POPULATION GROWTH AND THE BENEFITS FROM
OPTIMALLY PRICED EXTERNALITIES*
HARRY R. CLARKE
and
YEW-KWANG NG
La Trobe University
Monash University
r. INTRODUCTION
It is commonly believed that population growth makes a society worse off by exacerbating
resource and environmental problems. These are the concerns of Zero Population Growth
advocates (e.g. Paul Ehrlich, 1968) and opponents of international migration (e.g. Robert Rienow,
1981). In fact, even supporters of laissez faire in relation to population growth and proponents of
liberal immigration policies see congestion as an externality which limits the capacity of an
economy to absorb additional people (see Julian Simon, 1989, p.8).
In this article we show that, considering only economic effects, even if population growth, by
natural increase or immigration, increases congestion, pollution, and other forms of external costs,
that provided pre-existing citizens own the resources giving rise to the externalities, and provided
they efficiently price usage of such, that existing citizens must, in net average terms, be better off
with population growth than without it. In simple terms the increased revenues they gain from
efficient pricing at increased demand levels will be strictly greater than the monetary value of the
increased external costs together with the higher tax costs they incur as consumers of the
resources.
This suggests that the existence of externalities, per se does not provide efficiency grounds for
restricting population growth. At best it provides an argument for efficient pricing of resources
and for recognising that population growth can be immiserising for a pre-existing population if
that society chooses not to price scarce resources efficiently.
11. THEMODEL
For specificity consider the case of road congestion. The argument is readily adaptable to a
variety of pollution, public good and renewable resource issues involving external costs and
population increase.
Then, as illustrated in Figure I, let Q be total road usage and D,be the demand for road use by
pre-existing people. The average cost curve, AC, measures the time, petrol and other costs
* This work was done while Ng was visiting La Trobe University in 1990. We thank two anonymous referees
for their comments.
113
114
AUSTRALIAN ECONOMIC PAPERS
JUNE
associated with road usage. The corresponding marginal cost curve is indicated MC. Without
road pricing the equilibrium demand for travel is at E , where consumers are just indifferent
between travelling or not since marginal benefits from travel then equal average costs. At this
level of demand however marginal costs exceed marginal benefits due to the unpriced
‘congestion externality’. To maximise net social benefits the level of road usage has to be
restricted to Q, where marginal benefits from travel equal marginal costs. This demand level can
be achieved by taxing road usage at the rate t , = E,A which is the difference between marginal
and average costs at the road usage level Q , . For a more detailed discussion of this type of
analysis see Alan Walters (1961, 1987) and Richard Porter (1978).
Now let us introduce a discrete growth in population levels which shifts the demand curve to
D , in Figure 2. Note that the demand curve of existing citizens remains fixed at D , with this
change. Here, for simplicity, secondary general equilibrium effects of the population increase on
D , are ignored though their consideration would not alter substantially the analysis to follow.
With optimal road pricing at the increased level of total demand, the tax rate on travel is
increased to t2 = E,B. This increases the tax-inclusive price of travel from PI to P , and reduces
the consumption of pre-existing citizens from Q , to Q3 (= P,H).
Existing citizens are thus made worse off through the increased tax charges and congestion
costs they face by an amount equal in monetary value to the amount of consumer’s surplus they
lose. This is given by the area P,P,E,H. However the tax revenue yielded by optimal taxes can
be seen to increase by the amount t2Q2 - t l Q l . We now argue that, given downward-sloping
demands and a MC curve which is upward-sloping and above AC at any given output level (this
must be the case in the presence of congestion), the following holds.
Proposition: With increased population leading to an increased demand for a resource that is
subject to a congestion externality, the increase in tax revenues yielded by optimal taxes exceeds
the loss in consumer surplus experienced by the existing population.
To prove this let DT denote the change in tax revenue and DCS the change in consumer’s
surplus received by existing citizens given the increase in demand from D , to D,. As argued
above
D T = tzQz-tiQi
- DCS = area (P,P,E,H)
Now from the geometry of Figure 2
DT = area (P2PIE1H)+ area (HE,E,) + area (EJBE,) - area (GFAI)
i.e.
DT + DCS = area (HE@,)
+ area (E,IBE,) - area (GFA1).
Now denote total cost by TC. Then, by definition
AC = TCIQ.
1995
POPULATION GROWTH AND THE BENEFITS FROM OPTIMALLY PRICED EXTERNALITIES
FIGURE 1
Welfare and externalities with fixed population
MC
8 3
Q,
Q2
Q
FIGURE 2
Welfare and externalities with a population increase
115
116
AUSTRALIAN ECONOMIC PAPERS
JUNE
Hence
dAC-dTCIdQ
TC
so
Q-
dAC
= MC- AC.
dQ
Integrating both sides with respect to Q :
jQdAC= j(MC-AC)dQ
Now when Q = Ql, AC = F and when Q = Q2,AC = G.
Proceeding to definite integrals
Q,
G
QdAC=
F
I(
MC - AC)dQ
Q2
which proves that area(E,ABE,) = area (GFAB). (This result is similar to the well-known
theorem that the area bounded by two price lines and the demand curve equals the corresponding
area between the demand curve and the marginal revenue curve.)
Hence DT + DCS = area(HE,E,) which is positive given our assumptions about demand and
costs thereby proving the result.
In words, we have proven that the gain from the increased demand exceeds the loss in
consumer's surplus accruing to pre-existing citizens by the area of the curvilinear triangle HE,E,.
Thus if pre-existing citizens own the resources giving rise to the increased tax revenues, so it is
private property, and receive these revenues as income (or, if ownership is vested in the state,
public goods are distributed to existing residents) they will in average net monetary terms be
better off even though they face higher costs of using the resources themselves and increased
congestion costs.
This result moreover has a straightforward rationale. If new members of a society (whether
they be migrants or the progeny of existing citizens) have to pay for whatever external (or other)
costs they impose, they cannot make pre-existing people on average worse off. In short it is not
the additional people themselves who create or accentuate the problem of external costs in a
society but rather what they do. Appropriate resource pricing always prevents such actions from
imposing a net burden on existing citizens and, in fact, guarantees that the average welfare of
such people will increase.
1995
POPULATION GROWTH AND THE BENEFITS FROM OPTIMALLY PRICED EXTERNALITIES
117
This last point emphasises the fact that population control is not a generally useful procedure
for dealing with congestion externalities and external costs. A better procedure is to (where
possible) define property rights on the resources that society uses and to efficiently price usage of
these resources.
It might be objected that in the case of public goods it is unrealistic to suppose discriminatory
reimbursements of public goods can be made to pre-existing people alone. For the case of
immigration this argument can be countered by recognising that if ‘equal treatment’ is a
constitutional given that fees could be levied on entry that capture those unpaid for public good
gains that would otherwise accrue to immigrants. Clarke and Ng (1993b) show that in certain
cases property values will adjust to compensate pre-existing people for cost increases caused by
newcomers but that, if they are not, that entry charges may need to be levied. Of course it is
important to recognise that if discriminatory reimbursements are impossible that this can provide
a case for restricting population growth.
Clearly the general presumption in favour of population growth need not hold in the absence of
efficient pricing. Thus if, in the above example, road usage is unpriced then total equilibrium
usage will shift from E , to E , in Figure 2 and existing residents will enjoy reduced consumer
surplus with no compensating increase in tax revenues, i.e. they will, on average, be
unambiguously worse off unless there are other benefits from the higher population (e.g. in
reducing the per capita cost of providing public goods and social overheads).
Finally while our model is simple and ignores the supply side, allowing for competitive output
markets would not alter conclusions. Such markets provide improved opportunities for preexisting people to trade factor endowments and hence provide additional sources of efficiency
gain, see Clarke and Ng (1993a).
FINALREMARKS
It is often argued that transactions costs may outweigh the efficiency benefits that stem from
‘optimal’ resource pricing. In this event however it seems unlikely that external costs are
significant enough to justify even more drastic measures of population control: for discussion see
Yew-Kwang Ng (1986). A possible exception to this argument arises when population growth
stems from immigration since, in this event, even low external costs consequent on immigration
can be avoided by restrictive immigration policies and the resulting policy costs fall on
individuals excluded from the society.
The analysis presented has a range of applications in ‘congestion’ situations. Apart from
standard urban congestion issues more recent concerns centre on the demand for recreational
resources and wilderness congestion (see e.g. Charles J. Cicchetti and V. Keny Smith, 1976).
These concerns have become prominent in recent debates on the environmental consequences of
immigration (see e.g. Julian Simon, 1989, Ch.8).
The analysis can also be applied to externalities deriving from a failure to define property
rights on a resource (e.g. the free-access fishery or unpriced environmental resources such as air
and water subject to damage by pollutants). In this event D,and D 2 define the marginal benefits
accruing to society from the exploitation of the respective self-renewing resources. Q then refers
118
AUSTRALIAN ECONOMIC PAPERS
JUNE
to harvest rates and rates of pollution emission respectively. The average cost curve AC reflects
the actual costs borne by harvesters and polluters respectively and MC the corresponding
marginal costs. With these nomenclature changes essentially the same analysis given above
carries through and, again, pre-existing residents are better off in net monetary terms with higher
population and hence resource demands provided they own the resources that are optimally
priced.
Finally a referee has questioned whether our analysis implies an unbounded optimal population
and hence wage rates which approach zero. This issue does not arise if the source of new people
is international migration since then new people stop coming once the local wage is driven to
international levels. With emigration the same constraint means that progeny will emigrate when
wages fall below international levels. With respect to natural population growth (with emigration
excluded) however our analysis suggests that having more children always increases the
efficiency gains to pre-existing people. The ‘old’ generation always benefits from having more
progeny from an efficiency viewpoint. Of course the advantages we are describing are purely
efficiency advantages - no society will wish to see its national product growing while wages fall
to very low levels. If additional people increase the gains to pre-existing people the latter’s
demand for children can be expected to fall in any event for reasons set out in Becker (1981).
Distributional considerations also provide a practical limitation on a society’s desired population
size - a point discussed further in Clarke (1994): The basic idea is that while ‘third-best’ welfare
considerations might justify a limited worsening in income distribution given substantial enough
efficiency gains this argument cannot be extended to situations where distribution deteriorates
markedly. The functional distribution of income may deteriorate markedly if population size
becomes very large.
1995
POPULATION GROWTH AND THE BENEFITS FROM OPTIMALLY PRICED EXTERNALITIES
119
REFERENCES
Becker, Gary S . (1981), A Treatise on the Family (Cambridge, Mass: Harvard University Press).
Cicchetti, Charles J. and Smith, Kerry V. (1976) The Costs of Congestion: An Econometric
Analysis of Wilderness Recreation (Cambridge, Mass: Ballinger Publishing Company).
Clarke, Harry R. (1994), ‘Entry Charges on Immigrants’, International Migration Review,
vol. 28, no.2, Summer.
Clarke, Hany R. and Ng, Yew-Kwang (1993a), ‘Immigration and Economic Welfare: Resource
and Environmental Aspects’, Economic Record, vol. 69.
Clarke, Harry R. and Ng, Yew-Kwang (1993b), ‘When do Increased Property Values
Compensate Pre-existing People for Cost Increases Induced by Newcomers’, mimeograph.
Ehrlich, Paul (1968), The Population Bomb (New York: Ballantine).
Ng, Yew-Kwang (1986), ‘On the Welfare Economics of Population Control’, Population and
Development Review, vol. 12.
Porter, Richard C. (1978), ‘The Economics of Congestion : A Geometric Review’, Public
Finance Quarterly, vol. 6.
Rienow, Robert (1981), ‘Can We Still Close the Gates?’ The Humanist, vol. 41.
Simon, Julian L. (1989), The Economic Consequences of Immigration (Cat0 Institute, Oxford:
Basil Blackwell).
Walters, Alan A. (1987), ‘Congestion’, in J. Eatwell, M. Milgate and P. Newman (eds), The New
Palgrave: A Dictionary of Economics, vol. 1 (United Kingdom: Macmillan Press).
Walters, Alan A. (1961), ‘The Theory of Measurement of Private and Social Costs of Highway
Congestion’, Econometrica, vol. 29.