Question:
Suppose firm 1 and firm 2 merge. Call the new firm A. It has output xA and profit πA. Suppose there is Cournot competition after the merger. For now, we assume that the marginal cost of Firm A, the merged firm, still is 40 (the same as firm 3).
e) Compute quantities for both the merged firm and firm 3. Also, compute the market price and profits.
f) Is the total quantity produced (and sold) larger or smaller than before?
g) Compare the initial sum of profits of the two individual firms, π1 + π2, with the profits of the merged firm, πA. Explain and comment.
If the merged firm were able to exploit economies of scale it would affect costs, maybe even marginal costs. Assume that the marginal cost of the merged firm (only!) was not 40, but 30.
h) Is the merger profitable in this case? What happens to the non-merged firm's (firm 3) profits compared to the original situation with 3 firms?
i) Can you say something about how much reduction in the merged firm's MC must be able to achieve for the merger to become profitable?
j) Relate this to a real-world merger. Are they usually profitable? Can you give examples? Are there other things to consider than marginal cost?
Summary:
Questions related to the previous scenario of 3 firms is continued in this answer. The question is that if two firms in the Cornout market merge into one firm, what would the merger result in? how much of marginal cost would prevail in the market, etc are answered in a detailed in manner in the solution.
Answer:
(a) P = 200- xa- x3
ð Pxa = 200xa - xa2 - xax3
ð MRa = 200 - 2xa - x3
under FOC,
200 - 2xa - x3 = 40
ð xa = (160 - x3)/2
Again, due to symmetry, xa = x3
ð xa = (160 - xa)/2
ð xa = 160/3 = x3
ð X = 320/3
ð P = 200 - 320/3 = 280/3
ð πa = π3 = (280/3)*(160/3) - (160/3)*40 = 25600/9
ð π= 51200/9
(b) X = 120 and X' (new level) = 320/3
Clearly, X'< X
(c) π1 + π2 = 3200
πa = 25600/ 9 = 2844.44
The profits of the merged firm are below that of the sum of the individual firms earlier. This happens mainly because of the fact while total production decreases; there is no decrease in the cost of production. The price has increased, but the effect of decline in quantity sold exceeds that of the increase in price.
If the merged firm were able to exploit economies of scale it would affect costs, maybe even marginal costs. Assume that the marginal cost of the merged firm (only!) was not 40, but 30.
(d) The reaction curve of firm A now becomes:
xa = (170-x3)/2
The reaction curve of firm 3 is:
x3 = (160 - xa)/2
Solving it, we find:
xa = 60 and x3 = 50
Therefore, P = 200 - 110 = 90
Therefore, πa = 90*60 - 30*60 = 3600 and π3 = 50*90 - 40*50 = 2500
The profit of both, firm A and 3, increases.
(e) Suppose marginal cost for A = n
Then the reaction functions are:
xa = (200-n-x3)/2
The reaction curve of firm 3 is:
x3 = (160 - xa)/2
Solving it,
xa = (240-2n)/3, x3 = (240+2n)/6
Therefore, x = (360 - n)/3
Therefore, P = 200 - (360 - n)/3
ð P = (240 +n)/3
Now, for firm A,
{(240 +n)/3}*{(240-2n)/3} - {(240-2n)/3}*n = 3200
ð (240-2n)/3 [(240 +n)/3 - n] = 3200
ð (240 -2n)2 = 3200*9
ð 240 - 2n = 169.7
ð n = 35.15
So, below the MC of 35.15, the firm will make more profits than earlier.
(f) Mergers usually happen between the firms which are equal level of revenue. Also, they are usually profitable but not always. The merger of Towers Perrin and Watson Wyatt in 2010 is an excellent example which shows how the profits increase after merger.
However, transition and management changes are also important apart from marginal cost. The management and work ethics transitions have to be smooth so that the functioning of the firm in general and productivity of the workers in particular is not adversely affected.