میکرو پایه و اساس یک کشش ثابت از تابع تولید جایگزینی به روش مکانیزه

We consider an increase in the range of capital use as a form of mechanization. A constant elasticity of substitution (CES) production function is dynamically derived from Leontief production functions through the endogenous complementary relationship between capital accumulation and mechanization. This implies that a CES production function can be resolved into technological change that does not involve changes in total factor productivity. Furthermore, using the normalizing procedure of the CES production function developed by de La Grandville [de La Grandville, O., 1989. In quest of the Slutsky diamond. American Economic Review 79, 468–481], we investigate how mechanization is related to the elasticity of substitution in our endogenous growth model.

A constant elasticity of substitution (CES) production function was mathematically derived by Arrow et al. (1961) to consider various elasticities of substitution between capital and labor. The CES production function has played an important role in understanding economic growth. For example, de La Grandville, 1989, Klump and de La Grandville, 2000, Klump and Preissler, 2000, Miyagiwa and Papageorgiou, 2003 and Miyagiwa and Papageorgiou, 2007 used it to investigate the relationship between economic growth and the elasticity of substitution between capital and labor. Duffy and Papageorgiou, 2000 and Masanjala and Papageorgiou, 2004 applied it empirically to explain cross-country variations in economic growth.

Because we derived a CES production function from Leontief production functions through mechanization, the elasticity of substitution between capital and labor implied the difficulty of mechanization. Therefore, we could consider why the elasticity of substitution differs among industries or economies in time series analysis. By investigating the ratio of the growth rate of output per labor unit to the growth rate of capital per labor unit, we could easily infer the range of capital use. We also showed that a CES production function can be resolved into technological change that involves no change in TFP. Therefore, we have to carefully examine the empirical studies estimating the TFP because changes in TFP represent only part of the technological change.