Optimal Timing of Innovations

Abstract

IT is widely recognized that when innovators are unable to realize the full benefits generated by their innovations the profit motive may not provide an incentive strong enough for them to innovate at the socially optimal rate. On the other hand, it has not been recognized that competition between potential innovators to obtain priority rights (and profits) from innovations can result in premature applications of discoveries. The basic knowledge used by innovators is a free public good. Were this knowledge owned, its proprietor would introduce an innovation at the time when its present value would be maximized. However, since the basic knowledge is costless to the innovator, he introduces a discovery when it first becomes profitable instead of waiting until profits are maximized. Basic knowledge is thus overexploited comparably to public roads, fisheries, and oil and water pools,1 although in this case the excessive use of resources takes the form of their premature application. A simple numerical example illustrates this proposition. Suppose that an outlay of $2000 is required to activate a given innovation which saves $1 per unit of output of a certain product. The innovator, referred to here as the individual (or group) that develops the innovation for commercial use, will set the royalty rate at $1. Suppose that the interest rate is 10 per cent and that output is 200 in year t and increases by 10 units every year. Table 1 indicates three alternative earning streams for the potential innovator with a capital stock of $2000. Line 1 is the earning stream obtained from innovating immediately. Since output in year t-4 is 160, at a royalty rate of $1 per unit total earnings that year are $160 and will increase with output at the rate of $10 per year. Line 2 is the earning stream obtained from keeping the $2000 invested elsewhere in the economy at 10 per cent. Line 3 is the earning stream if the sum is invested as in Line 2 until year t and then diverted to the innovation. Obviously, the innovator will be best off by selecting the earning stream indicated by Line 3. So will society as a whole, since Line 3 represents a dominant earning stream. However, as long as any competitor by innovating at t1 (or even earlier) could earn more than 10 per cent he has an incentive to push back the date of the innovation. If entry is not restricted we would expect the discovery to be