University of Laneaster

Published date01 February 1973
AuthorHarry Townsend
DOIhttp://doi.org/10.1111/j.1467-9485.1973.tb00872.x
Date01 February 1973
Scottish
Journal
of
Political
Economy
Vol.
XX,
No.
1
ON
THE THEORY
OF
THE
VALUATION AND
ALLOCATION
OF
TIME:
REPLY
ALAN
W.
EVANS
I
shall comment
on
each of Flemming’s sections in turn.
1.
It
is somewhat ingenuous of Flemming to state that the main objection
of Johnson,
Oort,
and myself (JOE) to the traditional theory ‘is not one
of
substance but of interpretation
’.
It is quite true that the mathematics
of
the traditional theory can be interpreted in the way that Flemming suggests
so
that statements about
the marginal utility
of
leisure
in the theory
should really be about ‘the marginal utility of leisure
less
the marginal
utility
of
work,’ and this interpretation would be more in accord with the
situation the theoretical model attempts to represent.
So
far as
I
am aware,
however, there is
no
evidence to suggest that anyone else has ever interpreted
the theory in this way. Moreover since JOE’S revised theory is now available
I can see no reason why anyone should ever in the future undertake the
mental gymnastics required to interpret the traditional theory in this way. It
is noticeable, for example, that Flemming does not
use
the traditional theory
for the model in his Section
(V).
To use an analogy,
if
JOE,
in an art gallery, points out that a picture is
hanging upside down and suggests that it should in future be placed right way
up, it would be quite correct for Flemming to point out that the picture
is
the right way up if you stand
on
your head to look at it. But who is making
a point
of
substance rather than interpretation?
2.
Flemming states that ‘the identification
of
either branch
of
this condi-
tion [that the marginal rate of substitution equals the price ratio] with the
ratios
Ui/Uj
or
ri/rj
is by
no
means obvious.’ But the marginal rate
of
sub-
stitution of
X
for
Y
was defined by Hicks in
Value
and
Capital
as being the
quantity of
Y
which would just compensate the consumer for the loss
of
a
marginal unit
of
X,
and
so
far as
I
am aware the definition has not been
changed since. The marginal rate of substitution of the jth activity for the
ith activity
is
therefore the time in the ith activity which would just compen-
sate
the consumer for
the
loss of a marginal unit
of
time
in
the jth activity,
the definition which
I
used
in my paper.
It
can easily
be
shown that the
MRS,
which mathematically is represented as
-aa,/adi,
is equal to (but is not
of
of course
identified with
’)
Ui/Uj.
To
identify the
MRS
with
(Ui-p)/(Uj-p)
as Flemming suggests is to lose contact with the original definition, preserving
the form of words for the sake of
it,
scarcely a method of making progress in
economics or any other science.
Flemming is
on
surer ground
in
suggesting that the price ratio should be
reinterpreted to mean
(ri+p/A)/(rj+p/A)
where
LL/A
is the consumer’s
value
of
time in general; this certainly seems a plausible reinterpretation,
but it should be borne in mind that it
is
a reinterpretation, and that whereas
one knew before what the price ratio of two commodities was, now one does
not know since the value of
p/X
is unknown. The optimality condition that
13

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