Increasing Returns and Economic Progress
The Economic Journal, volume 38 (1928), pp. 527-42.
by Allyn A. Young


    My subject may appear alarmingly formidable, but I did not
intend it to be so. The words economic progress, taken by
themselves, would suggest the pursuit of some philosophy of
history, of some way of appraising the results of past and
possible future changes in forms of economic organisation and
modes of economic activities. But as I have used them, joined to
the other half of my title, they are meant merely to dispel
apprehensions, by suggesting that I do not propose to discuss any
of those alluring but highly technical questions relating to the
precise way in which some sort of equilibrium of supply and
demand is achieved in the market for the products of industries
which can increase their output without increasing their costs
proportionately, or to the possible advantages of fostering the
development of such industries while putting a handicap upon
industries whose output can be increased only at the expense of a
more than proportionate increase of costs. I suspect, indeed,
that the apparatus which economists have built up for dealing
effectively with the range of questions to which I have just
referred may stand in the way of a clear view of the more general
or elementary aspects of the phenomena of increasing returns such
as I wish to comment upon in this paper. 
    Consider, for example, Alfred Marshall's fruitful distinction
between the internal productive economies which a particular firm
is able to secure as the growth of the market permits it to
enlarge the scale of its operations and the economies external to
the individual firm which show themselves only in changes of the
organisation of the industry as a whole. This distinction has
been useful in at least two different ways. In the first place it
is, or ought to be, a safeguard against the common error of
assuming that wherever increasing returns operate there is
necessarily an effective tendency towards monopoly. In the second
place it simplifies the analysis of the manner in which the
prices of commodities produced under conditions of increasing
returns are determined. A representative firm within the
industry, maintaining its own identity and devoting itself to a
given range of activities, is made to be the vehicle or medium
through which the economies achieved by the industry as a whole
are transmitted to the market and have their effect upon the
price of the product. 
    The view of the nature of the processes of industrial
progress which is implied in the distinction between internal and
external economies is necessarily a partial view. Certain aspects
of those processes are illuminated, while, for that very reason,
certain other aspects, important in relation to other problems,
are obscured. This will be clear, I think, if we observe that,
although the internal economies of some firms producing, let us
say, materials or appliances may figure as the external economies
of other firms, not all of the economies which are properly to be
called external can be accounted for by adding up the internal
economies of all the separate firms. When we look at the internal
economies of a particular firm we envisage a condition of
comparative stability. Year after year the firm, like its
competitors, is manufacturing a particular product or group of
products, or is confining itself to certain definite stages in
the work of forwarding the products towards their final form. Its
operations change in the sense that they are progressively
adapted to an increasing output, but they are kept within
definitely circumscribed bounds. Out beyond, in that obscurer
field from which it derives its external economies, changes of
another order are occurring. New products are appearing, firms
are assuming new tasks, and new industries are coming into being.
In short, change in this external field is qualitative as well as
quantitative. No analysis of the forces making for economic
equilibrium, forces which we might say are tangential at any
moment of time, will serve to illumine this field, for movements
away from equilibrium, departures from previous trends, are
characteristic of it. Not much is to be gained by probing into it
to see how increasing returns show themselves in the costs of
individual firms and in the prices at which they offer their
products. 
    Instead, we have to go back to a simpler and more inclusive
view, such as some of the older economists took when they
contrasted the increasing returns which they thought were
characteristic of manufacturing industry taken as a whole with
the diminishing returns which they thought were dominant in
agriculture because of an increasingly unfavourable proportioning
of labour and land. Most of them were disappointingly vague with
respect to the origins and the precise nature of the
"improvements" which they counted upon to retard somewhat the
operation of the tendency towards diminishing returns in
agriculture and to secure a progressively more effective use of
labour in manufactures. Their opinions appear to have rested
partly upon an empirical generalisation. Improvements had been
made, they were still being made, and it might he assumed that
they could continue to be made. If they had looked back they
would have seen that there were centuries during which there were
few significant changes in either agricultural or industrial
methods. But they were living in an age when men had turned their
faces in a new direction and when economic progress was not only
consciously sought but seemed in some way to grow out of the
nature of things. Improvements, then, were not something to be
explained. They were natural phenomena, like the precession of
the equinoxes. 
    There were certain important exceptions, however, to this
incurious attitude towards what might seem to be one of the most
important of all economic problems. Senior's positive doctrine is
well known, and there were others who made note of the
circumstance that with the growth of population and of markets
new opportunities for the division of labour appear and new
advantages attach to it. In this way, and in this way only, were
the generally commonplace things which they said about
"improvements" related to anything which could properly be called
a doctrine of increasing returns. They added nothing to Adam
Smith's famous theorem that the division of labour depends upon
the extent of the market. That theorem, I have always thought, is
one of the most illuminating and fruitful generalisations which
can be found anywhere in the whole literature of economics. In
fact, as I am bound to confess, I am taking it as the text of
this paper, in much the way that some minor composer borrows a
theme from one of the masters and adds certain developments or
variations of his own. Today, of course, we mean by the division
of labour something much broader in scope than that splitting up
of occupations and development of specialised crafts which Adam
Smith mostly had in mind. No one, so far as I know, has tried to
enumerate all of the different aspects of the division of labour,
and I do not propose to undertake that task. I shall deal with
two related aspects only: the growth of indirect or roundabout
methods of production and the division of labour among
industries. 
    It is generally agreed that Adam Smith, when he suggested
that the division of labour leads to inventions because workmen
engaged in specialised routine operations come to see better ways
of accomplishing the same results, missed the main point. The
important thing, of course, is that with the division of labour a
group of complex processes is transformed into a succession of
simpler processes, some of which, at least, lend themselves to
the use of machinery. In the use of machinery and the adoption of
indirect processes there is a further division of labour, the
economies of which are again limited by the extent of the market.
It would be wasteful to make a hammer to drive a single nail; it
would be better to use whatever awkward implement lies
conveniently at hand. It would be wasteful to furnish a factory
with an elaborate equipment of specially constructed jigs,
gauges, lathes, drills, presses, and conveyors to build a hundred
automobiles; it would be better to rely mostly upon tools and
machines of standard types, so as to make a relatively larger use
of directly applied and a relatively smaller use of indirectly
applied labour. Mr Ford's methods would be absurdly uneconomical
if his output were very small, and would be unprofitable even if
his output were what many other manufacturers of automobiles
would call large. 
    Then, of course, there are economies of what might be called
a secondary order. How far it pays to go in equipping factories
with special appliances for making hammers or for constructing
specialised machinery for use in making different parts of
automobiles depends again upon how many nails are to be driven
and how many automobiles can be sold. In some instances, I
suppose, these secondary economies, though real, have only a
secondary importance. The derived demands for many types of
specialised production appliances are inelastic over a fairly
large range. If the benefits and the costs of using such
appliances are spread over a relatively large volume of final
products, their technical effectiveness is a larger factor in
determining whether it is profitable to use them than any
difference which producing them on a large or small scale would
commonly make in their costs. In other instances the demand for
productive appliances is more elastic, and beyond a certain level
of costs demand may fail completely. In such circumstances
secondary economies may become highly important.
    Doubtless, much of what I have said has been familiar and
even elementary. I shall venture, nevertheless, to pit further
stress upon two points, which may be among those which have a
familiar ring, but which appear sometimes to be in danger of
being forgotten. (Otherwise, economists of standing could not
have suggested that increasing returns may be altogether
illusory, or have maintained that where they are present they
must lead to monopoly.) The first point is that the principal
economies which manifest themselves in increasing returns are the
economies of capitalistic or roundabout methods of production.
These economies, again, are largely identical with the economies
of the division of labour in its most important modern forms. In
fact, these economies lie under our eyes, but we may miss them if
we try to make of large-scale production (in the sense of
production by large firms or large industries), as contrasted
with targe production, any more than an incident in the general
process by which increasing returns are secured and if
accordingly we look too much at the individual firm or even, as I
shall suggest presently, at the individual industry. 
    The second point is that the economies of roundabout methods,
even more than the economies of other forms of the division of
labour, depend upon the extent of the market-and that, of course,
is why we discuss them under the head of increasing returns. It
would hardly be necessary to stress this point, if it were not
that the economies of large-scale operations and of
"mass-production" are often referred to as though they could be
had for the taking, by means of a "rational" reorganisation of
industry. Now I grant that at any given time routine and inertia
play a very large part in the organisation and conduct of
industrial operations. Real leadership is no more common in
industrial than in other pursuits. New catchwords or slogans like
mass production and rationalisation may operate as stimuli; they
may rouse men from routine and lead them to scrutinise again the
organisation and processes of industry and to try to discover
particular ways in which they can be bettered. For example, no
one can doubt that there are genuine economies to be achieved in
the way of "simplification and standardisation," or that the
securing of these economies requires that certain deeply rooted
competitive wastes be extirpated. This last requires a definite
concerted effort -- precisely the kind of thing which ordinary
competitive motives are often powerless to effect, but which
might come more easily as the response to the dissemination of a
new idea. 
    There is a danger, however, that we shall expect too much
from these "rational" industrial reforms. Pressed beyond a
certain point they become the reverse of rational. I have
naturally been interested in British opinions respecting the
reasons for the relatively high productivity (per labourer or per
hour of labour) of representative American industries. The error
of those who suggest that the explanation is to be found in the
relatively high wages which prevail in America is not that they
confuse cause and effect, but that they hold that what are really
only two aspects of a single situation are, the one cause, and
the other effect. Those who hold that American industry is
managed better, that its leaders study its problems more
intelligently and plan more courageously and more wisely can cite
no facts in support of their opinion save the differences in the
results achieved. Allowing for the circumstance that British
industry, as a whole, has proved to be rather badly adjusted to
the new post-war economic situation, I know of no facts which
prove or even indicate that British industry, seen against the
background of its own problems and its own possibilities, is less
efficiently organised or less ably directed than American
industry or the industry of any other country. 
    Sometimes the fact that the average American labourer works
with the help of a larger supply of power-driven labour-saving
machinery than the labourer of other countries is cited as
evidence of the superior intelligence of the average American
employer. But this will not do, for, as every economist knows,
the greater the degree in which labour is productive or
scarce-the words have the same meaning-the greater is the
relative economy of using it in such indirect or roundabout ways
as are technically advantageous, even though such procedure calls
for larger advances of capital than simpler methods do. 
    It is encouraging to find that a fairly large number of
commentators upon the volume of the American industrial product
and the scale of American industrial organisation have come to
surmise that the extent of the American domestic market,
unimpeded by tariff barriers, may have something to do with the
matter. This opinion seems even to be forced upon thoughtful
observers by the general character of the facts, whether or no
the observers think in terms of the economists' conception of
increasing returns. In certain industries, although by no means
in all, productive methods are economical and profitable in
America which would not be profitable elsewhere. The importance
of coal and iron and other natural resources needs no comment.
Taking a country's economic endowment as given, however, the most
important single factor in determining the effectiveness of its
industry appears to be the size of the market. But just what
constitutes a large market? Not area or population alone, but
buying power, the capacity to absorb a large annual output of
goods. This trite observation, however, at once suggests another
equally trite, namely, that capacity to buy depends upon capacity
to produce. In an inclusive view, considering the market not as
an outlet for the products of a particular industry, and
therefore external to that industry, but as the outlet for goods
in general, the size of the market is determined and defined by
the volume of production. If this statement needs any
qualification, it is that the conception of a market in this
inclusive sense -- an aggregate of productive activities, tied
together by trade-carries with it the notion that there must be
some sort of balance, that different productive activities must
be proportioned one to another. 
    Modified, then, in the light of this broader conception of
the market, Adam Smith's dictum amounts to the theorem that the
division of labour depends in large part upon the division of
labour. This is more than mere tautology. It means, if I read its
significance rightly, that the counterforces which are
continually defeating the forces which make for economic
equilibrium are more pervasive and more deeply rooted in the
constitution of the modern economic system than we commonly
realise. Not only new or adventitious elements, coming in from
the outside, but elements which are permanent characteristics of
the ways in which goods are produced make continuously for
change. Every important advance in the organisation of
production, regardless of whether it is based upon anything
which, in a narrow or technical sense, would be called a new
"invention," or involves a fresh application of the fruits of
scientific progress to industry, alters the conditions of
industrial activity and initiates responses elsewhere in the
industrial structure which in turn have a further unsettling
effect. Thus change becomes progressive and propagates itself in
a cumulative way. 
    The apparatus which economists have built up for the analysis
of supply and demand in their relations to prices does not seem
to be particularly helpful for the purposes of an inquiry into
these broader aspects of increasing returns. In fact, as I have
already suggested, reliance upon it may divert attention to
incidental or partial aspects of a process which ought to be seen
as a whole. If, nevertheless, one insists upon seeing just how
far one can get into the problem by using the formulas of supply
and demand, the simplest way, I suppose, is to begin by inquiring
into the operations of reciprocal demand when the commodities
exchanged are produced competitively under conditions of
increasing returns and when the demand for each commodity is
elastic, in the special sense that a small increase in its supply
will be attended by an increase in the amounts of other
commodities which can be had in exchange for it.(1*) Under such
conditions an increase in the supply of one commodity is an
increase in the demand for other commodities, and it must be
supposed that every increase in demand will evoke an increase in
supply. The rate at which any one industry grows is conditioned
by the rate at which other industries grow, but since the
elasticities of demand and of supply will differ for different
products, some industries will grow faster than others. Even with
a stationary population and in the absence of new discoveries
(2*) in pure or applied science there are no limits to the
process of expansion except the limits beyond which demand is not
elastic and returns do not increase. 
    If, under these hypothetical conditions, progress were
unimpeded and frictionless, if it were not dependent in part upon
a process of trial and error, if the organisation of industry
were always such as, in relation to the immediate situation, is
most economical, the realising of increasing returns might be
progressive and continuous, although, for technical reasons, it
could not always proceed at an even rate. But it would remain a
process requiring time. An industrial dictator, with foresight
and knowledge, could hasten the pace somewhat, but he could not
achieve an Aladdin-like transformation of a country's industry so
as to reap the fruits of a half-century's ordinary progress in a
few years. The obstacles are of two sorts. First, the human
material which has to be used is resistant to change. New trades
have to be learnt and new habits have to be acquired. There has
to be a new geographical distribution of the population and
established communal groups have to be broken up. Second, the
accumulation of the necessary capital takes time, even though the
process of accumulation is largely one of turning part of an
increasing product into forms which will serve in securing a
further increase of product. An acceleration of the rate of
accumulation encounters increasing costs, into which both
technical and psychological elements enter. One who likes to
conceive of all economic processes in terms of tendencies towards
an equilibrium might even maintain that increasing returns, so
far as they depend upon the economies of indirect methods of
production and the size of the market, are offset and negated by
their costs, and that under such simplified conditions as I have
dealt with the realizing of increasing returns would be spread
through time in such a way as to secure an equilibrium of costs
and advantages. This would amount to saying that no real economic
progress could come through the operation of forces engendered
within the economic system a conclusion repugnant to common
sense. To deal with this point thoroughly would take us too far
afield. I shall merely observe, first, that the appropriate
conception is that of a moving equilibrium, and second, that the
costs which (under increasing returns) grow less rapidly than the
product are not the "costs" which figure in an "equilibrium of
costs and advantages." Moving away from these abstract
considerations, so as to get closer to the complications of the
real situation, account has to be taken, first, of various kinds
of obstacles. The demand for some products is inelastic, or, with
an increasing supply, soon becomes so. The producers of such
commodities, however, often share in the advantages of the
increase of the general scale of production in related
industries, and so far as they do productive resources are
released for other uses. Then there are natural scarcities,
limitations, or inelasticities of supply, such as effectively
block the way to the securing of any important economies in the
production of some commodities and which impair the effectiveness
of the economies secured in the production of other commodities.
In most fields, moreover, progress is not and cannot be
continuous. The next important step forward is often initially
costly, and cannot be taken until a certain quantum of
prospective advantages has accumulated. 
    On the other side of the account are various factors which
reinforce the influences which make for increasing returns. The
discovery of new natural resources and of new uses for them and
the growth of scientific knowledge are probably the most potent
of such factors. The causal connections between the growth of
industry and the progress of science run in both directions, but
on which side the preponderant influence lies no one can say. At
any rate, out of better knowledge of the materials and forces
upon which men can lay their hands there come both new ways of
producing familiar commodities and new products, and these last
have a presumptive claim to be regarded as embodying more
economical uses of productive resources than the uses which they
displace. Some weight has to be given also to the way in which,
with the advance of the scientific spirit, a new kind of interest
which might be described as a scientific interest conditioned by
an economic interest is beginning to infiltrate into industry. It
is a point of controversy, but I venture to maintain that under
most circumstances, though not in all, the growth of population
still has to be counted a factor making for a larger per capita
product -- although even that cautious statement needs to be
interpreted and qualified. But just as there may be population
growth with no increase of the average per capita product, so
also, as I have tried to suggest, markets may grow and increasing
returns may be secured while the population remains stationary. 
    It is dangerous to assign to any single factor the leading
role in that continuing economic revolution which has taken the
modern world so far away from the world of a few hundred years
ago. But is there any other factor which has a better claim to
that role than the persisting search for markets? No other
hypothesis so well unites economic history and economic theory.
The Industrial Revolution of the eighteenth century has come to
be generally regarded, not as a cataclysm brought about by
certain inspired improvements in industrial technique, but as a
series of changes related in an orderly way to prior changes in
industrial organisation and to the enlargement of markets. It is
sometimes said, however, that while in the Middle Ages and in the
early modern period industry was the servant of commerce, since
the rise of "industrial capitalism" the relation has been
reversed, commerce being now merely an agent of industry. If this
means that the finding of markets is one of the tasks of modern
industry, it is true. If it means that industry imposes its will
upon the market, that whereas formerly the things which were
produced were the things which could be sold, now the things
which have to be sold are the things that are produced, it is not
true. 
    The great change, I imagine, is in the new importance which
the potential market has in the planning and management of large
industries. The difference between the cost per unit of output in
an industry or in an individual plant properly adapted to a given
volume of output and in an industry or plant equally well adapted
to an output five times as large is often much greater than one
would infer from looking merely at the economies which may accrue
as an existing establishment gradually extends the scale of its
operations. Potential demand, then, in the planning of industrial
undertakings, has to be balanced against potential economies,
elasticity of demand against decreasing costs. The search for
markets is not a matter of disposing of a "surplus product," in
the Marxian sense, but of finding an outlet for a potential
product. Nor is it wholly a matter of multiplying profits by
multiplying sales; it is partly a matter of augmenting profits by
reducing costs.
    Although the initial displacement may be considerable and the
repercussions upon particular industries unfavourable, the
enlarging of the market for any one commodity, produced under
conditions of increasing returns, generally has the net effect,
as I have tried to show, of enlarging the market for other
commodities. The business man's mercantilistic emphasis upon
markets may have a sounder basis than the economist who thinks
mostly in terms of economic statics is prone to admit. How far "
selling expenses," for example, are to be counted sheer economic
waste depends upon their effects upon the aggregate product of
industry, as distinguished from their effects upon the fortunes
of particular undertakings. 

    Increasing returns are often spoken of as though they were
attached always to the growth of "industries," and I have not
tried to avoid that way of speaking of them, although I think
that it may be a misleading way. The point which I have in mind
is something more than a quibble about the proper definition of
an industry, for it involves a particular thesis with respect to
the way in which increasing returns are reflected in changes in
the organisation of industrial activities. Much has been said
about industrial integration as a concomitant or a natural result
of an increasing industrial output. It obviously is, under
particular conditions, though I know of no satisfactory statement
of just what those particular conditions are. But the opposed
process, industrial differentiation, has been and remains the
type of change characteristically associated with the growth of
production. Notable as has been the increase in the complexity of
the apparatus of living, as shown by the increase in the variety
of goods offered in consumers' markets, the increase in the
diversification of intermediate products and of industries
manufacturing special products or groups of products has gone
even further. 
    The successors of the early printers, it has often been
observed, are not only the printers of today, with their own
specialised establishments, but also the producers of wood pulp,
of various kinds of paper, of inks and their different
ingredients, of type-metal and of type, the group of industries
concerned with the technical parts of the producing of
illustrations, and the manufacturers of specialised tools and
machines for use in printing and in these various auxiliary
industries. The list could be extended, both by enumerating other
industries which are directly ancillary to the present printing
trades and by going back to industries which, while supplying the
industries which supply the printing trades, also supply other
industries, concerned with preliminary stages in the making of
final products other than printed books and newspapers. I do not
think that the printing trades are an exceptional instance, but I
shall not give other examples, for I do not want this paper to be
too much like a primer of descriptive economics or an index to
the reports of a census of production. It is sufficiently
obvious, anyhow, that over a large part of the field of industry
an increasingly intricate nexus of specialised undertakings has
inserted itself between the producer of raw materials and the
consumer of the final product. 
    With the extension of the division of labour among industries
the representative firm, like the industry of which it is a part,
loses its identity. Its internal economies dissolve into the
internal and external economies of the more highly specialised
undertakings which are its successors, and are supplemented by
new economies. Insofar as it is an adjustment to a new situation
created by the growth of the market for the final products of
industry the division of labour among industries is a vehicle of
increasing returns. It is more than a change of form incidental
to the full securing of the advantages of capitalistic methods of
production -- although it is largely that -- for it has some
advantages of its own which are independent of changes in
productive technique. For example, it permits of a higher degree
of specialisation in management, and the advantages of such
specialisation are doubtless often real, though they may easily
be given too much weight. Again, it lends itself to a better
geographical distribution of industrial operations, and this
advantage is unquestionably both real and important, nearness to
the source of supply of a particular raw material or to cheap
power counts for most in one part of a series of industrial
processes, nearness to other industries or to cheap transport in
another part, and nearness to a larger centre of population in
yet another. A better combination of advantages of location, with
a smaller element of compromise, can be had by the more
specialised industries. But the largest advantage secured by the
division of labour among industries is the fuller realising of
the economies of capitalistic or roundabout methods of
production. This should he sufficiently obvious if we assume, as
we must, that in most industries there are effective, though
elastic, limits to the economical size of the individual firm.
The output of the individual firm is generally a relatively small
proportion of the aggregate output of an industry. The degree in
which it can secure economies by making its own operations more
roundabout is limited. But certain roundabout methods are fairly
sure to become feasible and economical when their advantages can
be spread over the output of the whole industry. These potential
economies, then, are segregated and achieved by the operations of
specialised undertakings which, taken together, constitute a new
industry. It might conceivably be maintained that the scale upon
which the firms in the new industry are able to operate is the
secret of their ability to realise economies for industry as a
whole, while presumably making profits for themselves. This is
true in a way, but misleading. The scale of their operations
(which is only incidentally or under special conditions a matter
of the size of the individual firm) merely reflects the size of
the market for the final products of the industry or industries
to whose operations their own are ancillary. And the principal
advantage of large-scale operation at this stage is that it again
makes methods economical which would be uneconomical if their
benefits could not be diffused over a large final product. 

    In recapitulation of these variations on a theme from Adam
Smith there are three points to be stressed. First, the mechanism
of increasing returns is not to be discerned adequately by
observing the effects of variations in the size of an individual
firm or of a particular industry, for the progressive division
and specialisation of industries is an essential part of the
process by which increasing returns are realised. What is
required is that industrial operations be seen as an interrelated
whole. Second, the securing of increasing returns depends upon
the progressive division of labour, and the principal economies
of the division of labour, in its modern forms, are the economies
which are to be had by using labour in roundabout or indirect
ways. Third, the division of labour depends upon the extent of
the market, but the extent of the market also depends upon the
division of labour. In this circumstance lies the possibility of
economic progress, apart from the progress which comes as a
result of the new knowledge which men are able to gain, whether
in the pursuit of their economic or of their noneconomic
interests. 

NOTE

    In the accompanying construction (which owes much to Pareto),
a collective indifference curve, I, is defined by the condition
that, at equal cost, there would be no sufficient inducement for
the community to alter an annual production of x units of one
commodity and y units of another in order to secure the
alternative combination of the two commodities indicated by any
other point on the curve.(3*) Each commodity might be taken as
representative of a special class of commodities, produced under
generally similar conditions. Or one commodity might be made to
represent "other goods in general," the annual outlay of
productive exertions being regarded as constant. Alternatively,
one commodity might represent "leisure" (as a collective name for
all nonproductive uses of time). The other would then represent
the aggregate economic product.
    There will be equilibrium (subject to instability of a kind
which will be described presently) at a point P, if at that point
a curve of equal costs, such as d, is tangent to the indifference
curve. The curve of equal costs defines the terms upon which the
community can exchange one commodity for the other by merely
producing less of the one and more of the other (abstraction
being made of any incidental costs of change). Negative
curvature, as in d, reflects a condition of decreasing returns,
in the sense that more of either commodity can be had only by
sacrificing progressively larger amounts of the other. Although a
sufficient condition, the presence of decreasing returns is not a
necessary condition of equilibrium. There would be a loss in
moving away from P if equal costs were defined by the straight
line c, which represents constant returns. increasing returns,
even, are consistent with equilibrium, provided that the degree
of curvature of their graph is less than that of the indifference
curve. It might happen, of course, that returns would decrease in
one direction and increase in the other. Curve d, for example,
might have a point of inflexion at or near P. 

    Consider now the conditions of departure from equilibrium.
The curve i is drawn so as to represent potential increasing
returns between P and P1, which lies on a preferred indifference
curve. If these increasing returns were to be had merely for the
taking, if i were, for example, merely a continuation of the
upper segment of d or c, P would not be a point even of unstable
equilibrium. The advance from P to P1 would be made by merely
altering the proportions of the two commodities produced
annually. To isolate the problem of increasing returns it is
necessary to assume that P is a true point of equilibrium in the
sense that it is determined by a curve of equal costs, such as d
or c. The problem, then, has to do with the way in which the
lower segment of d or c can be transformed into or replaced by
such a curve as i. This requires, of course, that additional
costs be incurred, of a kind which have not yet been taken into
account. To diminish the amount of the one commodity which must
be sacrificed for a given increment of the other, some of the
labour hitherto devoted to its production must be used
indirectly, so that the increase of the annual output of the one
lags behind the curtailing of the output of the other. 
    This new element of cost might be taken into account by
utilising a third dimension, but it is simpler to regard it as
operating upon dx, the increment in x accompanying the movement
from P to P1, so as to move the indifference curve upon which P1
lies towards the left. It would be an error, however, to think
that the combinations of x with y and x + (dx) with y - dy (where
(dx) is the contracted form of dx) are themselves indifferent, so
that P1 is, in effect, brought over on to the original
indifference curve, I, and no advantage is reaped. The path from
P to P1 is a preferred route, not merely a segment of an
indifference curve. The cost of moving along that route is a
function of the rate (in time) of the movement. An equilibrium
rate (which need not be constant), such as would keep the
movement from P to P1 continuous and undeviating, would be
determined by the condition, not that (dx) and -dy should negate
one another, but that either an acceleration or a retarding of
the rate would be costly or disadvantageous. Because a mountain
climber adjusts his pace to his physical powers and to the
conditions of the ascent, it does not follow that he might as
well have stayed at the foot. Or, alternatively but not
inconsistently, the movement from P to P1 may be conceived as
made up of a series of small steps, each apparently yielding no
more than a barely perceptible advantage, but only because the
scale of reference for both costs and advantages depends at each
step upon the position which has then been reached. 
    Several sets of circumstances will affect the amount and
direction of the movement. (1) Even if i has no point of
inflexion, such as has been indicated at P1 (merely to simplify
the first stages of this analysis), it will sooner or later
(taking into account the " contraction,, of dx) become tangent to
an indifference curve. In the absence of any other factor making
for change, progress would then come to an end. (2) There may be
another possible alternative path of increasing returns extending
upwards from P and curving away from I. The most advantageous
route will then be a compromise between (or a resultant of) the
two limiting alternatives. In such circumstances the only
effective limitation imposed upon the extent of the movement may
come from the failure of elasticity of demand on one side or the
other. (3) Successive indifference curves cannot be supposed to
be symmetrical, in the sense that dy/dx remains the same function
of y/x. If, for example, the slope of successive indifference
curves at points corresponding to given values of y/x decreases
(indicating that the demand for the commodity measured in units
of y is relatively inelastic), freedom of movement in the
direction of P1 is reduced, while it becomes advantageous to move
a little way in the opposite direction along even such a path as
c or d. Under inverse conditions (with - dy/dx increasing
relatively to y/x for successive indifference curves) the extent
of the possible movement in the direction of P1 is increased.
This conclusion amounts to no more than the obvious theorem that
the degree in which the decreasing returns encountered in certain
fields of economic activity operate as a drag upon the securing
of increasing returns in other fields depends upon the relative
elasticities of demand for the two types of products. But this
consideration, like the others of which note has been made,
serves to make clear the general nature of the reciprocal
relation between increasing returns and the "extent of the
market." (4) Discoveries of new supplies of natural resources or
of new productive methods may have either or both of two kinds of
effects. They may tilt the curves of equal cost and they may
modify their curvature favourably. In either event a point such
as P is moved to a higher indifference curve, and the paths along
with further progress can be made are altered advantageously. 

NOTES:

1. If the circumstance that commodity a is produced under
conditions of increasing returns is taken into account as a
factor in the elasticity of demand for b in terms of a,
elasticity of demand and elasticity of supply may be looked upon
as different ways of expressing a single functional relations.

2. As contrasted with such new ways of organising production and
such new "inventions" as are merely adaptation of known ways of
doing things, made practicable and economical by an enlarged
scale of production.

3. The collective indifference is to be taken as an expository
device, not as a rigorous conception. The relative weights to be
assigned to the individual indifference curves of which it is
compounded will depend upon how the aggregate product is
distributed, and this will not be the same for all positions of
P.