SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS
DECEMBER, 1977
TECHNOLOGICAL CHANGE AND LABOR’S RELATIVE SHARE:
THE MECHANIZATION OF U.S. COTTON PRODUCTION*
Marshall A. Martin and Joseph Havlicek, Jr.
Prior to World War II, labor’s share in the U.S.
manufacturing and agricultural sectors was relatively
constant. Keynes [9] called this “a bit of a miracle.”
Several studies [4, 10] have shown that labor’s share
in the U.S. manufacturing sector has increased in the
post-war period. The opposite appears to have been
the case for U.S. agriculture. Two studies [11, 14]
indicate that labor’s relative share in the U.S. agri-
cultural sector has declined in the post-war period.
There has been a substantial substitution of
capital for labor in both the manufacturing and
agricultural sectors in the post-war period. The
secular increase in the wage-rental ratio has en-
couraged substitution of capital for labor. However,
while this argument alone might explain the observed
decline in labor’s share in the agricultural sector, it
does not explain what has occurred in the manu-
facturing sector. Moreover, this argument excludes
another important characteristic of both sectors in
the post-war period: technological change.
Adoption of labor-saving technology has been
quite rapid in the U.S. agricultural sector during the
last several decades [5]. The most rapid substitution
rate of machinery for labor in the agricultural sector
has occurred in the South. Kaneda [8] notes that the
high rate of technical change in the Southeast and
Delta regions since World War II is a reflection of
cotton production mechanization.
This article has two objectives: (a) to indicate
why both elasticity of factor substitution and bias of
technical change must be known in order to deter-
mine labor’s relative share of output value, and (b) to
illustrate empirically the importance of these two
parameters for the case of U.S. cotton production
mechanization.
ELASTICITY OF FACTOR SUBSTITUTION
AND TECHNOLOGICAL CHANGE
Mathematical analysis in this section is based on
two assumptions: (a) the production function is
homogeneous of degree one with two homogeneous
inputs, capital (K) and labor (L), and (b) perfect
competition prevails in both input and output
markets. Output for a given industry over time (t) is
represented by a production function, Y = f(K, L, t).
Over the relevant range of production, both marginal
products are strictly positive (fκ >0, fL > 0) and
both decrease monotonically (fκκ < 0, fLL < 0, and
1kl > θ)∙
Changes in factor shares are dependent on two
important parameters: (a) elasticity of factor sub-
stitution, and (b) bias of technology being adopted.
Elasticity of factor substitution refers to ease of
substitution of one input for another for a given
output level. Elasticity of factor substitution may be
defined as proportionate rate of change in the factor
ratio divided by the proportionate rate of change in
the factor price ratio. Mathematically, elasticity of
factor substitution (σ) may be expressed as:
Hicks [6] classified technical change according
to its initial effect on the marginal physical product
of capital and labor. Technical change which leaves
Marshall A. Martin is Assistant Professor, Department of Agricultural Economics, Purdue University, and Joseph Havlicek, Jr. is
Professor, Department of Agricultural Economics and Statistics, Virginia Polytechnic Institute and State University.
*Journal Paper No. 6885, Indiana Agricultural Experiment Station. The authors are indebted to Robert L. Thompson, Jerry
A. Sharples, James K. Binkley, and anonymous Journal reviewers for helpful comments on an earlier version of the manuscript.
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