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Joan Robinson
The Production Function and the Theory of Capital
1
Joan Robinson
“The Production Function and the Theory of Capital”
The Review of Economic Studies, Vol. 21, No. 2 (1953 - 1954), pp. 81-106
2
D. G. Champernowne
“The Production Function and the Theory of Capital: A Comment”
The Review of Economic Studies, Vol. 21, No. 2 (1953 - 1954), pp. 112-135
3
Robert M. Solow
“The Production Function and the Theory of Capital”
The Review of Economic Studies, Vol. 23, No. 2 (1955 - 1956), pp. 101-108
4
Joan Robinson
“The Production Function and the Theory of Capital--A Reply”
The Review of Economic Studies, Vol. 23, No. 3 (1955 - 1956), p. 247
The Production Function and the Theory
of Capital
INTRODUCTION
The dominance in neo-classical economic teaching of the concept of a production
function, in which the relative prices of the factors of production are exhibited as a
know-
function of the ratio in which they are employed in a given state of technical
ledge, has had an enervating effect upon the development of the subject, for by con-
attention
of factors it has distracted
centrating upon the question of the proportions the
but more rewarding questions of the influences governing
from the more difficult
supplies of the factors and of the causes and consequences of changes in technical
knowledge. the function has been a powerful instrument of mis-
Moreover, production 0 f where L is
education. The student of economic theory is taught to write f (L, C)
a of C a quantity of capital and 0 a rate of output of commodities.'
quantity labour, in of
is to man-hours
He instructed assume all alike, to measure L
workers and labour;
a unit of
involved in choosing
he is told about the index-number problem
something he will forget
and then in the hope that
output ; he is hurried on to the next question, a
to in does he has become professor,
is measured. Before ever he
ask what units C ask, to the next.
so habits of on one generation
and sloppy thought are handed from The in existence at
The is not an answer. capital
question certainly easy one to
" of the environment in which labour
any moment may be treated simply as part This is the
a alone.
works."2 We then have production function in terms of labour goods
the the supply of concrete capital
right procedure for short period within which for it
not line to means
does but the a very weak take,
alter, outside short period it is of capital (which can be made over
a change in the stock
that we cannot distinguish the weather (an act of God).
the from a change in
long run by accumulation) in
the existence
look a of of all
We stock as the specific list goods
may upon capital of But
at moment work-in-progress in the pipe lines production).
any (including any change in
of the short period, for
this again is of no use outside the strict bounds of and
of methods production
the ratio of capital to labour involves a re-organisation all the
a in the sizes of many or goods
requires change shapes, and specifications
in the 3
list.
appearing original Should
As soon as leave host of
a difficulties appear.
we the short period, however, costs ?
be to or its
power past
capital valued according its future earning with a certain
When we know the future expected rate of output associated of
if a rate interest,
then, we are given
and future prices and costs,
capital good, expected which will
we can value the capital good as a discounted stream of future profit it
earn. But to do so, we have to begin by taking the rate of interest as given, whereas
the main purpose of the production function is to show how wages and the rate of
and
conditions
as the by technical
interest (regarded wages of capital) are determined
the factor ratio.
i Throughout this essay we shall be abstracting from land as a factor of production, so we will not
bother the student with it.
2 .
General Theory, p. 2 4
Keynes, I tenth man joins nine who are digging a hole, nine more
8 In Professor Robertson's example, when a and a bucket to fetch beer. (Economic Fragments,
expensive spades are turned into nine cheaper spades
P. 47-)
8I
OF STUDIES
THE REVIEW ECONOMIC
82
money
Are we then to value capital goods by their cost of production ? Clearly power
the purchasing
we can specify
nor unless
is here there
cost of production neither to
effect,
that is, in
units,
of wage
terms
cost in
goods
we the capital
but may
of money, of a of labour.
their cost in terms unit standard
measure to
in the past is congenial
as time expended
To treat capital a quantity of labour nature of
for to the essential
point of it corresponds
the production-function view, employ-
in
in essence,
of Investment consists,
as a factor production.
regarded
capital is making
saving
while
which will its fruits in the future
in a yield
now way
labour
ing products available for the workers to consume in the meantime; and the
current that was expended
in the fact that a unit of labour
of capital consists
productiveness in the is more valuable to-day than a unit expended to-day,
at a certain time past
are
its fruits already ripe.
because of whole
lies at the root the
a which
we encounter fundamental
But here difficulty is
in a form. All work
is pure
of capital. A unit of labour never expended
problem of goods of some kind or another. When Adam delved and
done with the assistance in existence. The cost
were evidently a spade and a spindle already
there
Eve span before
be constructed
and they must
the cost of goods, since
of includes capital
capital between
the of time
over period
is interest
of the cost of capital
be used, part
they can work was done in capital goods and the time when
the moment when constructing a of capitalism,
are a stream of output. This is not just consequence
they producing will yield a
to-day, which
of expended
a society a unit labour,
for in socialist
equally the same as a unit which will yield a product
in time, is not thing
product five years'
to-morrow. even if it were possible to measure capital simply in terms of labour
Finally, of units is ?
what composed
the C
not have answered
time, we still should question: of as in
is to
we are it natural think capital measured
accumulation,
When discussing in from consuming
of consists refraining
of The process accumulation
terms product. we consider what
to the of But when addi-
to stock wealth.
order
in add
output
current a we must measure
of makes,
to resources given amount accumulation
tion productive the stock of made
to by
the addition
in labour for equipment
capital units, productive in
how much is done constructing
an of work
increment upon
adding capital depends of an labour. as we move
of hour's
not the in terms final Thus,
it, upon cost, product, in terms of
one on a function to another, measuring capital
from point production to see the effect
we have to know the rate in order upon pro-
product, product-wage in labour
duction of the ratio of capital to labour. Or if we measure units,
changing would be
to see how much accumulation
have to know the in order
we product-wage with the
a of But the rate alters
to produce given increment capital. wage
required both for a of and
one stand quantity product
the factors : cannot
of symbol, C,
ratio of labour time.
a quantity the which the function to analyse,
All the same, problem production professes
although it has been too much puffed up by the attention paid to it, is a genuine
is cleared a few
problem. To-day, in country Alpha, a length of roadway being is by made
in Beta a road the same being
with bulldozers near-enough quality)
men ; (of of men
of men with and ox-carts. In Gamma thousands are
hundreds
by some picks the all
shovels and little baskets to remove soil. When possible
with wooden
working made for in national character and and for
have been differences climate,
allowances for
in the state of it seems pretty clear that the main reason
differences knowledge, in than in
is that in some sense is more plentiful Alpha
this state of affairs capital of of it
Gamma. Looked at from the point view an individual capitalist, would not
were at
finance the
in if unlimited available)
to use methods Gamma
pay Alpha (even at the of view of it
rate of interest which is ruling, and looked from point society,
PRODUCTION FUNCTION AND THE THEORY OF CAPITAL 83
THE
to raise all the labour available in
effort of accumulation
would need a prodigious is a real one. We cannot
even to the Beta level of technique. The problem
Gamma the element of common-
to rescue
without an effort
function
the production
abandon in it.
been entangled
sense that has
THE QUANTITY OF CAPITAL
is called. The capital
is it is what its name
"Capital" is not what capital called, in existence at that moment.
all the goods
of time are
in existence at a moment
goods Blanc.
Mont
nor
heap
a rubbish
neither
in existence. It includes
It is not all the things " " are is that they have value, that is
The characteristic by which goods specified tin is not a
an empty petrol
Alpha
in country
other. Thus,
over each
power
purchasing
" where old tins are a source of valuable industrial raw
good," whereas in Gamma
it is.
material, It is so actual objects, called
The list of goods is quite specific. many particular from
the same name differ
under
grouped
blast furnaces, etc., etc. Goods
overcoats, and these must not be over-
each other in the details of their physical specifications twenty years
in their ages are also important. A blast furnace
looked. Differences in other respects,
old is not equivalent to a brand new one of the same specification
is relevant
one. There another
new
to a brand
old equivalent
is twenty days
egg
nor an to an one
wear and egg
one it,
An requires body
characteristic of the goods. overcoat or
one are and two bodies
eat one or mouth, they useless,
mouth to it. Without body, in them. But a blast furnace
share using
of time) cannot
mouths (at a given moment iron.
iron into Therefore
to ore
of turn
a of numbers bodies
be used range
can by certain a
of its rate of as function
an account output
of blast furnace includes
the description a not discuss
shall problems,
we short-period
it. (Since
the number of bodies operating
of in with
each of equipment, the situations
working piece
actually
of bodies
the number most to it.)
is appropriate
we is the number which technically
which shall be
concerned, the which is quite different. Of two overcoats,
is aspect of goods
There another is on the of Mrs. who is
one body Jones,
completely similar in all the above respects, is on the of Mrs.
delight at her fine appearance. Another body
with inward
purring income what it she is obliged
who is her husband's being is,
because,
Snooks, grizzling In what follows we shall not discuss this aspect of
clothes.
to buy mass-produced is an overcoat IV), and
that an overcoat IV) (Mark
goods at all. We take it (Mark
no nonsense. who of individual is not a thing what we can
this who's goods
Now, enormous to the items
a of we have evaluate
all To it as quaantity goods
handle at easily. express the in terms of the real cost of pro-
of it is composed. We can evaluate goods
which the to make
the work and existing goods required
ducing them-that is, formerly or
in some unit of power, we can
of their purchasing
them, or in terms value expressed is, what the stock of goods will
to their productivity-that
evaluate them according is in it.
the future if work done with
in conjunction
become three evaluations equivalent results ; there
In a of all yield
position equilibrium to another the
is a quantity which can be translated from one number by changing
the of It entails that there have been no events
unit. This is definition equilibrium. between the
the relation
over the relevant of past time which have disturbed
period that the human in the situation
a stock of and beings
of goods,
valuations given
various the future to be just like the past-entirely devoid of such disturbing
are expecting the rate of to-day is the rate which was expected to rule
ruling
events. Then profit the
now extant was and
the decision to invest in good made,
to-day when any capital of are to the
expected future receipts, capitalised at the current rate profit, equal
are to them.
cost of the which expected produce
capital goods
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