The Optimum Lag of Imitation Behind Innovation

This file is a single-author theoretical essay, originally contributed to a volume honoring Fredrik Zeuthen. Machlup’s scope is deliberately precise: he defines innovation as the first productive application of a new idea and imitation as later adoption by other producers, then asks what lag between the two best promotes productivity. His thesis is that neither instant imitation nor prolonged monopoly is socially desirable; the productive economy needs a lag long enough to make innovation worth undertaking, but short enough for diffusion to realize the gain.

In other words, competitive imitation after some, not too extended, interval not only is the vehicle by which technological advance becomes effective as a general increase in productivity, but it is also a spur to innovation and thus helps towards there being more to imitate.

The essay first contrasts monopoly worlds, where imitation is irrelevant, with multi-firm industries, where diffusion determines whether productivity gains become general. Machlup’s central conceptual move is to treat imitation not as a mere threat to invention, but as both the mechanism of social benefit and a source of competitive pressure. Too little imitation dulls incentives; too much, if instantaneous, destroys the expected profits needed to finance risky development.

He then formalizes the problem through sunk costs, quasi-rents, discounting, and expected imitation lags. The innovator bears research, development, experimentation, and implementation costs that imitators need not repeat; the temporary surplus earned before competition erodes price is the quasi-rent. Innovation is undertaken only when expected quasi-rents over the lag are sufficient, in present value terms, to cover sunk costs.

An innovation will pay for itself if the quasi-rents received over the years of the imitation lag will fully cover the sunk cost of innovation.

This model reframes patents as devices for extending the expected life of quasi-rents, not as simple rewards for invention. But Machlup stresses that formal patent duration and effective protection diverge. Circum-invention and substitutes may destroy rents before a patent expires; conversely, trademarks, goodwill, and market entrenchment may extend rents beyond it. Because distant income is heavily discounted and increasingly uncertain, very long patent terms add little incentive while delaying diffusion.

The section on variable patent terms grants the strongest possible case for tailoring protection to each project, then shows why it fails. Innovations differ radically in cost and payoff:

Any uniform period of protection fixed for all kinds of projects must needs be too long for some and too short for others.

Yet a perfectly adjustable system would require impossible governmental foresight about costs, rents, interest rates, substitutes, and innovators’ expectations. With zero interest it could justify absurdly long monopolies; with positive interest the added value of remote patent years quickly disappears. The policy problem therefore cannot be solved by mechanically “fitting” protection to every invention.

Machlup next shifts from project-level adequacy to social optimality. A fixed patent term might be designed to induce some desired total amount of innovative outlay, but it would also delay imitation for innovations that needed less protection. The cost is the postponed general use of better methods. His most subtle argument concerns expectations: if innovators optimistically expect a longer rent period than actually occurs, society may obtain both innovation and rapid diffusion. Pessimism leaves profitable social advances untried.

To buy innovation by paying with unnecessarily long delays of imitation is a poor bargain for society to make.

The later discussion adds that patent duration itself may alter the distribution of effective rent periods. Longer terms can stimulate costly inventing-around, causing earlier rent termination in some cases, while also allowing other innovators to entrench themselves for longer. Thus longer protection may be simultaneously ineffective as an incentive and wasteful as a barrier to imitation.

Machlup ends without deriving a numerical optimum. The relevance of the essay lies instead in its critique of the simple pro-patent assumption that more protection means more innovation. Productivity growth depends on a balance between expected private recovery and rapid social diffusion, and the balance likely lies much nearer the innovator’s natural head start than conventional patent terms.

One must suspect that governmental intervention to delay imitation for periods of 16 years or longer is an ineffectual and wasteful way of promoting innovation.