but also that imitation is costly. No firm would invest in imitation knowing that it would
earn zero profits in the ensuing Bertrand eq~i l ibr ium.S~i milarly, we could suppose that
licensing is feasible, but that the antitrust laws prohibit no-competition clauses in licensing
contracts, or that such covenants are difficult to enforce. No firm would pay a positive
amount for a blueprint if the licensor were unable to commit itself to refrain from
subsequent entry into Bertrand ~ o m ~ e t i t i o n . ~
An entrepreneur may target her research efforts at any of the continuum of state-of-theart
products. If she undertakes R&D at intensity II for a time interval of length df, then
she will succeed in taking the next step up the quality ladder for the targeted product
with probability idt. This formulation mimics the one-shot, partial equilibrium, patentrace
models of Lee and Wilde (1980) and others. It implies that R&D success bears a
Poisson probability distribution with an arrival rate that depends only on the current
level of R&D activity.
We allow free entry into the race for the next generation product. A unit of R&D
activity requires a, units of labour per unit of time for both an incumbent and for
newcomers. That is, we implicitly suppose that potential entrants can, via inspection of
the goods on the market, learn enough about the state of knowledge to mount their own
research efforts, even if the patent laws (or the lack of complete knowledge about best
production methods) prevent them from manufacturing the current generation products.
This specification captures in part the often noted, public-good characteristics of
technology.
Without any cost advantage, industry leaders do not invest resources to improve
their own state-of-the-art products.' To see this, note that a research success would leave
the leader with a two-step advantage over its nearest competitor, and thus enable it to
increase its price to A ~ WT.h is would yield a flow of incremental profits equal to AT =
(1-l / h 2 ) -~( I - l /A)E = (1-l/A)E/A, which, however, is strictly less than the incremental
profits (1 -l/A)E that accrue to a non-leader who achieves a research success.
So leaders seeking to upgrade the quality of their own products cannot successfully
compete for financing with non-leaders. Put differently, a leader would strictly prefer to
devote any research funds it may raise to R&D aimed at developing a leadership position
in a second market rather than to R&D aimed at widening an existing lead in its own
market.
We consider now the entrepreneur's choice of industry in which to target R&D
efforts, and the optimal scale of those efforts. The prize for a research success in some
industry is a flow of profits that will last until the next success is achieved in the same
industry. We have seen that the profit flows T are the same for all industries w. Therefore,
an entrepreneur will be indifferent as to the industry in which she devotes her R&D efforts
provided that she expects her prospective leadership position to last equally long in each
one. We focus hereafter on the symmetric equilibrium in which all products are targeted
5. In Grossman and Helpman (1991), we develop a two-country model in which factor prices differ across
countries. Then imitation may be profitable in the low-wage country, because success in creating a clone yields
strictly positive profits to the imitator in the ensuing duopoly equilibrium.
6. As a referee has pointed out to us, if licensing were feasible and contracts unrestricted, an innovator
would always prefer to license her new technology to the nearest rival rather than to compete with that rival
in the product market.
7. This is essentially the same result as in Reinganum (1982). She shows that a challenger has greater
incentive to undertake risky R&D than an incumbent, in a one-shot patent race. Here, leaders do not undertake
R&D at all, because the supply of challengers is perfectly elastic. In Grossman and Helpman (1991) we assume
that leaders, by dint of their past R&D successes, are able to improve upon their own products at lower
(expected) cost than outsiders. With this modification of the model, we find equilibria with positive R&D by
both leaders and challengers.