Acquisitions of Up-Start Firms by Incumbents: Large software companies often produce a variety of different software, and sometimes a small up-start develops a competing product. The large firm then faces a decision of whether to compete with the up-start or whether to “acquire” it. Acquiring an up-start firm implies paying its owners to give up and join your firm. Since the two firms will jointly make less money than the merged firm can make on this product, the two parties have to negotiate an acquisition price. What price will emerge will depend on the market conditions the firms face as well as the way the bargaining unfolds. In end-of-chapter exercises 24.5 and 24.9, we discussed two bargaining models that we apply here. In the first, known also as an ultimatum game, one firm would make a take-it-or-leave-it offer, and the other either accepts or rejects. In the second, the parties make alternating offers until an offer is accepted.2 you should have concluded that they will split the gains equally. Assume these bargaining outcomes throughout this exercise.
A: Suppose that the firms face a linear downward sloping demand curve, the same constant marginal cost and no recurring fixed costs.
(a) Let Y denote the overall gain in profit to the industry if an acquisition deal is cut. How is
Y divided between the firms under three bargaining environments: An ultimatum game in which the incumbent firm proposed an acquisition price, an ultimatum game in which the up-start firm proposes the price and an alternating offer game.
(b) Which of your answers in (a) might change if firm 2 is very impatient while firm1 can afford to be patient?
(c) Let Y B represent the overall gain in profit when the alternative to a deal is Bertrand competition; let Y C represent the same when the alternative is Cournot competition and let Y S represent the same when the alternative is Stackelberg competition. Which is biggest? Which is smallest?
(d) Let πM denote monopoly profit; let πC denote one firm’s Cournot profit; and let πSL and πSF denote the Stackelberg leader and follower profits. In terms of these, what will be the acquisition price under the three bargaining settings if the alternative is Bertrand competition? What about if the alternative is Cournot competition or Stackelberg competition?
(e) Which of these acquisition prices is largest? Which is smallest?
(f) Do you think acquisition prices for a given bargaining setting will be larger under Cournot competition than under Stackelberg competition? Does your answer depend on which bargaining setting we are using?
(g) If part of the negotiations involves laying the groundwork to set expectations about what kind of economic environment will prevail in the absence of a deal, what would you advise the upstart firm to say at the first meeting with the incumbent? Do your answers depend on what kind of bargaining environment you expect?
(h) Would your advice be any different for the incumbent?
B: Let firm1 be the large incumbent firm and firm2 the up-start firm. Assume they have no recurring fixed costs and both face the same constant marginal cost c. The demand for the product is given by x (p) = A−α p.
(a) Suppose the firms expect to be Bertrand competitors if they cannot agree on an acquisition price. If firm1 is the proposer in the ultimatum bargaining game, what is the sub game perfect acquisition price? What if firm2 is the proposer?
(b) What is the acquisition price if the two firms engage in the alternating offer game?
(c) Repeat (a) for the case where the two firms expect to be Cournot competitors.
(d) Repeat (b) if the two firms expect to be Cournot competitors. How does it compare to the answer you arrived at in (b)?
(e) Repeat (a) if the two firms expect firm1 to be a Stackelberg leader?
(f) Repeat (b) if the two firms expect firm1 to be the Stackelberg leader?
(g) Suppose A = 1000, c = 40 and α = 10. What is the acquisition price in each of the cases you analyzed above? Can you make intuitive sense of these?