Capital and Labor Substitution Elasticity Measure
A Capital and Labor Substitution Elasticity Measure is an elasticity of substitution measure for the sensitivity of the changes in cost of capital in response to a (one percent) cost of labor change (with all other factors held as equal).
- Context:
- output: a Capital and Labor Substitution Elasticity Value, which can range from being zero elasticity to being elasticity of one to being infinite elasticity (e.g. for an entirely robotized economy).
- It can be calculated as [math]\displaystyle{ \frac{d \ln(k/n)}{d \ln(MPL/MPK)} }[/math].
- …
- Counter-Example(s):
- See: Unit of Economic Capital, Unit of Labor, Mass Technological Unemployment, Labor Supply Elasticity.
References
2018
- (Cuadrado et al., 2018) ⇒ Francisco Alvarez-Cuadrado, Ngo Van Long, and Markus Poschke. (2018). “Capital-labor Substitution, Structural Change and the Labor Income Share.” In: Journal of Economic Dynamics and Control 87
- ABSTRACT: Recent work has documented declines in the labor income share in the United States and beyond. This paper documents that this decline was more pronounced in manufacturing than in services in the U.S. and in a broad set of other industrialized economies, and shows that a model with cross-sectoral differences in productivity growth and in the degree of capital-labor substitutability is consistent with these trends. We calibrate the model exploiting additional information on the pace of structural change from manufacturing to services, on which the model also has predictions. We then conduct a decomposition to establish the relative importance of several potential drivers of changes in factor income shares and structural change that have been proposed in the literature. This exercise reveals that differences in the degree of capital bias of technical change across sectors, combined with differences in substitution possibilities, are key determinants of the observed patterns.
- QUOTE: Figure 3: The common component of the labor income share in 17 countries, 1970-2007 (displays fitted values from the regressions in equations (3) and (4).)
2014
- (Piketty, 2014) ⇒ Thomas Piketty. (2014). “Capital in the Twenty-First Century." Harvard University Press. ISBN:9780674369559
- QUOTE: In thinking about these questions, economists often use the concept of a “production function,” which is a mathematical formula reflecting the technological possibilities that exist in a given society. One characteristic of a production function is that it defines an elasticity of substitution between capital and labor: that is, it measures how easy it is to substitute capital for labor, or labor for capital, to produce required goods and services.
For example, if the coefficients of the production function are completely fixed, then the elasticity of substitution is zero: it takes exactly one hectare and one tool per agricultural worker (or one machine per industrial worker), neither more nor less. If each worker has as little as 1/ 100 hectare too much or one tool too many, the marginal productivity of the additional capital will be zero. Similarly, if the number of workers is one too many for the available capital stock, the extra worker cannot be put to work in any productive way.
Conversely, if the elasticity of substitution is infinite, the marginal productivity of capital (and labor) is totally independent of the available quantity of capital and labor. In particular, the return on capital is fixed and does not depend on the quantity of capital: it is always possible to accumulate more capital and increase production by a fixed percentage, for example, 5 or 10 percent a year per unit of additional capital. Think of an entirely robotized economy in which one can increase production at will simply by adding more capital.
- QUOTE: In thinking about these questions, economists often use the concept of a “production function,” which is a mathematical formula reflecting the technological possibilities that exist in a given society. One characteristic of a production function is that it defines an elasticity of substitution between capital and labor: that is, it measures how easy it is to substitute capital for labor, or labor for capital, to produce required goods and services.
2011
- http://homepage.ntu.edu.tw/~mao/Exercise-Elasticity%20of%20Substitution%20between%20Capital%20and%20Labor.pdf
- The elasticity of substitution between capital and labor is defined as :[math]\displaystyle{ \frac{d \ln(k/n)}{d \ln(MPL/MPK)} }[/math].
As we discussed in the lecture, this quantity measures the extent to which firms can substitute capital for labor as the relative productivity or the relative cost of the two factors changes. When this number is large, it means that firms can easily substitute between capital and labor. Geometrically, it measures the curvature of the isoquant. In general, the elasticity of substitution depends on the amount of capital and labor employed.
- The elasticity of substitution between capital and labor is defined as :[math]\displaystyle{ \frac{d \ln(k/n)}{d \ln(MPL/MPK)} }[/math].
1961
- (Arrow et al., 1961) ⇒ Kenneth J. Arrow, Hollis B. Chenery, Bagicha S. Minhas, and Robert M. Solow. (1961). “Capital-labor Substitution and Economic Efficiency.” In: The Review of Economics and Statistics.
- QUOTE: In many branches of economic theory, it is necessary to make some assumption about the extent to which capital and labor are substitutable for each other. In the absence of empirical generalizations about this phenomenon, theorists have chosen simple hypotheses, which have become widely accepted through frequent repetition.