Financing a Strategic Investment under Quantity Competition: Suppose you own a firm that has invented a patented product that grants you monopoly power. Patents only last for a fixed period of time — as does the monopoly power associated with the patent. Suppose you are nearing the end of your patent and you have the choice of investing in research that will result in a patented technology that reduces the marginal cost of producing your product.
A: The demand for your product is linear and downward sloping and your current constant marginal cost is MC. There is one potential competitor who faces the same constant MC. Neither of you currently face any fixed costs, and the competitor observes your output before he decides whether and how much to produce.
(a) If this is the state of things when the patent runs out, will you change your output level? What happens to your profit?
(b) Suppose you can develop an improved production process that lowers your marginal cost to MC′ (c) If MC′ is relatively close to MC, will you be able to keep your competitor out? In this case, might it still be worth it to invest in the technology?
(d) If the technology reduces marginal costs by a lot, might it be that you can keep your competitor from producing? If so, what will happen to output price?
(e) Do you think that investments like this—intended to deter production by a competitor—are efficiency enhancing?
(f) Suppose the potential competitor could also invest in this technology. Might there be circumstances under which your firm will invest and your competitor does not?
B: Suppose again that demand is given by x = A −αp, that there are currently no fixed costs, that all firms face a constant marginal cost c and that you are about to face a competitor (because your patent on the good you produce is running out).
(a)What will happen to your output level if you simply engage in the competition by producing first. What will happen to your profit?
(b) If you lower your marginal cost to c′ < c by taking on a recurring fixed cost FC, what will be your profit assuming that your competitor still produces. (If you have done exercise 25.4, you can use your results from there to answer this.)
(c) Suppose that A = 1000, c = 40 and α = 10. What is the highest FC can be for you to decide to go ahead with the investment if the new marginal cost is c′ < c and assuming the competitor cannot get the same technology? Denote this FC1 (c′).
(d) Now consider the competitor. Suppose he sees that firm1 has invested in the technology (and thus lowered its marginal cost to c′.) Firm 2 finds out that the patent on firm 1’s technology has been revoked—making it possible for firm 2 to also adopt the technology at a recurring fixed cost FC. What is the highest FC at which firm 2 will adopt the technology? Denote this FC2.
(e) Suppose c′ = 20. For what range of FC will firm1 adopt and firm 2 not adopt the technology even if it is permitted to do so?