A New Approach to Consumer Theory
Author(s): Kelvin J. Lancaster
Source:
The Journal of Political Economy,
Vol. 74, No. 2 (Apr., 1966), pp. 132-157
Published by: The University of Chicago Press
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A
NEW APPROACH TO
CONwXSUMER THEORY*
KELVIN J. LANCASTER
Johns Hopkins
University
I.
THE
CURRENT STATUS
OF CONSUMER THEORY
m
TIHE
theory
of consumer
behavior in
deterministic situations
as
set out
by,
say, Debreu
(1959, 1960)
or
Uzawa
(1960)
is a
thing
of
great aesthetic
beauty, a jewel set
in a glass case. The
product of a long process
of refinement
from the nineteenth-century
utility theo-
rists through Slutsky
and Hicks-Allen to
the
economists of
the last
twenty-five
years,1 it
has been shorn
of
all
irrelevant
postulates
so
that it
now stands
as an
example
of how
to extract
the minimum
of
results
from
the
minimum of assump-
tions.
To the process
of slicing away with
Occam's
razor,
the author
made
a
small
contribution (I 957).
This brought forth
a
reply by Johnson (1958)
which suggest-
ed, somewhat tongue-in-cheek,
that the
determinateness
of
the
sign
of
the substi-
tution effect
(the only
substantive
result
of
the theory
of
consumer
behavior)
could
be
derived from
the proposition
that
goods
are
goods.
Johnson's comment,
on
reflection,
would
seem
to
be
almost the best
sum-
mary that can be given
of the current
*
The
author
wishes to
acknowledge
helpful
comments
from
various
sources,
including Gary
Becker,
Harry
Johnson,
and colleagues
and students
at
Johns
Hopkins
University,
especially Carl
Christ,
F. T.
Sparrow,
William
Poole, C.
Blackorby,
T.
Amemiya, and T.
Tsushima.
1
The
American Economic
Association
Index of
Economic
Journals
lists
151
entries
under
category
2.111
(utility,
demand, theory
of the
household)
over the
period
1940-63.
state
of
the theory of
consumer behav-
ior. All
intrinsic properties
of particular
goods,
those properties that
make a dia-
mond
quite obviously
something dif-
ferent
from a
loaf of bread,
have been
omitted
from
the theory, so
that
a
con-
sumer who
consumes diamonds alone is
as
rational
as
a
consumer who
consumes
bread
alone, but one who
sometimes con-
sumes
bread, sometimes diamonds
(cete-
ris
paribus,
of
course), is
irrational. Thus,
the
only
property
which
the
theory
can
build
on is
the property
shared
by
all
goods,
which is
simply
that they
are
goods.
Indeed,
we can
continue the
argument
further,
since
goods
are
simply what
con-
sumers
would
like
more
of;
and
we
must
be neutral with
respect
to differences
in
consumer tastes
(some
consumers
might
like more
of
something that
other con-
sumers
do
not
want),
that
the ultimate
proposition
is
that goods are what
are
thought of
as
goods.
In
spite
of
the
denial of
the
relevance
of
intrinsic
properties to the
pure theory,
there
has
always
been
a
subversive un-
dercurrent
suggesting
that
economists
continue
to
take account
of
these
prop-
erties.
Elementary textbooks
bristle with
substitution
examples about
butter
and
margarine,
rather
than about
shoes and
ships,
as
though
the authors believed
that
there
was
something
intrinsic
to
butter
and
margarine that
made
them
good substitutes
and
about
automobiles
and
gasoline that
made
them
somehow
intrinsically complementary.
Market re-
132
NEW
APPROACH TO
CONSUMER
THEORY
133
searchers,
advertisers,
and
manufactur-
ers
also
act as
though
they
believe that
knowledge
of
(or belief
in) the
intrinsic
properties of
goods is
relevant to
the way
consumers will
react toward
them.
The
clearest
case of
conflict
between
a belief
that
goods
do have
intrinsic
prop-
erties relevant to
consumer
theory but
that
they
are
not taken
into
account
has
been
the
long
search for a
definition
of
"intrinsic
complementarity." The
search
was
successful
only
where
Morishima
(1959)
turned
from
traditional
theory to
an
approach
somewhat
similar
to
that
of
the
present
paper.
Perhaps the
most
important
aspects
of consumer
behavior
relevant
to
an
economy
as
complex
as
that
of
the
United
States
are
those of consumer
reactions
to
new
commodities and
to
quality varia-
tions. Traditional
theory
has
nothing
to
say
on
these.
In
the
case of
new com-
modities,
the
theory
is
particularly help-
less.
We
have
to
expand
from
a
commod-
ity space
of
dimension
n
to
one
of
dimen-
sion
n
+
1,
replacing
the
old
utility
function
by
a
completely
new
one,
and
even
a
complete
map
of
the consumer's
preferences
among the
n
goods
provides
absolutely
no
information
about
the
new
preference
map.
A
theory which can
make
no use of
so much
information
is
a
remarkably
empty
one.
Even
the
tech-
nique
of
supposing the
existence
of a
utility function
for
all
possible
goods,
in-
cluding
those
not
yet
invented,
and
re-
garding
the
prices
of
nonexistent
goods
as
infinite-an
incredible
stretching
of
the
consumers'
powers
of
imagination-
has no
predictive
value.
Finally
we
can
note the
unsuitability
of
traditional
theory for
dealing with
many
of
the
manifestly
-important
aspects
of
actual
relationships
between
goods
and
consumers
in
I.
F.
Pearce's
(1964)
recent
heroic
but rather
unsuccessful
at-
tempts to deal
with complementarity,
substitution, independence,
and
neutral
want associations
within the convention-
al framework.
H. A NEW APPROACH
Like
many
new approaches, the
one
set out
in
this
paper draws upon
several
elements that
have been utilized
else-
where.
The
chief
technical novelty
lies
in breaking away
from the traditional
approach that
goods are the direct
ob-
jects
of
utility
and, instead, supposing
that
it
is
the properties
or
characteristics
of
the goods
from which utility is derived.
We
assume
that consumption
is
an ac-
tivity
in which
goods, singly
or in com-
bination,
are
inputs and
in
which
the
output
is
a
collection of characteristics.
Utility
or
preference
orderings
are as-
sumed
to
rank collections of characteris-
tics
and
only
to
rank
collections
of
goods
indirectly through
the characteristics
that
they possess.
A meal
(treated
as
a
single good) possesses
nutritional
charac-
teristics
but it
also
possesses
aesthetic
characteristics,
and different
meals
will
possess these
characteristics
in different
relative
proportions.
Furthermore,
a
din-
ner
party,
a
combination
of
two
goods,
a
meal
and a social
setting, may
possess
nutritional,
aesthetic,
and
perhaps
in-
tellectual characteristics
different
from
the
combination obtainable
from a
meal
and
a
social
gathering
consumed
sepa-
rately.
In
general-and
the
richness
of
the ap-
proach springs
more
from
this than
from
anything
else-even
a
single good
will
possess
more
than
one
characteristic,
so
that the
simplest
consumption
activity
will
be
characterized
by joint
outputs.
Furthermore,
the
same
characteristic
(for example,
aesthetic
properties)
may
be included
among
the
joint
outputs
of
many
consumption activities
so
that
134
KELVIN J. LANCASTER
goods
which
are apparently
unrelated
in
certain
of their
characteristics
may
be
related
in
others.
We
shall assume
that
the
structure
we
have
interposed
between
the
goods
them-
selves
and
the
consumer's
preferences
is,
in
principle,
at least,
of
an objective
kind.
That
is, the
characteristics
possessed
by
a good
or a combination
of goods
are the
same
for all consumers
and,
given
units
of
measurement,
are
in
the same
quanti-
ties,2
so
that the
personal
element
in
con-
sumer
choice arises
in
the
choice
between
collections
of
characteristics
only,
not
in
the
allocation
of
characteristics
to
the
goods.
The
objective
nature
of the
goods-
characteristics
relationship
plays
a cru-
cial
role
in
the
analysis
and enables
us
to
distinguish
between objective
and
pri-
vate
reactions to
such
things
as
changes
in
relative
prices.
The essence
of
the
new
approach
can
be
summarized
as
follows,
each
assump-
tion
representing
a break with tradition:
1.
The good,
per
se,
does
not give
util-
ity
to the
consumer;
it
possesses
charac-
teristics,
and
these
characteristics
give
rise
to
utility.
2. In
general,
a
good
will possess
more
than
one
characteristic,
and
many
char-
acteristics
will be
shared
by
more
than
one
good.
3. Goods
in
combination may
possess
characteristics
different
from
those
per-
taining
to
the
goods
separately.
A
move
in
the
direction
of
the first
assumption
has
already
been
made
by
various workers
including
Strotz
(1957,
1959)
and
Gorman
(1959),
with
the
"utility
tree"
and
other
ideas associating
a
particular
good
with
a
particular
type
2
Since
the units in which the
characteristics are
measured
are
arbitrary,
the objectivity
criterion
relating
goods
and
characteristics
reduces
to
the
requirement
that
the
relative
quantities
of a
par-
ticular
characteristic
between unit
quantities
of
any
pair
of goods
should
be
the
same for
all
consumers.
of utility.
The theory
set
out here
goes
much
further
than
these
ideas.
Multiple
characteristics,
structurally
similar
to
those
of
the
present
paper
but
confined
to
a
particular
problem
and
a
point
util-
ity
function,
are implicit
in the
classical
"diet problem"
of
Stigler
(1945),
and
multidimensioned
utilities
have been
used by
workers
in
other
fields,
for ex-
ample,
Thrall
(1954).
The third
assump-
tion,
of
activities involving
complemen-
tary
collections
of
goods,
has been
made
by
Morishima
(1959)
but
in
the context
of
single-dimensioned
utility.
A variety
of
other
approaches
with
similarities
to that
of
the
present
paper
occur
scattered
through
the literature,
for
example,
in
Quandt
(1956),
or
in
Becker
(1965),
or in
various
discussions
of
investment-portfolio
problems.
These
are
typically
set out
as ad
hoc approaches
to
particular
problems.
Perhaps
the
most
important
aspect
of
this paper
is
that the
model
is
set out
as a
general
replacement
of
the traditional
analysis
(which
remains
as
a
special
case),
rather
than
as
a
special
solution to
a
special
problem.
It
is clear
that
only by
moving
to
mul-
tiple
characteristics
can
we
incorporate
many
of
the intrinsic
qualities
of
indi-
vidual
goods.
Consider
the
choice be-
tween
a
gray
Chevrolet
and
a
red Chev-
rolet. On ordinary
theory
these
are
either
the
same
commodity (ignoring
what
may
be
a
relevant
aspect
of
the
choice
situa-
tion)
or
different commodities
(in
which
case
there
is no a
priori presumption
that
they
are close
substitutes).
Here
we
re-
gard
them
as
goods
associated
with satis-
faction
vectors
which
differ
in
only
one
component,
and
we
can
proceed
to
look
at the
situation
in
much
the
same
way
as
the
consumer-or even the
economist,
in
private
life-would
look
at it.
Traditional
theory
is forever
being
forced
to
interpret
quite
common real-life
NEW
APPROACH
TO
CONSUMER
THEORY
135
happenings,
such
as the effects of adver-
tising
in
terms
of
"change
of
taste,"
an
entirely non-operational concept since
there
is no
way
of
predicting the relation-
ship between preference before and
after
the change.
The
theory outlined
here, al-
though extremely
rich
in
useful
ways
of
thinking about consumer behavior,
may
also
be thought to run the danger of
add-
ing to the economist's extensive collec-
tion
of
non-operational concepts.
If this
were true, it need not, of course, inhibit
the
heuristic application
of
the theory.
Even
better, however, the theory
implies
predictions that differ from those of
tra-
ditional theory, and the predictions
of
the new
approach
seem
to fit better
the
realities
of consumer behavior.
III.
A MODEL OF CONSUMER BEHAVIOR
To obtain a working model
from
the
ideas outlined above, we shall
make some
assumptions which are,
on
balance,
nei-
ther
more nor less heroic
than
those
made
elsewhere in
our
present economic
theo-
rizing and which are intended to be
no
more and
no
less permanent parts
of
the
theory.
1. We shall regard
an individual
good
or
a collection
of
goods as a
consumption
activity
and
associate
a
scalar
(the
level
of
the activity) with it. We
shall assume
that
the
relationship
between
the
level
of
activity k,
Yk,
and the goods
consumed
in
that activity to be both
linear
and ob-
jective,
so
that,
if
Xj
is
the
jth
commodity
we have
Xj=
aikyk,
(1)
k
and the vector
of
total goods required
for
a given activity vector
is
given
by
x=Ay.
(2)
Since
the relationships
are
assumed
objective, the equations
are assumed
to
hold
for all individuals, the
coefficients
ajk
being
determined
by
the
intrinsic
properties
of
the
goods
themselves
and
possibly
the
context
of
technological
knowledge
in
the
society.
2.
More heroically,
we shall
assume
that
each
consumption
activity produces
a
fixed
vector
of characteristics3
and that
the relationship
is again
linear,
so
that,
if
zi
is the
amount
of the
ith
characteris-
tic
Z
=
bikyk,
(3)
k
or
z=
By.
(4)
Again,
we shall
assume that
the
coeffi-
cients
bik
are
objectively
determined-in
principle,
at least-for
some
arbitrary
choice
of
the
units
of
zi.
3. We
shall
assume
that
the
individual
possesses
an ordinal
utility
function
on
characteristics
U(z)
and that
he
will
choose
a
situation
which
maximizes
U(z).
U(z)
is
provisionally
assumed
to possess
the
ordinary
convexity properties
of
a
standard
utility
function.
The chief
purpose
of making the
as-
sumption
of linearity
is
to
simplify
the
problem.
A viable
model could
certainly
be produced
under
the
more
general
set
of
relationships
Fk(151X)
=
01
k
=
...
m
(5)
The model
could be analyzed
in
a similar
way to that
used
by
Samuelson
(1953b)
and others
in
analyzing
production,
al-
though
the
existence
of much
jointness
among
outputs
in
the
present
model
pre-
sents difficulties.
IThe assumption
that
the consumption
tech-
nology
A,
B is fixed
is a convenience
for
discussing
those
aspects
of
the model
(primarily
static)
that
are the chief
concern
of this
paper.
The consequences
of relaxing
this particular
assumption
is
only
one
of
many
possible
extensions
and expansions
of
the
ideas
presented
and are
discussed
by the
author
elsewhere
(Lancaster,
1966).