This document provides a detailed analysis and reconstruction of the economic analysis contained within Malthus's 1798 Essay on Population. It begins by elaborating on Malthus's implied production function, showing how it captures diminishing returns. It then models Malthus's "simple" model of a society without property in the "savage state," demonstrating its stability. Finally, it rationalizes Malthus's more sophisticated model of a capitalist economy and examines implications like the relationship between productive and unproductive population and the role of preventative checks. The overall aim is to shed light on the internal logical coherence and ideological motivations of Malthus's seminal work.

1. ANALYSIS AND IDEOLOGY IN
MALTHUS’S zyxwv
ESSAY ON POPULATION zyx
*
A. M. C. WATERMAN
St John’s College, Winnipeg zyxw
It is generally acknowledged that Robert Malthus composed his first, anonymous Essay
on Population in zyxwvut
1798 in order to refute the ideas of human perfectibility advanced by
Condorcet and Godwin. It is less widely realised that Malthus was not so much concerned,
even then, to attack the idea of perfectibility in general as to demonstrate the impossibility
of achieving it by theparticularrouteproposed by Condorcet, Godwin and the other ‘Jacobins’.
For the latter desired an unmaking of all existing institutions, above all the abolition or at
least the drastic redistribution of private property. The subject of property is the key-stone
that completes the fabric of political justice’ wrote Godwin (1798, vol. 11, p.420), and let it
never be forgotten that accumulated property is usurpation’ (p.444). Apologists for the
established order could afford to ignore perfectibility. But the political circumstances of 1798
made it urgently necessary to answer the Jacobin attack on property. Of all who rose to the
challenge, Malthus was by far the most successful.
The story of Malthus’s crucial intervention in the antiJacobin debate of the 1790s, and
of the far-reaching ideological and scientific consequences of that intervention, is long and
complex. I have attempted to do it justice elsewhere (Waterman 1991) and to supply proper
evidence for my belief that the chief target of the Essay was Godwin’s attack upon ‘the
established administration of property’. What I propose in this article is to reconstruct the
‘economicanalysis’which may be found in the Essay, and to showhow that analysisis consistent
with the ideological purpose I have attributed to its author.
Tivo misunderstandings may easily arise from the second of these aims and it is important
that I should try to dispel them at the outset. In the first place, I make no claim that a
mathematical model of Malthus’s analysis -even if it perfectly captures the logical structure
of his argument -canprove that he wrotetheEssay to counter the Jacobin attack on property.
We can never prove that our theories are true: we may only falsify them. Having based my
‘conjecture’upon textual and historical evidencetherefore, it seems proper to expose it to the
possibilityof ’refutation’.If the mathematical reconstructionis congruent with an interpretation
of the Essay zyxwvut
as a defenceof property, that interpretation survivesthe test of internal consistency.
In the second place, no disparagement of Malthus’s achievementis intended by the suggestion
that it was ideologically motivated. Motives are never pure, nor need they be for knowledge
* Research supported by SSHRCC and the University of Manitoba. The author is grateful to all who
havemade comments on previousdrafts, especially Robert Dorfman, Samuel Hollander, Donald Winch
and two anonymous referees.
203

2. 204 zyxwvutsrqpon
AUSTRALIANECONOMIC PAPERS JUNE zyx
to grow. Arguments forged in the heat of polemic are tested by criticism. Those which prove
robust may eventually count as ‘contributions to knowledge’.
The economic analysis of the zyxwvut
Essay on Population is founded upon the famous ’ratios’
of food and population growth. The ’ratios’imply diminishing returns, as Marshall (1920,
p.179, n.1) maintained against Cannan (1903, p.144). Diminishing returns without a production
function are like a grin without a cat. Given competitive factor pricing zyxw
-which Malthus
accepted -a diminishing-returns production function implies rent. Seventeenyears after the
First Essay Malthus (1815) was among those who discoveredthe relation between diminishing
returns and rent. Samuelson (1947, pp.296-98) was the first to specifya Malthusian production
function. Five years later Stigler (1952, p.190) showed that the ratios implied a logarithmic
form of this function.
Of course Malthus had no idea of a ’production function’ in his head in 1798 or even in
1815, and it would be folly to represent him as ‘doing something which he would not -or
even could not -himself have accepted as an account of what he was doing’ (Skinner, 1969,
p.6). But ‘. ..within every classical economist there is to be discerned a modern economist
trying to be born’ (Samuelson, 1978, 1415). It is in that spirit that I shall first try to capture
in mathematical form what Malthus’s production function would have been had he actually
used one, and then make use of it by formalising in modern terms the analytical content of
the Essay. It is important to note that my formalisation differs in a crucial respect from those
applied by Costabile (1983, 1985) and Rowthorn (1985) to Malthus’s Principles (1836). For
in the latter, Malthus’s labour-commanded’ standard of value is used to elucidate the rigour
and completenessof his theories of wages, prices, ‘general gluts’ and economic growth. But
the argument of the Essay is conducted almost entirely in terms of what would now be called
a ‘corn model’: and such a model has been reconstructed in this article.
The benefits of formalising the Essay are considerable. In the first place it enables us to
examinethe structure and coherenceof Malthus’s polemic. Just how is the zyx
slatus quo founded
upon a stable equilibrium system? Why is it optimal? Why is the preventive check uniquely
capable of improvingthe lot of the poor? And secondly,it helps us to sort out certain puzzles
that have bedevilled Malthusian scholarship from time out of mind. How do we disentangle
the merely ecologicalmodel applicable to ’the savage state’ from the sophisticated model of
a capitalist economy with which it is conflated in all recensions of the Essay? What is the
relation of ’productive’and ’unproductive’population in Malthusian theory? What notion
of ‘optimum population’, if any, did Malthus entertain? Why did Malthus come to believe
that ’a progressive rise of rents seemsto be necessarily connectedwith the progressive cultivation
of new land, and the progressive improvement of the old’ (1836, p.173)?
An apparatus, necessarilyrather complex, which permits us to answer all of these questions
is developed below in four stages. In Section I Stigler’sproduction function is elaborated to
capture the full sense of Malthus’s argument. It is then used in Section zyx
I1 as the basis of
Malthus’s ‘simple’or ecological model of the circular causation of food and humans in the
‘savage state’. Section zyxwvut
111is a rational reconstruction of the ‘sophisticated’model implicit in
the anti-Godwin arguments but never fully spelled out in any version of the Essay. The
optimality of equilibrium is demonstrated, and the relation between ’productive’ and
’unproductive’population made clear. Section IV contains the principal corollaries of the
analysis, in particular the analytical and ideological significance of the ’preventive check’.

3. 1992 ANALYSIS AND IDEOLOGY zyxwvu
205
A zyxwvutsrq
concluding section employs the principal results in support of a reappraisal of Malthus’s
ideological program.
I. THEMALTHUSIAN
PRODUCTION
FUNCTION
Stigler’s formulation zyxwvuts
-later rediscovered by Lloyd (1969)-though suggestive,is inadequate
to capture the full range of the classical production theory in general or of Malthus’s in
particular. I have elsewhere developed a complete account of the Malthusian production
function (Waterman 1987, pp.259-62) and what follows is a summary re-statement.
The ’means of subsistence’are a homogeneous food-stuff (‘corn’) produced at a rate of zy
F units per period; population and work-forceare one and the same and at full employment
supplyN units of homogeneous labour input per period. Then the Stigler-Lloyd formulation
may be represented as
F = LlnN (1)
where L is a parametricfunction. However, I believe that Samuelson(1978, pp.1415-16) is correct
in statingthat ’theclassicistsin effect assumethat output is produced by a production function
involvingland input and a zyxwvu
dose of labour-cum-capital input’. Each new entrant to the work-
force comes furnished with the necessary complement of buildings, tools, livestock and so
forth, and these must be produced. Hencethe ’productive’work-force is employed both ‘directly’
on the land, and ’indirectly’in equipping itself with capital goods. Let there be u different
capital goods, the technically-determined capital-labour ratio of the sth good being zy
k
,
. Let
A be a vector of available lands. Capital intensities and the land vector are shift parameters
of the function describing L:
L = L(A, kl, k2, . . ., ku).
Let capital goods be produced by labour alone, the amount of labour required to produce
one unit of the sth good being j ; and its rate of depreciation 6
,
. Then the labour required
to maintain ks constant when N grows at the proportionate rate n is
@ = j&,(6,+n)N
and total ‘indirect’labour
Define y zyxwvuts
I 1- Cjsk-nCjk, then the land-scarce production function becomes
F = L(A, kl, k2, . . . ku)lnQN).
(3)
Malthus was well aware of the fact that (5) does not operate under conditions of free land.
‘It has been universallyremarked, that all new coloniessettled in healthy countries wherethere
was plenty of room and food, have constantly increased with astonishing rapidity in their

4. 206zyxwvutsrqpo
AUSTRALIANECONOMICPAPERS JUNE zyx
population’ (1798, p.101; see also pp.101-8, especially the note on pp.106-7). Malthus here
envisaged the possibility of free land. In such a case population growth proceeds at the
biologicalmaximum rate, zyxwvu
2
.Supposethat the rate of population growth increasesas the excess
of the zyxwvutsrq
per capita ’meansof subsistence’f zyxwv
1 FIN over some (socially determined) subsistence
allowance, zyxwvuts
S. Then
n zyxwvutsrq
= m(f-S),m > 0, (6)
from which the land-free production function is simply
F = (S+ii/m)N. (7)
Given the parametersof L, y, S, ii and m (and provided S+ ii/m<L/e)a valueof N = Nm>e
will exist at which (5) and (7) are simultaneouslysatisfied. We may therefore specifyMalthus’s
implicit production function as:
equation (7) for N<Nm;
equation (5) for NrN,.
It is this production function, I believe, which ought to be employed in any rational
reconstruction of the ‘economic analysis’contained in the Essay on Population. zyx
11. THE’SIMPLE’
MALTHUSIAN
MODEL
Consider a society in the ‘savage state’ (1798, pp.39-52) without private property in land,
and without food or labour markets. Individual workers fabricate their own tools, build their
own dwelling, provide their own clothing and so forth, hence the distinction between ‘direct’
and ’indirect’labour does not appear and we can take y = 1. Labour is assigned to food
production, and food to individuals, by some non-market mechanism such as custom, tribal
council, or fiat of the ruler.
I have analysed the properties of this model elsewhere (Waterman 1988), from which it
appears:
(a) the simple Malthusian model is closely similar in formal structure to that employed
by Hume in his essay ‘Of the Balance of Trade’;
(b) stability requires that the marginal product of labour should be less than the average
product.
The stabilitycondition is, of course,implied by diminishingreturns, guaranteed for all (land-
scarce) points on the production function by the specificationof (5). Malthus’smuch maligned
’ratios’, which even his strongest supporters have tended to play down (e.g.,Mill, 1909,p.359),
turn out to be of key analytical significance. For by implying a production function which
-over the relevant range -exhibitsuniversaldiminishing returns to labour, they are sufficient
for stability of the system which jointly determines the equilibrium levels of population and
food.
It is worthwhileto consider the methodological implications of this result, for they have
eluded some distinguished commentators on the Essay.

5. 1992 zyxwvutsrqpon
ANALYSIS AND IDEOLOGY 207 zyx
According to Schumpeter (following Cannan, 1917), the argument of the zyxw
First Essay zy
...clearly was intended to mean that population was actually and inevitably
increasing faster than subsistence and that this was the reason for the misery
observed. The geometrical and arithmetical ratios of these increases, to which
Malthus like earlier writers seems to have attached considerable importance, as
well as his other attempts at mathematical precision, are nothing but faulty
expressions of this view which can be passed by here with the remark that there
is of course no point whatever in trying to formulate independent ‘laws” for the
behaviour of two interdependent quantities.
(Schumpeter, 1954, p.579)
It is apparent that Schumpeter was seriously misled in this passage. The formulation of
‘independent ‘laws” for the behaviour of ...interdependent quantities’ is, in fact, the very
essence of ‘economicanalysis’. Every fresher learns how to formulate ‘supply’and ‘demand’
as a pair of ’independent ‘laws”’ relating price and quantity, and to solve for equilibrium
values of the ‘twointerdependent quantities’. Everygraduate student learns how to investigate
the stability of that equilibrium by specifying adjustment functions and solving the resulting
set of differential equations. The %orrespondence’between the stationary solution of the
disequilibrium model and the comparative statics results (Samuelson, 1947) was becoming
well-known by the time Schumpeter wrote.
Malthus needed one law’ to describe the dependence of population on food, and another
to describe the dependence of food on population. And he needed his ratios (or some similar
device for generating diminishing returns) in order to guarantee the stability of his system.
By means of these simpleingredients he constructed a typicalexampleof the ‘circular-causation’
models which as Trevor Swan (1962) showed are applicable to a very large class of social
phenomena.
Circular-causation models are apt for graphical illustration. Equation (5) describes the
‘schedule’or ’propensity’of food to vary with population when land is scarce. Equation (7)
describesthe ’propensity’of food to vary with population when land is free. The two equations
are plotted in Figure 1, wherethey intersect at zyxwv
I
? The Malthusian production function is thus
the solid line OPQ-extended. (It is clear from this, and from the equations which lie behind
it, that Malthus’s production function is almost ’well-behaved’in Inada’s sense. F(0) = 0, zy
F(N)>0, and F(00) = 0;but F“(N) zyxwvu
5 0 rather than F“(N)c0, and F(0)= zyx
(S+E/m) c 00).
From equation (6) we obtain the ‘schedule’or ’propensity’of population to vary with food
by setting n = 0 and writing F = SN. In later editions of his Essay Malthus used the word
’tendency’in something like the sense of the modern ex ante ‘schedule’or ’propensity’. (See
McCleary, 1953, pp.114-28, on the Senior-Malthus correspondence.) Figure 1 shows the F =
0 and zyxwvutsr
N = 0 loci intersecting at point Q, so determining a stable equilibrium of food (Fo*)
and population (NO*).If land were always scarce a second, unstable, node would exist where
the plot of (5) intersectstheN = 0locus. This possibility is evaded by the free-landassumption,
which locates the unstable equilibrium in the origin.
Malthus used the ‘simple’model to demonstrate in typicallyeighteenth-century fashion that
the laws of Nature’ operate in society, as in the physical universe, to preserve the stability
of equilibrium, restoring the status quo or something like it after any temporary disturbance
(see Waterman 1988). The greater part of the First Essay, however, is based upon a far more

6. 208 AUSTRALIAN zyxwvut
ECONOMICPAPERS JUNE zyx
original and sophisticated model zyxwvu
-never fully specified, only hinted at in many places -
in which private property and competitive factor markets determine a food/population
equilibrium that is short of the ecologicalmaximum. The social surplus is thereby maximised
and those institutionsof societyrehabilitated which Godwin (1793, 1797)and the other Jacobins
had sought to discredit. To this version of the Malthusian model we now turn. zyx
111. THE’SOPHISTICATED’
MALTHUSIAN
MODEL
The argument of Section I1 is applicable to an aboriginal society; or -at its outset -
to Mr. Godwin’sbeautifulsystem of equalityrealised in its utmost purity’(Malthus 1798,p.181).
War and contention cease. Unwholesome trades and manufactories do not exist.
Crowds no longer collect together in great and pestilent cities for purposes of
court intrigue, of commerce, and vicious gratifications. Simple, healthy and
rational amusements take place of drinking, gaming and debauchery ... The
greater part of the inhabitants of this terrestrial paradise live in hamlets and
farmhouses scattered over the face of the country ...All men are equal.
(pp.181-82)
Before long, however, the growth of population reduces zyxw
f to some critical level and This
beautiful fabric of the imagination vanishes at the severetouch of truth’(p.189). The ‘chilling
breath of want’leads to a Hobbesian war of all against all (p.190), from which society would
emerge, ’in a very short period ...constructed upon a plan not essentially different from
that which prevails in every known State at present; ...divided into a class of proprietors,
and a class of labourers, and with self-love for the mainspring of the great machine’(p.207).
It would seem from this passage, as also from pp.286-89 and 344, that Malthus envisaged
a two-class society. ‘Proprietors’of land are the ‘ownersof surplus’(p.204): all others belong
to ’thatclass of peoplewhose onlypossessionis their labour’(p.86;seealso pp.287-88). However,
a middle classis also recognisedto exist (pp.367-69), though subsumed, we may suppose,under
The Rich’, who ’bearbut a small proportion in’pointof numbers to the poor’(p.289). Some
of these are capitalistic farmers or ‘cultivators’(p.30), owning no land but venturing their
‘capitals’in agricultural production. It is this class which plays the crucial role in the action
of the ‘sophisticated’ model.
Assume that competition drives the real return to combinedlabour-and-capitalto its marginal
product. From zyxwvut
(5) this will be L/N, per employed worker. Capitalists control the whole of
this return, paying some as wages and keeping the rest as profit. Let the real (‘corn’) wage
be zyxwvutsrq
W.Define all kswith referenceto the employed part of the work-force,N,. Then the ‘corn’
cost of production of the fixed capital stock is WNe.Cj&s, or WNd, where J I Q&s. The
corresponding value of ’workingcapital’ advanced as wages is WN,. Hence the total capital
stock is WN,(l+J) measured in ‘corn’units. Let the rate of return be r, then the total return
to capital is WNg(l+J), or Wr(l+J) per employed worker. Hence the marginal product is
divided between a wage and a profit component according to:
L/N, = W+ Wr(l+J). (8)

7. 1992 ANALYSIS AND IDEOLOGY zyxwvu
209zyx
Assume that employment is determined by the demand for labour, perfectly inelastic for a
given stock of fixed capital goods and a given set of technically determined k-ratios.
Accordingto Malthus adjustment to equilibrium of employment, capital stock, factor prices,
and output takes place very spasmodically (1798, 29-31). Temporarily high wages cause
population to increase whilst capital and employment remain constant and unemployment
rises. Falling per capita real income eventually halts population growth, but raises the rate
of return by (8). Capitaliststhen increaseemployment,increasing fiied capital stock by ‘indirect’
and food production by ‘direct’labour. When the rate of profit has fallen to some minimum,
r*, at which accumulation stops, the work-force is fully employed at the wage-rate zyx
W and
the ‘oscillation’is repeated (Waterman, 1987). Merely for purposes of stability analysis this
process may be approximatelyrepresentedin continuous time. The effect of doing so is analysed
in the Appendix, in which it is shown that the ‘sophisticated’model has a stable equilibrium
at which zyxwvut
WY zyxwvutsrq
= zyxwvut
S,r = r* and N* = L/(xS) where X I l+r*(l+J). zyxw
I f
Now the equilibrium level of population in the simple model is seen from (6)and zyx
(5) to
be NO* = (151s)
In NO*; whereas in the ‘sophisticated’ model equilibrium population is
N1* = L/(XS).Since 1/X is the relative share of labour in total variable-factor return at full
employment, its order of magnitude will ensure that Nl*<No*. Thus private property, as
Godwin correctlynoted, ’maybe consideredas stranglinga considerableportion of our children
in their cradle’ (1793, vol. zyxwvu
11, p.467). Malthus implicitly granted Godwin’s point and turned
it against him. For the First Essay was written to show that
It is to the established administration of property, and to the apparently narrow
principle of self-love,that we are indebted for all the noblest exertions of human
genius, allthe finer and more delicateemotions of the soul, for everything,indeed,
that distinguishes the civilized, from the savage state ...
(pp.286-87)
Private property in land, together with competitive labour and food markets, by containing
population below the ecologicalmaximum, createthat surplus upon which civilisationdepends.
Let the surplus, or rent to landlords, be
Where F(N) is equation (5) and P(N) is total production costs as a function of population
work-forcewhen there is full employment. When labour is paid the subsistence wage, W =S,
P(N) = XSN. Rent is maximised when R‘ = 0 and R“ < 0. The first will be the case when
N = N1* = L/(XS);the second is always true because of (5). But (5) is an implication of
the ’ratios’. In the ‘sophisticated’version of Malthus’s model, that is to say, the function of
the notorious ’ratios’is ideologicalas much as analytical. By implyingthe almost-well-behaved
land-scarce production function (5) they guarantee that ‘self-love’and ’property’will together
maximisethat social surplus upon which all ’that distinguishes the civilised, from the savage
state’ depends.
Under ’the established administration of property’ landlords appropriate the surplus over
and above what is required for their own maintenance. This may be, and actually is spent
on the employment of those who provide personal services, ‘ornamental luxuries’, and ’the

8. JUNE
210 AUSTRALIANECONOMIC zyxwvu
PAPERS zyxwvu
noblest exertions of human genius’ such as clergymen and College Fellows. Now ‘the fund
appropriated to the maintenance of labour, would be, the aggregatequantity of food possessed
by the owners of land beyond their own consumption’ (p.205). Since Malthus assumed that
landlords’own consumptionis negligible (p.289), this means that a very much larger population
can be supported than N1*. zyxwvu
Q zyxwv
I . ‘ / I /
I zyxwvutsr
I I I /
I I / C I
N = O
F=O
FTGTTRE 1
The ‘Circular Causation’ of Food and Population
From (9) and (5) total rent at equilibriumis zyxwvu
R* = L(ln@*Ni*)-l). Suppose this is expended
by landlords in services, the construction of country houses, ’tythes’for the support of the
church, and domestically manufactured ‘ornamental luxuries’. Then the maximum number
of workers who can be employed in theseways (provided that wages areequalised acrosssectors)
will be
Maximum total population will therefore be

9. 1992 ANALYSIS AND IDEOLOGY 21 zyx
1 zyx
Since it has been establishedthat zyxwvut
N1* zyxwvu
c NO*,
it followsthat N1* zyxw
c N c NO*.
Malthus followed
the terminology,though not the reasons, of the ‘FrenchOEconomists’in regarding ‘alllabour
employed in manufactures as unproductive. Comparing it with the labour employed upon
the land, I should be perfectly disposedto agreewith them zyxwv
...(p.329). When all land is owned
by a small landlord class, that is to say, population will be divided into ’productive’and
’unproductive’labour; and the maximum size of such a population will be less than what
might obtain (for the same L) in a non-market society.
Figure 2 displays these relations, and the results of Section I11 upon which they are based.
For diagrammatic simplicity zyxwvuts
F(N) is drawn upon the assumption that y = 1. Points P and
Q appear as in Figure 1as do NO*and Fo*.
The equilibrium population locus, obtained by
setting (10) = 0, is the vertical line at N1*. Equilibrium production (F1*)is thus at point
X on the production function, where the slope of the tangent RX-extended measures the
marginal product of the labour-capital composite factor. This is equal to the unit cost of
production, XS, when labour is paid the subsistence wage, WY = S.Hence the share of
production received by labour is measured by the vertical distance N1* the share received
by capitalistsby UT and the landlords’surplus, maximised when productivepopulation/work-
force is N1*, by the distance TX. If landlords use this surplus to provide employment for
Fl
Nm Y* zyxwv
N &* N
-Productive Unproductive ,
Population Population
FIGURE 2
Equilibrium of ‘Productive’ and ‘Unproductive’ Population
in the Sophisticated Model

10. 212 AUSTRALIANECONOMIC PAPERS JUNE zyx
’unproductive’workers at the wage-rate zyxwv
w* zyxwv
= S,total population will be ON,and the
’unproductive’population N1*& Population at which land becomes scarceis zyxw
ONm as before.
IV. SOME
OTHER
IMPLICATIONS zyxwv
OF THE MALTHUSIAN
PRODUCTION
FUNCTION
The argument of the preceding sections has implications for severalfeatures of Malthusian
Political Economy which we may here review briefly.
a) Optimum Population
Spengler has noted that ‘Malthus did not conceive of an income optimum, or maximum
per capita income, population’ (Spengler, 1972, p.61). Notwithstanding Samuelson’s attempt
to determinean optimum population from his -modified-version of the Malthusian model
(Samuelson, 1947,pp.296-99) it is clear from the production function described by equations zy
(5) and (7) together that in terms of Malthus’s own conceptual framework his idea is nothing
but a curiosum.
Let the optimum population, @, be defined as that equilibrium level of population at
which f is maximised atfO zyxwvu
ip/@.Since when all ks are constant
f(N) = zyxwvuts
N - ‘ ( F N - ~ (12)
the first-order conditions are satisfied whenf = FN; in terms of diagrams like Figures 1 and
2, that is to say, when a ray from the origin is tangential to the production function. Note
that from (5) and (9) the equality off with FN implies that Ro = 0. ‘Optimum Population’
in the modern sense is that at which total rent is zero.
Now it is clear from a glance at Figures 1 and 2 that f = FN at any point on the ray OP
-that portion of the production function described by (7) - and at no point beyond P.
Population is always ‘optimal’when land is free: never when land is scarce. If land were always
and everywherescarceequation (5) alone would describe the production function, and hence
an ‘optimum population’ in the usual, non-Malthusian sense, could be determined. Since it
is necessary, from (12), that FN(N0) = p / @ ,
it followsfrom (5) that p = L and therefore
that @ = e/y. An ‘optimum population’ exists in this imaginary case, and it exhibits
Samuelson’s ‘one-sidedstability-instability’.But its order of magnitude would be about that
of a single family.
b) Income Distribution
Sincefrom (8) the combinedincomes of capitalistsand workerswill always be L, the relative
share of landlords in primary production will be l-(ln@N))-l. Hence as population rises,
the relative share of landlords will increase. When ’productive’labour is fully employed in
the sense that the quantity demanded and supplied of labour is equal to the population/work-
force, then the relative share of ’productive’ labour is (hln@N))-’ and of capital is
(1-W(XlnCvrJ))-l. For a given N the relative share of labour will thereforerise with the degree
of employment and that of capital will fall, and vice versa. If population rises, the relative

11. 1992 ANALYSIS AND IDEOLOGY 213 zyx
sharesof both capitaland ’productive’labour will fall for a given degreeof employment.Though
changes in available land (for example, the draining of the Fens) or in capital-labour ratios
may raise zyxwvutsrq
L and hence increase at first the absolute incomes of capital and labour, they can
have no effect upon relative shares. And at stationary equilibrium, when W has again fallen
to Sand Nincreased, the relative sharesof capital and labour will be lower, and that of landlords
larger.
c) Technical Progress
Technical Progressmay be of the Hicks-neutral kind postulated by Eltis (1984)and Costabile
and Rowthorn (1985)in their Malthusian models. In such casea temporal shift of the Lfunction
from whatever cause increases all incomes for given N and Ne but leaves relative shares
unchanged.
Population will not remain ‘given’however. Suppose the ‘sophisticated’Malthusian model
at stationary equilibrium. Then N1* zyxwvu
= L/(XS),hence the relative share of labour-and-capital
will be ln~*L/(XS)]’l. A once-for-all increase of L which leaves all ks (and therefore y*)
unchanged will therefore have a perverse effect upon income distribution. For though at first
the wage-rateand profits will rise, the resulting growth in population will bring about a new
equilibrium at which the real wage is once again zyxwv
W = zyxw
S,and the relative shares of capital
and labour have fallen.
‘Harrod-neutral’, or labour-augmenting technical progress, by increasing some or all the
ksratios, would increase L and reduce y*. If the latter effect is dominant, relative shares of
labour-and-capital can be increased at stationary equilibrium. The real wage will once more
be at subsistence, however.
d) The Preventive Check’
In the First Essay Malthus - following a tradition which goes back to Plato (1945, 60)
-recognised that prudential considerations deterred many from early marriages and hence
acted as a check upon population (1798, pp.63-70). In the second and subsequent editions
this effectwas notionally separatedfrom its ‘consequentvices’and advocatedas zyxw
’moral restraint’.
In terms of the analytical framework of this article, the preventive check, with or without
vice, is a parameter of the function governing zyxwv
S, the socially-determined subsistence wage.
All other things being equal, an increase in ’moral restraint’ (or mere prudence) will raise S
.
It is evident from (b) and (c) above that this is the only possible way of improving both
the relativeand the absoluteposition ofproductive labourat stationary equilibrium.An increase
in S raises W pari p p u . Given X, the relative shares of both capital and labour will rise
at the expense of landlords, for their combined relative share, ln@L/(xS))-l, will rise. In
Figure 2 the effect of increased ’moral restraint’ is to rotate both the rays OU-extended and
Orextended anti-clockwise. The point of tangency,X,movesto the left along the production
function. Hence at stationary equilibrium total production is lower; the landlords’share both
absolutely and relatively lower; shares of both labour and capital relatively higher; and the
real wage absolutely higher.
We may learn from this why the Malthusian tradition of ‘Christian Political Economy’s0
assiduouslypromoted working-class education for smaller familiesand higher living standards

12. 214 AUSTRALIAN ECONOMIC PAPERS zyxwvu
JUNE zy
(Waterman, 1983, 1991). We may also see why Malthusian population theory, hastily erected
in 1798as an antiJacobin scarecrow,was transmuted within a generation into one of the Thirty-
nine Articles of ‘Philosophic Radicalism’.
V. THEIDEOLDGICAL
FUNCTION
OF MALTHUSS
POPULATION
THEORY
It is a measure of Malthus’s importance, as Schumpeter (1954, p.481) remarked, that he
continues to stir controversyto this day. An anti-Malthusian tradition beginningwith Hazlitt
and Southey zyxwvutsr
(Annual Review, 1803, p.299) regards the inclusion of ’moral restraint’ in the
1803recension as destructive of his argument. As Bagehot put it, ‘In its first form the Essay
on Populationwas conclusiveas an argument, only it was based on untrue facts; in its second
form it was based on true facts, but it was inconclusiveas an argument’ (Bagehot, 1889, vol.
V
)
. It is this tradition that Stigler (1952, p.191) transmitted when he claimed that ‘Malthus
capitulated, while still claimingvictory zyxwvu
...Given the ., .efficacy of moral restraint, Godwin
had carried the issue’. On the other hand a pro-Malthusian tradition which included the
Edinburgh Review (Fontana 1985, p.55-6) and virtually all economists of Malthus’s own day
regarded his refutation of Godwin as decisive.
The explanation of this puzzle, I believe, is quite straightforward. The Romantics thought
the debate was about perfectibility. The Whigs, the Edinburgh Review and the economists
thought it was about theestabhhed administrationofproperty. If the formeristhe case Godwin
was the winner and Stigler’s appraisal correct. If the latter, Malthus was the winner: but no
modern formulation of his arguments has yet quite grasped the point of the Essay. It is my
claim that the rational reconstruction of Malthus’s analysis presented in this article supports
(though it can not ’prove’) the view that his chief target was not the Romantic idea of
perfectibility but Godwin’s ‘Jacobin’attack on ’the established administration of property’
which Godwin himself regarded as the ‘key-stonethat completesthe fabric’of political Justice
(1793, Book VIII).
The ‘simple’ model shows that the abolition of property (etc.) will be self-reversing. The
‘sophisticated’ model shows that with private property and wage-labour that surplus is
maximised at equilibrium upon which depends all ’that distinguishes the civilized, from the
savage state’. Godwin was correct to say that privateproperty strangles‘a considerableportion
of our children in their cradle’ (the amount NO* in Figure 2). But that turns out to be a
good thing because it keeps average per capita income above subsistence.
In this context it is clear that ’moralrestraint’,whilst conceding the possibilityof indefinite
progress (whichwas what Godwin understood by ’perfectibility’),actuallystrengthensthe case
against Godwin’sattack on property. For in a society with private property and a market
for labour services, and in which the institution of marriage assigns the cost of procreation
to the parents, it would be rational to defer marriage. Hence ‘self-love’reinforces the duty
of ’moralrestraint’. But in Godwin’sutopia, without property, without any predictable reward
to labour servicesand without any legallyenforced obligation to recognise, let alone support,
one’s children, the ’passion between the sexes’-often in conflict with social duty -would
operate with no economic sanction to restrain it.
Mr. Godwin acknowledgesthat in his system, “the ill consequences zyx
of a numerous
family will not come so coarsely home to each man’s individual interest as they

13. 1992 zyxwvutsrqpon
ANALYSIS AND IDEOLOGY zyxwvu
215 zyx
do at present”. But I am sorry to say that, from what we know hitherto of the
human character, we can have no rational hope of success, without this coarse
application to individual interest, which Mr. Godwin rejects.
(Malthus, 1803, pp.385-86)
Malthus had no truck with the ultra-Tory paranoia of the zyxwv
Anti-Jacobin Review. He was
a Whig, a friend of progress and quite sincerein his desire for the betterment of the labouring
classes. But he repudiated the Romantic doctrine that ’perfectibility’would be achieved by
abolishing property and other institutions. For Malthus and those who developed his ideas
up to the 1830s(Waterman, 1983, 1991)moral improvement was not endogenousbut exogenous.
Religious and moral improvement of the labouring poor (leading to a parametric increase
in zyxwvuts
5
‘
) was the sovereign, indeed the only, way to achieve that amelioration of the human
condition that the Jacobins and other Romantics only dreamed of.
APPENDIX
Stability of the Sophisticated’ Model
From (8) the full employment wage is
Wf zyxwvuts
= L / ( W (-41)
where X = l+r*(l+J). Equation (6) must then be modified to replace f with the average
working-class income, w i WN,JN, equal to L/(xN)at full employment. Thus population
growth can be approximated as zyxwvu
N = rn(L/X-sN). (A21
The nearer the system to full employment and the quicker the response of population the
better will this approximation be.
Let the wage-bill be G zyxwvu
a New, hence the proportionate rate of change of employment,
ne = GIG- WIW. (A31
Let the supply of labour be Ns = Ns( K N),and the rate of wage-change determined by excess
demand: zyxwvut
W/
W = +(Ne-Ns( W,N));4‘>0, +(O) = 0. (-44)
Now whatever the level of population or employment, the total variable-factor return which
capitalists divide between themselves and their employees is always L. Hence the greater the
excess of the full-employment wage-bill, L/X,over the actual wage-bill, G, the higher the rate
of profit and the greater the incentive to increase G and so employ more workers to make
new capital goods and ’to turn up fresh soil, and to manure and improve more completely
what is already in tillage’(Ma1thus1798,p.30-31). Let us, therefore, assume the rate of increase

14. 216 AUSTRALIAN ECONOMIC PAPERS JUNE zyx
of the wage-bill to be an increasing function of the rate of unemployment zyx
G/G zyxwvut
= zyxwvuts
x(N-N,); zyxwvu
x’>O, ~’(0)= 0. (AS)
It follows from (A3), (A4) and (A5) that
From (5), by use of N, and ne for Nand n and differentiationwith respect to the time variable,
the rate of change of food production is
F = L(ne-’i2/y). (A7)
Since y was defined as zyxwvu
1- CjSk-nCjk,
Equations(a),
(A3),(A4), (A5),(A6),(A7)and (A9) describethe out-of-equilibriumbehaviour
of the ‘sophisticated’Malthusian model when the parameters A, k,, js, u, r*, m, zy
S,and the
parametersof the 4, zyxwvuts
x and Ns functionsaregiven. Equation (A2)
is sufficientfor global stability
given that m >O and S>O.For if N = 0then zyxwvu
N* = L/(xS), and hence W = S
.Since W = 0,
4 = 0 and therefore N, = N,( W ,
W ) = W .It then follows from (AS) that x = 0; and
since 4 = x = 0, then ne = ‘
i
, = y = 0. From (A7) therefore, F = 0. Hence y* = 1- CjSk
and the equilibrium output of food is Fc = Lln((1- VSk)L/(xS)).
Since w* = L/(W*), r
= r*. The equilibrium stock of fixed capital goods is the vector W(kl,k2, ... , ku).
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