ON SWITCHING OF TECHNIQUES IN TWO‐SECTOR MODELS*
| Date | 01 February 1988 |
| Published date | 01 February 1988 |
| Author | J. E. Woods |
| DOI | http://doi.org/10.1111/j.1467-9485.1988.tb01032.x |
Scoaish
JoumcllofPoliricnl
Economy,
Vol.
35,
No.
1,
February
1988
0
1988
Scottish
Economic
Society
ON
SWITCHING
OF
TECHNIQUES IN
TWO-SECTOR
MODELS*
J.
E.
WOODS
Towers
and
Perrin,
London
I
In this Note,
I
derive some simple results on switching of techniques for a
two-sector, single-product industries, circulating capital model in which only
one sector has alternative processes of production. This paper can be viewed
as a (somewhat belated) response to Gallaway and Shukla (1974), who
attempted to provide a sufficient condition for the absence
of
reswitching and
capital reversing from such a model. Though Garegnani (1976) and Sat0
(1976) subsequently demonstrated by means of numerical examples that
reswitching could occur in the presence
of
the Gallaway-Shukla capital-
intensity condition, no general conclusions were drawn about the possibilities
of switching
of
techniques. The purpose
of
my
paper is to rectify this
omission.
I1
In this Section, I describe the model and derive its essential properties.
Assume that the first sector has only one process
of
production, denoted by
(I)
=(all, azl;
11),
and the second has two processes,
(ZIa)
and
(I@),
where
(111)
=
(at,,
a;;
1;),
1
=
a,
/?;
aij
is the input of commodity
i
and
1,
the direct
labour input required per unit of output
of
commodity
j,
i,
j
=
1,
2,
with
superscript to denote the relevant process in the second industry. Technique
(1)
consists
of
processes
(I)
and
(111).
Choosing the first commodity as
numeraire and assuming that the wage is paid
at
the end
of
the production
period,
I
have as the price equations for technique
(1):
1
=
(1
+
r)(all
+p1uaZl)
+
wY1
p'=(l
+r)(&+p?&)+ w'l;
p'
denoting the relative price of the second commodity and
w'
the real wage.
Non-incriminatory acknowledgements are due to Professor Ian Steedman and the
referee for helpful comments. The
first
version
of
this paper was written while
I
was visiting
the Department of Economics, Queen Mary College, London for the academic year
1985-6:
I am grateful to the Department for the generous provision
of
facilities. Though I
revised the paper after joining Towers and Pemn, readers should note that
I
write in a
personal capacity, not as a corporate representative.
Date
of
receipt of final manuscript:
24
August
1987.
84
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