COMPETITION, MONOPOLY AND THE INCENTIVE
TO INVENT: A REPLY
YEW-KWANG NG
Monash University
In a recent paper in this journal,’ Davis makes four separate comments on my paper
“Competition, Monopoly and the Incentive to Invent”.’ I accept one and wish to question
the validity of the other three. My conclusion stands despite his comments (including the
one I accept as a good point).
The controversy concerns “Arrow’s model . . . of a comparison of the magnitude of
the incentive to invent, in an industry with constant costs under conditions of alternatively
perfect competition and monopoly. If the former market structure prevails the inventor
is a profit maximizer (independent of the firms competing in the product market) who,
upon producing a cost-reducing invention, sells his knowledge to the competing firms for
a royalty . . . per unit of production. His incentive to invent is his total royalty receipts.
If the product market is monopolistic, the inventor is the monopolist, and his incentive
to invent is the increase in monopoly profits resulting from lower cost^."^
Arrow shows that the incentive to invent is greater under competition. Demsitz
reverses this conclusion by doubling the demand curve facing the monopolist so as to
equate the pre-invention outputs under competition and monopoly. However, by so doing,
the post-invention output is greater under monopoly. To equate pre-invention, postinvention outputs, the elasticities of demand and the demand curves themselves, I consider
in my previous paper a second invention and re-establish Arrow’s conclusion. Davis comments on my argument on four points which are briefly discussed below.
First, Davis asserts that my method “only works for a succession of drastic inventions.
It fails in the case of non-drastic inventions, which casual empiricism would suggest are
the more f r e q ~ e n t ” .While
~
agreeing with this casual empiricism, it may be noted that
the case of drastic invention is used mainly to simplify analysis. For non-drastic inventions,
it is difficult to hold both pre-invention and post-invention outputs the same for competition and monopoly. By holding pre-invention outputs the same, a non-drastic invention will lead to a higher output under competition. However, the conclusion that
Kevin Davis, “Competition, Monopoly and the Incentive to Invent - A Comment”, Australian
Economic Papers, vol. 14, 1975.
Australian Economic Papers, vol. 10, 1971.
Davis, op. cit., p. 128.
fbid., p. 130, “A non-drastic invention (when the reduction in cost is relatively small) is defined as
those situations where the inventor’s profit-maximizing royalty charge to the competitive industry
is constrained by the necessity that the new unit cost of production plus the royalty charge must
be no greater than the old unit cost of production. If this constraint is ineffective, the invention is
termed drastic.” (pp. 128-9).
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1977
COMPETITION, MONOPOLY
155
incentive is greater under competition may be established for this case by showing that
the incentive is greater under competition than monopoly by a larger proportion than the
post-invention output is greater under competition than monopoly.
Examine Figure 1 where the first invention reduces the (constant) unit cost of product
from c t o c' so that output under both competition and monopoly i s y , with the competitors paying the per unit royalty p' c' to the first inventor. Consider a second nondrastic invention that would reduce cost to e". For the case of competition, the maximum
rate of royalty this second inventor can charge is c' c', and hence his incentive is measured
by the rectangle c' c" ws. For the case of monopoly, the incentive is p" c" zr - p' c' xy.
It is not difficult t o show that this equals the area c' c" zx,' which is smaller than the
incentive under competition of c' c" ws by a larger proportion than the ratio of post invention outputs, i e., c"z/c"w.
FIGlJRE 1
D
Secondly, Davis argues that I overlook the fact that, while the monopolist has only to
reduce cost from c' to c" in his second invention, the second inventor in the case of competition may have t o reduce cost from c t o c" since the knowledge of the first-invention
need not be available t o him. This I take to be a valid contribution by Davis. However, I
would not say that this invalidates my conclusion. According t o the measures of incentive
given by Davis as quoted in the second paragraph of this paper, my conclusion that the
incentive t o invent is greater under competition is still valid. What Davis correctly points
out is that the cost of making the invention may also be greater. To what extent is this
significant depends on whether the knowledge of the first invention is known by the
second inventor. For many cases, such knowledge is available but the first inventor may
'
Either by noting that p' p" ry = xzry, or by noting that the extra profit is measured by the difference
between C' and C' until C' cut the MR curve, after which the extra profit is measured by the
difference between MR and C".
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AUSTRALIAN ECONOMIC PAPERS
JUNE
still get royalty through patent rights. But the fact that commercial users of the first
invention have to pay royalty does not necessarily mean that a second inventor will be
prevented from using the knowledge in his second invention. For such cases, the cost
differential in invention between monopoly and Competition may be trivial.
Thirdly, “A more important criticism of Ng’s approach is that there seems to be no
justification for equating post-invention industry sizes. The level of industry output after
the invention depends on the profit-maximizing behaviour of the inventor in both circumstances. Since this differs with the structure of the industry, there is no reason to expect
the post-invention industry sizes to be equal. While it may be theoretically plausible to
equate post-invention industry sizes, to do so is irrelevant if one wishes to study real world
events”.6 I agree that I would be hard put to give examples of “real world events” where
both pre-invention and post-invention industry sizes are equal, but they are held equal to
isolate the effect of market structure. I cannot see why this is theoretically plausible but
irrelevant. If we just hold pre-invention outputs and elasticities of demand constant, it
is debatable whether we have abstracted away all the irrelevant matters, as the demand
curve facing the competitive industry lies to the left of that facing the monopolist and
the post-invention output will be smaller under competition with royalty charge. For the
whole economy, an expansion in one industry signifies a contraction in some other
industries. It is difficult to have a fair comparison without holding post-invention outputs
equal as well.
Fourthly, Davis argues that my conclusion is invalid as I allow two or more inventors
when the product market is competitive and only one inventor (the monopolist himself)
under monopoly. “ . . . if the second invention is also made by the first inventor. There
is then no difference between the monopolistic and the competitive ~ i t u a t i o n . ”Arrow
~
assumes for a good reason that, for the monopoly case, only the monopolist himself can
invent. Even if some other person undertakes the invention, he has to sell his invention
to the monopolist to gain any revenue. The amount the monopolist is willing to pay for
the invention will still be affected by his existing profit. Hence there is no difference of
any consequence whether we assume someone else or the monopolist himself invents.
However, this is not the case for competition. A new inventor need not sell his invention
to the old inventor but may sell it to the competitors. The consequent loss in future
royalties to the old inventor will not be fully taken into account by the new inventor,
except in a fairyland of zero “transaction costs” where the old inventor can bribe the new
inventor without incurring any extra costs and without calling forth blackmailers pretending t o engage in new invention.8 Since, for the case of competition, the incentive to
invent is the same as the case of monopoly if the invention is undertaken by the first
inventor himself but the incentive is larger if undertaken by some other inventor, it
seems fair to conclude that the incentive to invent is larger under competition, as the
second invention may be undertaken by any other inventor as well as the first inventor.
*’
Davis, op. cit., p. 130.
Ibid.. p 131.
C j : , Ng, “Recent Developments in the Theory of Externality and the Pigovian Solution”, Economic Record, vol. 47, 1971, pp. 170-1, and the interchange between Swan, Walsh and myself in
The Economic Record, vol. 51,1915.