Joan Robinson
Joan Robinson
Joan Robinson
THE TECHNIQUE
CHAPTER 1
THE ASSUMPTIONS
1
THE purpose of this book is to demonstrate that the analysis
of the output and price of a single commodity can be conducted
by a technique based upon the study of individual decisions.
The fundamental assumption is that each individual acts in
a sensible manner, in the circumstances in which he finds
himself, from the point of view of his own economic interests.
A technique which would study the economic effects of
neuroses and confused thinking would be considerably more
complicated than the technique here set out.
When the fundamental assumption is made, every economic
tendency can be analysed by a series of questions. What would a
sensible man do in such a case1 Thus a priori analysis can be
made to advance the study of economic phenomena some way
towards a position in which the effects of economic tendencies
in the real world can be checked by statistical investigations.
The technique is based upon the separation of the elements
in the situation which influence the decisions of the individual
into two parts, which are assumed to be independent of each
other. The two parts of the situation are represented by two
curve ..
Thus, when we are considering the decision of an individual
producer as to how much of his commodity to sell, the condi-
tions of demand, which (abstracting from advertisement and
other marketing costs) lie entirely outside his control, are repre-
sented by a demand curve; and the costs of producing various
outputs are represented by a cost curve. By considering the
conditions of demand represented by the demand curve and his
own costs of production, the seller can decide what output to
15
16 ECONOMICS OF IMPERFECT COMPETITION n. r
2
Some elementary definitions are set out in this chapter. 1
Others are introduced as the argument proceeds.
A commodity is a consumable good, arbitrarily demarcated
from other kinds of goods, but which may be regarded for prac-
tical purposes as homogeneous within itself.
A firm is a concern very similar to the firms of the real world,
but which produces only one commodity, and is controlled by
a single independent interest.
The controlling interest of a firm is an entrep1·eneur. For long-
period problems the entrepreneur is conceived to require a cer-
tain reward, sufficient to induce him to continue in business,
which is independent of the amount of his output.
An industry is any group of firms producing a single com-
modity. The correspondence of such an industry to the in-
dustries of the real world is not perhaps very close. But in some
cases, where a commodity in the real world is bounded on all
sides by a marked gap between itself and its closest substitutes,
the real-world firms producing this real-world commodity will
conform to the definition of an industry sufficiently closely to
make the discussion of industries in this technical sense of some
interest.
A demand curve represents a list of prices at which various
amounts of a certain commodity will be bought in a market
during a given period of time. Such conceptions as the amount
of raw cotton bought in the world per year, or the number of
motor cars bought in England per month, or the number of
silk stockings bought in Berwick Market per day, may be
represented by a demand curve.
Similarly a supply curve represents the amounts of output of
a commodity, during a given period of time, which will be
associated with different prices.
1 These definitions are constructed appropriately to the analysis which is to
follow. For otber purposes different definitions might be requirod.
c
18 ECONOMICS OF Il\:IPERFECT COl\fPETITION BK.l
THE GEOMETRY
Ll_
Unlta of Output. Average Cost. Total Cost. Marginal Cost.
20 200 -
11 21 231 31
12 22 264 33
13 23 299 35
·-
or
Units of Output. Average Coot. Total Cost. Marginal Cost.
10 20 200 -
ll 19 209 9
12 18 216 7
13 17 221 5
The first example shows rising costs, the second falling costs. If
costs are constant, marginal and average cost are equal. Thus:
10 20 200 -
11 20 220 20
12 20 240 20
8 22 176 -
9 21 189 13
10 20 200 11
11 19 209 9
12 18! 222 13
13 1St 2371- 15t
14 lSl 253! 16!
2
These relationships can be represented diagrammatically by
means of marginal and average curves. According to the usual
convention, output is measured on the x axis and cost per unit
(average or marginal) on they axis. As we have seen, so long as
the marginal curve lies below the average curve, the average
curve must be falling; and so long as the marginal curve lies
above the average curve, the average curve must be rising. If
the average curve is at first falling and then rising, the marginal
curve will cut the average curve at its lowest point, for the
average curve can only fall while the marginal curve lies below
it, and only rise while the marginal curve lies above it. Similarly,
CB'. 2 THE GEOMETRY 29
if an average curve is at first rising and then falling, the marginal
curve will cut it at its highest point.
The two curves must leave they axis at the same point, since
the average and marginal cost of an indefinitely small output
are the same.
It is possible, as we have seen, to calculate marginal cost
if the average costs of two successive outputs are known, or
in other words, if the slope of the average cost curve is
known. But ·in order to derive average cost from marginal
cost it is necessary to know the course of the marginal curve
up to the output in question. We can find the total cost of n
units if we can calculate the cost of I unit, plus the additional
cost of the 2nd, plus the additional cost of the 3rd, and so
forth up to the additional cost of the nth unit. The total cost
of any output is thus shown by the area lying below the curve
of marginal costs for all outputs up to the output in question.
Then, by dividing by n, we can find the average cost.
3
We must now explore the geometrical relationships between
the:::;e two cmTes. The fundamental relationship between average
',
''
'' ....... ,
........... , E
·---.....
--· ------
)1f
0 Q
FIG. 3.
and marginal curves is that for any given output (OQ in Fig. 3)
the area lying below the marginal curve (AEQO) is equal to
the rectangle (BDQO) subtended by the average curve.
30 ECONOMICS OF IMPERFECT COMPETITION Bx.J
0 Q
FIG. 4.
0 Q
FIG. 5.
FIG. 6.
0 Q
FIG. 7.
curve corresponding to the less elastic curve must cut the line
DQ below the point at which it is cut by the marginal curve cor-
responding to the more elastic average curve, and the marginal
curves must cut each other to the left of the line DQ.
5
The relationship between a particular average curve and the
corresponding marginal curve will depend upon the elasticity 1 of
the average curve. When the average curve is rising the marginal
values must be positive whatever the elasticity of the curve,
and when the average curve is falling, but its elasticity is
greater than unity, so that an increase in output leads to an
increase in total cost, the marginal values must be positive; but
if the elasticity of the average curve is equal to unity, so that
total costs are unchanged by an increase in output, marginal
cost is equal to zero, and if the average curve has an elasticity
,,
0 ............
' . .... , . ,
..., .....
' .. ' • , , .. l'rf
~~ & -,,
of less than unity the corresponding marginal curve will show
negative values. 2
1See p. 18 for the definition of elasticity.
1We have so far taken our examples from cost curves, and if the average
curve which we are considering shows the costs of output to any business unit
it is impossible that it should have an elasticity of less than unity, for it is
impossible for the total cost of a greater output to be less than the total cost
of a smaller output. But we are here studying the relationships of marginal and
average curves as such, only taking cost curves as an example for the sake of
convenience. The fact that when an average curve is inelastic the marginal
values are negative is of importance when we come to consider average and
marginal revenue (see p. 53, below).
CR.2 THE GEOMETRY 35
The case for straight lines is illustrated in Fig. 8.
For any average curve the elasticity is infinite where it cuts
they axis, and at that point the marginal curve coincides with
it. The elasticity is zero where it cuts the x axis. The elasticity is
unity for a straight line at the half-way point. Above this point
the average curve is elastic, and the marginal values are posi-
tive; below it the average curve is inelastic, and the marginal
values are negative.
It is possible to see, quite generally, how the exact vertical
distance between the marginal and average curves will depend
on the elasticity of the average curve. The greater the elasticity
of the average curve at a given point, the closer will the mar-
ginal curve lie to it.
Thus, in Fig. 6 above, the greater the elasticity at a given
point D, the smaller will be the slope of the tangent AD, the
smaller will be the distance AB, and the nearer will E lie to D.
If the average curve is perfectly elastic, it will lie parallel to the
x axis, the marginal curve will coincide with it, and costs will
be constant. The extra cost of producing one more unit at each
E
Fro. 9.
point is then equal to the average cost of the output at that and
every other point.
The relationship between average value, marginal value and
elasticity can be precisely formulated.
(Footnote contintud]
An average cost curve of unit elasticity is not theoretically impossibls_ If
the outlay necessary to produce the minimum unit of output will serve for an
indefinitely large output without any additional cost, we should have an
average cost curve of the form of a rectangular hyperbola, and the marpnal
curve would coincide with the y and x axes. Broadcasting to various numbem
of :U.tenera might, perhaps, afford an example of such a.n average cost curve.
36 ECONOMICS OF IMPERFECT COl\iPETITION Bx. 1
(FIG. 9). Let PM be the average value for any output OM, and CM
the marginal value.
Draw a tangent to the average curve at P to cut the y axis
in A and the x axis in E.
Then the elasticity 1 of the average curve at Pis!~·
Now the triangles APF and PEM are similar.
PE PM
•·. AP= AF"
But AF=PC .
••• the elasticity at P = ~~
_average value
-average value- marginal value·
If elasticity is e, average value A and marginal value M,
then e=~; A=M-e-, and M=Ae-l.
A-M e-1 e
From this formula the ratio of the marginal to the average value
can be deduced as soon as the elasticity of the average curve is
known. Thus, for instance, if the average curve is a rectangular
hyperbola asymptotic to the axes, so that elasticity is equal
to unity for all outputs, then the marginal value is zero for
all outputs, that is to say, the marginal curve coincides with
the axes. If the elasticity of the average curve is equal to in-
finity, e- ~ is equal to unity, and the average and marginal
e
values are equal.
If e =2, M =!A,
if e =!, M =-A, and so forth.
The elasticity of a rising curve is regarded as negative. 1 For
a rising curve the marginal value is greater than the average
value.
Thus if e- -!, M =3A,
if e - - I, M = 2A,
if e = -2, M =-~A, and so forth.
J Marshall, Principles, p. 102.
2 This is illogical, but convenient. It makes no difference to the results
whether the elasticity of a rising curve is regarded as positive or negative,
provided that it is treated as of opposite sim to the elasticity of a falling cuvre.
OB.I THE GEOMETRY 37
6
Next we must show the relationship of marginal and average
curves in certain peculiar cases. These are of importance, both
because they contribute to an understanding of the general
relationships, and because they will be necessary to us in our
M M I
I
I
I I
I I
I I
I I
I
,
I
,,
I
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I
,,
I I
, ,' A
,
,' A ,,
,,
I
(
,,
I
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I
••
••
••
•
''
•
'•
•
\
.•",, A
•, : ',~
---------.11
r-- ...... _
FIG. 12.
....... .
...
......
......
....
...
' I
I
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A
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',M
FIG. 13.
£ £ £
1 101 101 -
2 102 51 1
3 103 34-l 1
4 104 26 1
.. .. ..
.. ..
100 200 2 I
I
In this case marginal cost is constant and average cost falls
as output increases. The average curve is a rectangular hyper-
bola subtending an area equal to the fixed cost (£100 in the
above example) and the marginal cost curve is a horizontal line
to which the average curve is asymptotio.l
A
----------------------------------------------fti
FIG. 14.
B~------~,-,------~~~~
.... ,............ M .
A
FIG. 15.
FIG. 16.
10
It is further necessary to consider the movements of curves.
We shall be mainly concerned with changes in the position of
average curves. These may be of various types. An average
curve may be raised so that its slope, at a given output, is the
same as before. The tangents, at that output, are then parallel.
Or it may retain the same slope at any given price. The tangents,
at that price, are then parallel. Or the curve may move in such
a way that its elasticity, either at a given output or at a given
price, is the same as before, in which case its slope will be
different.• If the elasticities are the same at one output, it can
1 The reader unacquainted with the tec,hnique is recommended to illustrate
this and the following relationships by drawing diagrams for them.
1 F"Or a reader unacquainted with the relationship between slope and eJas.
OK, 2 THE GEOMETRY 43
be she>wn that the tangents, at that output, will meet on the
x axis. Similarly, if the elasticities are the same at one price, the
tangents, at that price, will meet on they axis.1 Average curves
which stand in this relationship to each other will be found of
service in the succeeding argument, and it is convenient to have
a name for them. Two average curves which have the same
elasticity at a given price are described as iso-elasticat that price.
Average curves, of course, may also move in any other way,
so that neither the slopes nor the elasticities are the same at any
price or at any output, but the above relations, so to speak,
map out the field of possible changes.
11