COMPETITION, MONOPOLY, AND THE INCENTIVE TO
INVENT
Y. K. NG
University of N e w England
I
The purpose of this note is to make a methodological comment on Demsetz’s
criticism of Arrow in a recent paper.l Arrow argues that the incentive to
invent is greater under competitive than under monopolistic conditions.
Demsetz argues that Arrow’s deduction is false. We shall show that the
argument of Demsetz is questionable. However, we are not concerned with
the comments of Kamien and Schwartz, and Yamey.*
In the following section we show that incentive to invent is actually greater
under competition. In section 111, we discuss the effects of expectations on the
conclusion.
I1
Arrow’s assumptions and conclusions are best set out in his own words.
“I will examine here the incentives to invent for monopolistic
and competitive markets, that is, I will compare the potential profits
from an invention with the costs. The difficulty of appropriating the
information will be ignored; the remaining problem is that of indivisibility in use, an inherent property of information. A competitive situation here will mean one in which the industry produces
under competitive conditions, while the inventor can set an arbitrary
royalty for the use of his invention. In the monopolistic situation, it
will be assumed that only the monopoly itself can invent. . . . It will
be argued that the incentive to invent is less under monopolistic than
under competitive conditions but even in the latter case, it will be
less than is socially de~irable.”~
1 H.
Demsetz, “Information and Efficiency: Another Viewpoint”, Journal of Law and
Economics, 12, 1969. Cf. K. J. Arrow, “Economic Welfare and the Allocation of
Resources for Invention”, in National Bureau of Economic Research, The Rate and
Direction of Inventive Activity: Economic and Social Factors (Princeton University
Press, 1962).
*M. I. Kamien and N. L. Schwartz, “Market Structure, Elasticity of Demand and
Incentive to Invent”, Journal of Law and Economics, 13, 1970; B. S. Yamey,
“Monopoly, Competition and Incentive to Invent: A Comment”, Journal of Law and
Economics, 13, 1970.
3 AKOW,up. cit., p. 619.
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The argument of Arrow and the counter-argument of Demsetz may be
shown in Figure 1, which is similar to Demsetz’s Figure 2. Let c and c‘,
respectively, be the per unit cost of production (assumed constant by Arrow)
before and after the invention. The inventor selling to a competitive industry
sets the per unit royalty, p’ - c‘, so as to maximize the rectangle, p’c‘xy. This
results in a price, p’, and marginal revenue, M R , equals c‘. The inventor would
be willing to invest in inventing if the cost of the invention to him is less than
p’c‘xy, his royalty.
In the case of monopoly, however, the monopolist has a profit of pcut
before the invention. After the invention, his profit would be p’c‘xy. Hence
he would invent only if the cost is less than p’c‘xy-pcut. Hence Arrow
concludes that the incentive to invent is less under monopoly.
Demsetz criticizes Arrow on two counts. First, “Arrow’s inventor not only
produces an invention but, in addition, he possesses the monopoly power to
This
discriminate in the royalty charges he sets for the two indu~tries”.~
criticism may be dismissed out of hand. The two industries (monopolistic and
competitive) postulated by Arrow do not exist simultaneously: they are
mutually exclusive hypothetical alternatives. What Arrow tries to show is that
incentive to invent under competition is greater than it would be if the industry
FIGURE 1
4
Op. cif., p. 16.
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COMPETITION, MONOPOLY, AND INCENTIVE TO INVENT
47
were monopolized. Moreover, under Arrow’s assumptions (see the quotation
above), the monopolist himself only can innovate. Hence there is no question
of a royalty charge in the case of monopoly.
We come now to Demsetz’s second and more interesting criticism. He
argues that, in discussing the incentive to invent, we must isolate the normal
restrictive effect of monopoly on output. Hence he defines M R in Figure 1 to
be the demand curve facing the competitive industry, and the demand curve
of the monopolist remains the same, i.e., D . Then, for any given constant unit
cost, both the monopoly and the competitive industries will produce the same
rate of output. In this case, the incentive to invent in the monopoly industry is
p’c’xy -pcut, whilst that for the competitive industry is p’c‘wv, which is
proved to be smaller for the linear case.5. Demsetz then concludes that “the
incentive to invention is just the reverse of what Arrow concluded”.6
It seems to me that Demsetz’s method of isolating the restrictive effect of
monopoly on output is questionable. The pre-invention output levels of
competition and monopoly are equalized, but the post-invention levels are
not; the monopoly output ( p ’ y ) is twice that of the competition output ( p ’ v ) .
This causes a bias in favour of monopoly. In fact, Demsetz is able to show
that the incentive to invent is higher under monopoly than under competition
precisely because the post-invention output is greater under monopoly. We
wish to argue that, if both the pre-invention and post-invention output levels
are equalized, as devised in the following paragraph, Arrow’s conclusion that
the incentive to invent is smaller under monopoly is valid.
Consider Figure 2, which is similar to Figure 1. The monopoly output after
the invention is p’y. To equalize competition and monopoly output, assume
D to be the demand curve for both the monopoly and competitive industries.
Hence, p’y is also the output under competition. Now consider another invention which would reduce the cost further to c”. The post-invention output
(from now on we are referring to the second invention) will be the same for
both industries, i.e., p”r. We are thus considering a case where both the preinvention and post-invention outputs, prices and elasticities of demand‘ are
the same for both industries, and hence eliminating the bias in favour of any
industry.
Now the incentive to invent is measured by p”d’zr - p’c‘xy in the case of
monopoly. The corresponding magnitude for competition is p”d’zr. The difference is due to the fact that, in the case of competition, a new inventor will not
take the loss of the old inventor (p’c‘xy) into account, whilst the loss of monoEDemsetz, o p . cit., pp. 20-21.
B o p . cit., p. 17.
’For the effect of the elasticity of demand, see Kamien and Schwa-,
o p . cit.
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FIGURE 2
Q
polistic profit, p'c'xy, will be taken into account. As p"d'zr is clearly greater
than p"C'zr - p'c'xy, we have re-established Arrow's conclusion. In general,
it may be said that the monopolist will hesitate to undertake an invention
because of his existing excess profit, but there is no such limitation in the case
of competition. It would thus be rather surprising if the incentive to invent
could be greater under monopoly.s It, therefore, should be a relief to most
economists that this has been shown to be false.
I11
In the above discussion and that of Arrow and Demsetz, the problems of
time and expectations have not been taken into account. In practice, of course,
the amount of incentive depends on how long the expected return from the
invention will 1ast.O If this aspect of the problem is taken into consideration,
it seems that monopoly acquires higher marks than in the static case.
Consider Figure 2 and redefine c as the present unit cost of production.
Both industries produce output, cu, with the monopolist earning profits of
pcut and the competitive industry paying the same amount of royalty to the
We are here abstracting, as Arrow and Demsetz do, from the possible practical difficulties for the inventor under competition to collect the royalty.
9 I am grateful to the referee who drew my attention to this problem.
8
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COMPETITION, MONOPOLY, AND INCENTIVE TO INVENT
49
previous inventor. Now in considering an invention A which will reduce unit
cost to c', the inventor will not only take account of the size of p'c'xy, but also
of the length of time for which the benefit of this invention will last. In particular, if there is another invention, B, which reduces the cost further to c",
invention A will no longer yield any return. However, if invention B is
bound to happen in a certain time, say, five years hence, in both the monopolistic and the competitive case, our conclusion in section I1 is still valid.
The inventor in the competitive case values the invention at five times p'c'xy,
and the monopolist values it at five times (p'c'xy - pcut). Hence the incentive to invent is still higher in the competitive case.
Nevertheless there is another point which must be considered. The monopolist will undertake or buy the invention only if it is profitable for him to
do so. Otherwise, he can delay or refuse to undertake the invention. On
the other hand, in the case of competition, the new inventor B will carry out
the invention if it is profitable for him to do so. He will consider the size
of p"c"zr and the date and effectiveness of a future invention. But he will take
no account of p'c'xy which measures the loss of royalty to the inventor A.
This likely behaviour of the future inventors will influence the expected
returns of the present inventor. Thus, whilst both the monopolist and inventor
A are subject to the risk of a future invention, the uncertainty faced by the
monopolist is somewhat reduced by his control, to some extent, of the future
invention.
It is, however, dangerous to conclude that the next invention will come
faster under competitive conditions, so that the present incentive to invent is
less than in the monopoly case. This is because the next inventor must also
take into account the likelihood of yet another invention so that he will be
reluctant to commit himself unless he is pretty sure of the gain. Thus the
outcome depends on the expectations of the present inventor which in turn
depends on his expectation of the expectation of the next inventor, and so on.
With this complication, it is difficult to say a priori that returns from investment will last longer or shorter than in the monopolistic case. What perhaps
can be said is only that uncertainty is higher.
From the above discussion, it seems that, with respect to the amount of
incentive to invent, monopoly ranks higher than competition because of lower
uncertainty, but at the same time ranks lower than competition because of the
lower return per period. Without precise knowledge of the relative strengths of
the two opposite forces, we cannot say unequivocally which market structure
is superior with respect to the amount of incentive to invent.