PRIVATE GOOD, EXTERNALITY, PUBLIC GOOD*
| DOI | http://doi.org/10.1111/j.1467-9485.1970.tb00488.x |
| Author | Alan W. Evans |
| Published date | 01 February 1970 |
| Date | 01 February 1970 |
PRIVATE
GOOD,
EXTERNALITY,
PUBLIC
GOOD*
ALAN
W.
EVANS
In
two recent investigations into the economic problems of externality the
authors have noted in passing that the welfare or optimality conditions
in
the case of a consumption externality seemed identical with the welfare
conditions in the case of public goods as originally stated by Samuelson.’
The purpose of this paper is to demonstrate that the welfare conditions for
a public good are a special case of the welfare conditions for a consumption
externality where a public good
is
defined as a good ‘which all enjoy in
common in the sense that each individual’s consumption of such
a
good
leads to
no
subtraction from any other individual’s consumption of that
good
’
(Samuelson
[4]).
Since the welfare conditions for a private good are
also a special case of the welfare conditions for a consumption externality,
it
follows that we have a range of externality with the pure private good and
the pure public good as polar cases.
In
a recently published paper Samuelson has altered his definition
of
a
public good and has redefined it as simply
any
good ‘with the property of
entering into two or more persons’ preference functions simultaneously
’
[8
p.
1021.
i.e. any good with an external effect in consumption.
If
this
definition is adopted the whole range of consumption externality is defined
as publicness and the distinction between ordinary externality and a type
of externality which could otherwise be described
as
publicness
is
blurred.
Since Samuelson’s earlier definition of a public good quoted in the first
paragraph of this paper does define a special case of consumption externality
and the welfare conditions for this special case are shown in this paper to
differ from those for the usual consuniption externality it
is
suggested here
that this definition should
be
retained. Therefore the term ‘public good’
will be used in this paper
in
the sense implied by the earlier definition rather
than the later.
*
This article arises from a research project on land use planning financed by the
Social Science Research Council.
1
Buchanan and Stubblebine
[l,
p.
3831
‘A
point worthy
of
brief note is that
our
analysis allows the whole treatment
of
externalities to encompass the consideration
of
purely collective goods.
As
students of public finance theory will have recognised,
the Pareto equilibrium solution discussed in this paper is similar, indeed is identical,
with that which was presented by Paul Samuelson in his theory
of
public expenditure.
The summed marginal rates
of
substitution
.
.
.
must be equal to marginal costs.’
Dolbear
[3,
p.
35111
‘
Readers
who
are familiar with Samuelson
[4,5]
will recognise the
condition
[for
optimal externality]. Samuelson suggested that Pareto optimality for a
public good requires the sum (over consumers)
of
the marginal rates
of
substitution
of the public good
for
the private good to equal the marginal rate of transformation.
The same condition is used for this example.’
I9
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