This PDF is a selection from an out-of-print volume from the National
Bureau of Economic Research
Volume Title: The Rate and Direction of Inventive Activity: Economic
and Social Factors
Volume Author/Editor: Universities-National Bureau Committee for
Economic Research, Committee on Economic Growth of the Social
Science Research Council
Volume Publisher: Princeton University Press
Volume ISBN: 0-87014-304-2
Volume URL: http://www.nber.org/books/univ62-1
Publication Date: 1962
Chapter Title: Economic Welfare and the Allocation of Resources
for Invention
Chapter Author: Kenneth Arrow
Chapter URL: http://www.nber.org/chapters/c2144
Chapter pages in book: (p. 609 - 626)
Economic Welfare and the Allocation of
Resources for Invention
KENNETH J. ARROW
THE RAND CORPORATION
INVENTION is here interpreted broadly as the production of know-
ledge. From the viewpoint of welfare economics, the determination
of optimal resource allocation for invention will depend on the tech-
nological characteristics of the invention process and the nature of
the market for knowledge.
The classic question of welfare economics will be asked here: to
what extent does perfect competition lead to an optimal allocation of
resources? We know from years of patient refinement that competition
insures the achievement of a Pareto optimum under certain hypotheses.
The model usually assumes among other things, that (1) the utility
functions of consumers and the transformation functions of pro-
ducers are well-defined functions of the commodities in the economic
system, and (2) the transformation functions do not display indivisibi-
lities (more strictly, the transformation sets are convex). The second
condition needs no comment. The first seems to be innocuous but
in fact conceals two basic assumptions of the usual models. It pro-
hibits uncertainty in the production relations and in the utility func-
tions, and it requires that all the commodities relevant either to pro-
duction or to the welfare of individuals be traded on the market. This
will not be the case when a commodity for one reason or another
cannot be made into private property.
We have then three of the classical reasons for the possible failure
of perfect competition to achieve optimality in resource allocation:
indivisibilities, inappropriability, and uncertainty. The first problem
has been much studied in the literature under the heading of marginal-
cost pricing and the second under that of divergence between social
and private benefit (or cost), but the theory of optimal allocation of
resources under uncertainty has had much less attention. I will sum-
marize what formal theory exists and then point to the critical notion
of information, which arises only in the context of uncertainty. The
NOTE: I have benefited greatly from the comments of my colleague, William Capron.
I am also indebted to Richard R. Nelson, Edward Phelps, and Sidney Winter of The
RAND Corporation for their helpful discussion.
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WELFARE ECONOMICS AND INVENTiVE ACTIVITY
economic characteristics of information as a commodity and, in
particular, of invention as a process for the production of information
are next examined. It is shown that all three of the reasons given above
for a failure of the competitive system to achieve an optimal resource
allocation hold in the case of invention. On theoretical grounds a
number of considerations are adduced as to the likely biases in the
misallocation and the implications for economic organization.'
Resource Allocation under Uncertainty
The role of the competitive system in allocating uncertainty seems to
have received little systematic attention.2 I will first sketch an ideal
economy in which the allocation problem can be solved by competition
and then indicate some of the devices in the real world which approxi-
mate this solution.
Suppose for simplicity that uncertainty occurs only in production
relations. Producers have to make a decision on inputs at the present
moment, but the outputs are not completely predictable from the in-
puts. We may formally describe the outputs as determined by the in-
puts and a "state of nature" which is unknown to the producers. Let
us define a "commodity-option" as a commodity in the ordinary sense
labeled with a state of nature. This definition is analogous to the differ-
entiation of a given physical commodity according to date in capital
theory or according to place in location theory. The production of a
given commodity under uncertainty can then be described as the
production of a vector of commodity-options.
This description can be most easily exemplified by reference to
agricultural production. The state of nature may be identified with the
weather. Then, to any given set of inputs there corresponds a number
of bushels of wheat if the rainfall is good and a different number if
rainfall is bad. We can introduce intermediate conditi.ons of rainfall
1
For other analyses with
similar points of view, see R. R. Nelson, "The Simple
Economics of Basic Scientific Research," Journal of Political Economy, 1959, pp. 297—306;
and C. J. Hitch, "The Character of Research and Development in a Competitive
Economy," The RAND Corporation, p. 1297, May 1958.
2
The
first studies lam aware of are the papers of M. Allais and myself, both presented
in 1952 to the Colloque International sur le Risque in Paris; see M. Allais, "Généralisation
des theories de l'équilibre économique général et du rendement social au cas du risque,"
and K. J. Arrow, "Role des valeurs bousières pour Ia repartition Ia meilleure des risques,"
both in Economèirie,
Colloques Internationaux du Centre National de Ia Reclierche
Scientifique, Vol. XL, Paris, Centre National de Ia Recherche Scientifique, 1953.
Allais'
paper has also appeared in Econometrica, 1953, pp. 269—290. The theory has received a
very elegant generalization by G. Debreu in Theory of Values, New York, Wiley, 1959,
Chap. VII.
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ALLOCATION OF RESOURCES FOR INVENTION
in any number as alternative states of nature; we can increase the
number of relevant variables which enter into the description of the
state of nature, for example by adding temperature. By extension of
this procedure, we can give a formal description of any kind of uncer-
tainty in production.
Suppose—and this is the critical idealization of the economy—we
have a market for all commodity-options. What is traded on each
market are contracts in which the buyers pay an agreed sum and the
sellers agree to deliver prescribed quantities of a given commodity
if
a certain state of nature prevails and nothing if that state of
nature does not occur. For any given set of inputs, the firm knows
its output under each state of nature and sells a corresponding quantity
of commodity-options; its revenue is then completely determined. It
may choose its inputs so as to maximize profits.
The income of consumers is derived from their sale of supplies,
including labor, to firms and their receipt of profits, which are assumed
completely distributed. They purchase commodity-options so as to
maximize their expected utility given the budget restraint imposed by
their incomes. An equilibrium is reached on all commodity-option
markets, and this equilibrium has precisely the same Pareto-optimality
properties as competitive equilibrium under certainty.
In particular, the markets for commodity-options in this ideal
model serve the function of achieving an optimal allocation of risk
bearing among the members of the economy. This allocation takes
account of differences in both resources and tastes for risk bearing.
Among other implications, risk bearing and production are separated
economic functions. The use of inputs, including human talents, in
their most productive mode is not inhibited by unwillingness or
inability to bear risks by either firms or productive agents.
But the real economic system does not possess markets for com-
modity-options. To see what substitutes exist, let us first consider a
model economy at the other extreme, in that no provisions for reallo-
cating risk bearing exist. Each firm makes its input decisions; then
outputs are produced as determined by the inputs and the state of
nature. Prices are then set to clear the market. The prices that finally
prevail will be a function of the state of nature.
The firm and its owners cannot relieve themselves of risk bearing in
this model. Hence any unwillingness or inability to bear risks will
give rise to a non optimal allocation of resources, in that there will be
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WELFARE ECONOMICS AND INVENTIVE ACTIVITY
discrimination against risky enterprises as compared with the opti-
mum. A preference for risk might give rise to misallocation in the
opposite direction, but the limitations of financial resources are likely
to make underinvestment in risky enterprises more likely than the
opposite. The inability of individuals to buy protection against un-
certainty similarly gives rise to a loss of welfare.
In fact, a number of institutional arrangements have arisen to miti-
gate the problem of assumption of risk. Suppose that each firm and
individual in the economy could forecast perfectly what prices would
be under each state of nature. Suppose further there were a lottery
on the states of nature, so that before the state of nature is known any
individual or firm may place bets. Then it can be seen that the effect
from the viewpoint of any given individual or firm is the same as if
there were markets for commodity-options of all types, since any
commodity-option can be achieved by a combination of a bet on the
appropriate state of nature and an intention to purchase or sell the
commodity in question if the state of nature occurs.
References to lotteries and bets may smack of frivolity, but we need
only think of insurance to appreciate that the shifting of risks through
what are in effect bets on the state of nature is a highly significant
phenomenon. If insurance were available against any conceivable
event, it follows from the preceding discussion that optimal allocation
would be achieved. Of course, insurance as customarily defined covers
only a small range of events relevant to the economic world; much
more important in shifting risks are securities, particularly common
stocks and money. By shifting freely their proprietary interests among
different firms, individuals can to a large extent bet on the different
states of nature which favor firms differentially. This freedom to in-
sure against many contingencies is enhanced by the alternatives of
holding cash and going short.
Unfortunately, it is only too clear that the shifting of risks in the
real world is incomplete. The great predominance of internal over
external equity financing in industry is one illustration of the fact that
securities do not completely fulfill their allocative role with respect
to risks. There are a number of reasons why this should be so, but I
will confine myself to one, of special significance with regard to inven-
tion. In insurance practice, reference is made to the moral factor as a
limit to the possibilities of insurance. For example, a fire insurance
policy cannot exceed in amount the value of the goods insured. From
the purely actuarial standpoint, there is no reason for this limitation;
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