1

In this question we are not given the costs, so we take total revenue as the sole profit criteria here.

We differenciate the equations to get the equilibrium prices/profit maximising prices.

before merger the profit maximising prices were $60 for both p1 and p2 while after the merger, the total revenues also merge and now profit maximising prices are $70 for p1 and p2.

NOTE: WE HAVE ASSUMED p1=p2 as given in the question itself along with profit maximising equation of firm1 from which profit maximising equation of both the firms when together was calculated.