Arrow-The_economic_implication_of_learning_by_doing

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The Review of Economic Studies, Ltd.

The Economic Implications of Learning by Doing

Author(s): Kenneth J. Arrow

Reviewed work(s):

Source:

The Review of Economic Studies,

Vol. 29, No. 3 (Jun., 1962), pp. 155-173

Published by: Oxford University Press

Stable URL: http://www.jstor.org/stable/2295952 .

Accessed: 21/11/2012 17:21

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The

Economic

Implications

Learning

Doing

It is by now incontrovertible that increases in per capita income cannot be explained

simply by increases in the capital-labor ratio. Though doubtless no economist would

ever have denied the role of technological change in economic growth, its overwhelming

importance relative to capital formation has perhaps only been fully realized with the

important empirical studies of Abramovitz [1] and Solow [11]. These results do not

directly contradict the neo-classical view of the production function as an expression of

technological knowledge. All that has to be added is the obvious fact that knowledge is

growing in time. Nevertheless a view of economic growth that depends so heavily on an

exogenous variable, let alone one so difficult to measure as the quantity of knowledge,

is hardly intellectually satisfactory. From a quantitative, empirical point of view, we are

left with time as an explanatory variable. Now trend projections, however necessary

they may be in practice, are basically a confession of ignorance, and, what is worse from a

practical viewpoint, are not policy variables.

Further, the concept of knowledge which underlies the production function at any

moment needs analysis. Knowledge has to be acquired. We are not surprised, as edu-

cators, that even students subject to the same educational experiences have different

bodies of knowledge, and we may therefore be prepared to grant, as has been shown

empirically (see [2], Part III), that different countries, at the same moment of time, have

different production functions even apart from differences

in natural resource endowment.

I would like to suggest here an endogenous theory of the changes in knowledge which

underlie intertemporal and international shifts in production functions. The acquisition

of knowledge is what is usually termed " learning," and we might perhaps pick up some

clues from the many psychologists who have studied this phenomenon (for a convenient

survey, see Hilgard [5]). I do not think that the picture of technical change as a vast

and prolonged process of learning about the environment in which we operate is in any

way a far-fetched analogy; exactly the same phenomenon of improvement in performance

over time is involved.

Of course, psychologists are no more in agreement than economists, anid there are

sharp differences of opinion about the processes of learning. But one empirical generali-

zation is so clear that all schools of thought must accept it, although they interpret it in

different fashions: Learning is the product of experience. Learning can only take place

through the attempt to solve a problem and therefore only takes place during activity.

Even the Gestalt and other field theorists, who stress the role of insight in the solution of

problems (Kohler's famous apes), have to assign a significant role to previous experiences

in modifying the individual's perception.

A second generalization that can be gleaned from many of the classic learning expelri-

ments is that learning associated with repetition of essentially the same problem is subject

to sharply diminishing returns. There is an equilibrium response pattern for any given

155

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156 REVIEW OF ECONOMIC STUDIES

stimulus, towards which the behavior of the learner tends with repetition. To have

steadily increasing performance, then, implies that the stimulus situations must themselves

be steadily evolving rather than merely repeating.

The role of experience in increasing productivity has not gone unobserved, though

the relation has yet to be absorbed into the main corpus of economic theory. It was early

observed by aeronautical engineers, particularly T. P. Wright [151, that the number of

labor-hours expended in the production of an airframe (airplane body without engines) is

a decreasing function of the total number of airframes of the same type previously produced.

Indeed, the relation is remarkably precise; to produce the Nth airframe of a given type,

counting from the inception of production, the amount of labor required is proportional

to N-1/3. This relation has become basic in the production and cost planning of the

United States Air Force; for a full survey, see [3]. Hirsch (see [6] and other work cited

there) has shown the existence of the same type of " learning curve " or " progress ratio,"

as it is variously termed, in the production of other machines, though the rate of learning

is not the same as for airframes.

Verdoorn [14, pp. 433-4] has applied the principle of the learning curve to national

outputs; however, under the assumption that output is increasing exponentially, current

output is proportional to cumulative output, and it is the former variable that he uses to

explain labor productivity. The empirical fitting was reported in [13]; the estimated

progress ratio for different European countries is about *5. (In [13], a neo-classical

interpretation in terms of increasing capital-labor ratios was offered; see pp. 7-11.)

Lundberg [9, pp. 129-133] has given the name " Horndal effect" to a very similar

phenomenon. The Horndal iron works in Sweden had no new investment (and therefore

presumably no significant change in its methods of production) for a period of 15 years,

yet productivity (output per manhour) rose on the average close to 2 % per annum. We

find again steadily increasing performance which can only be imputed to learning from

experience.

I advance the hypothesis here that technical change in general can be ascribed to

experience, that it is the very activity of production which gives rise to problems for which

favorable responses are selected over time. The evidence so far cited, whether from

psychological or from economic literature is, of course, only suggestive. The aim of this

paper is to formulate the hypothesis more precisely and draw from it a number of economic

implications. These should enable the hypothesis and its consequences to be confronted

more easily with empirical evidence.

The model set forth will be very simplified in some other respects to make clearer the

essential role of the major hypothesis; in particular, the possibility of capital-labor sub-

stitution is ignored. The theorems about the economic world presented here differ from

those in most standard economic theories; profits are the result of technical change; in a

free-enterprise

system, the rate of investment will be less than the optimum; net investment

and the stock of capital become subordinate concepts, with gross investment taking a

leading role.

In section 1, the basic assumptions of the model are set forth. In section 2, the

implications for wage earners are deduced; in section 3 those for profits, the inducement

to invest, and the rate of interest. In section 4, the behavior of the entire system under

steady growth with mutually consistent expectations is taken up. In section 5, the diver-

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THE ECONOMIC IMPLICATIONS OF LEARNING BY DOING 157

gence between social and private returns is studied in detail for a special case (where the

subjective rate of discount of future consumption is a constant). Finally, in section 6,

some limitations of the model and needs for further development are noted.

1. THE MODEL

The first question is that of choosing the economic variable which represents

" experi-

ence ". The economic examples given above suggest the possibility of using cumulative

output (the total of output from the beginning of time) as an index of experience, but this

does not seem entirely satisfactory. If the rate of output is constant, then the stimulus to

learning presented would appear to be constant, and the learning that does take place is a

gradual approach to equilibrium behavior. I therefore take instead cumulative gross

investment (cumulative production of capital goods) as an index of experience. Each

new machine produced and put into use is capable of changing the environment in which

production takes place, so that learning is taking p!ace with continually new stimuli.

This at least makes plausible the possibility of continued learning in the sense, here, of a

steady rate of growth in productivity.

The second question is that of deciding where the learning enters the conditions of

production. I follow here the model of Solow [12] and Johansen [7], in which technical

change is completely embodied in new capital goods. At any moment of new time, the new

capital goods incorporate all the knowledge then available, but once built their productive

efficiency cannot be altered by subsequent learning.

To simplify the discussion we shall assume that the production process associated

with any given new capital good is characterized

by fixed coefficients, so that a fixed amount

of labor is used and a fixed amount of output obtained. Further, it will be assumed that

new capital goods are better than old ones in the strong sense that, if we compare a unit of

capital goods produced at time t, with one produced at time t2 > tl, the first requires the

co-operation of at least as much labor as the second, and produces no more product.

Under this assumption, a new capital good will always be used in preference to an older

one.

Let G be cumulative gross investment. A unit capital good produced when cumulative

gross investment has reached G will be said to have serial number

G. Let

A(G) = amount of labor used in production with a capital good of serial number G,

y(G) output capacity of a capital good of serial number G,

x total output,

L total labor force employed.

It is assumed that A(G)

is a non-increasing

function, while y(G) is a non-decreasing

function.

Then, regardless of wages or rental value of capital goods, it always pays to use a capital

good of higher serial number before one of lower serial number.

It will further be assumed that capital goods have a fixed lifetime, T. Then capital

goods disappear

in the same order as their serial numbers. It follows that at any moment

of time, the capital goods in use will be all those witlh

serial numbers from some G' to G,

the current

cumulative gross investment. Then

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TheReviewofEconomicStudies,Ltd.TheEconomicImplicationsofLearningbyDoingAuthor(s):KennethJ.ArrowReviewedwork(s):Source:TheReviewofEconomicStudies,Vol.29,No.3(Jun.,1962),pp.155-173Publishedby:OxfordUniversityPressStableURL:http://www.jstor.org/stable/2295952.Accessed:21/11/201217:21YouruseoftheJSTORar...

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