Efficient Cobb-Douglas Production Function

This small note with a swollen Appendix illustrates how foreign ownership data and aggregate production function assumptions can be used to deduce what Canadian domestic output and national income might be if there were less foreign capital. The appendix spells out the calculation procedure, which depends heavily on the assumed ease with which labour can be substituted for capital in the production process. Consider first two extreme possibilities. On the one extreme, if there were no substitution possible between capital and labour, then any reduction in the stock of capital would lead to proportionate drops in output and employment. In this sort of world, anything that jeopardizes the inflow of capital required to finance the technically-necessary capital-labour ratio has high costs in terms of unemployment and foregone income. At the other extreme, if there is perfect substitution between capital and labour, and if foreign capital is paid the value of its marginal product, then changing the amount of foreign capital would have no effect on national income. Domestic output would drop if the foreign capital were not present, but the amount of the drop would be just equal to the amount of output formerly used to pay the return on the foreign capital. Somewhere between these two extremes lies the constant-returns CobbDouglas production function assumed in the present calculations. Under these assumptions, we need both capital and labour to get any output, but any combination of capital and labour can be usefully employed in cooperation. However, as labour is substituted for capital, the amount of extra labour required to replace one unit of capital increases as the amount of capital decreases. Under these conditions, therefore, it comes 1 The idea of using a Cobb-Douglas production function to estimate the consequences of less foreign investment is based on earlier work by Phil Neher. 2 The foreign ownership data and the assumed production function for business output have been developed as parts of the aggregate quarterly model RDX2. The theory, equations, and variables of the model are described in J. F. Helliwell, H. T. Shapiro, G. R. Sparks, I. A. Stewart, F. W. Gorbet, and D. R. Stephenson: The Structure of RDX2. Ottawa, Bank of Canada, 1971. (Bank of Canada Staff Research Studies, No. 7.)

The output elasticities of inputs seem all about what an applied researcher is concerned with. The Cobb-Douglas production functions formulae possess the convenient property that the exponents of inputs readily represent the output elasticities of inputs such that the sum of these exponents reveal whether there are increasing, constant or decreasing returns to scale. However, there are also some inconveniencies with this type of production functions. In this paper we will investigate three of them. First of all, the short run marginal cost functions obtained from the Cobb-Douglas type of production functions can be both convex and concave depending on the magnitude of the technical coefficient of labor input. Unfortunately, this awkward behavior cannot be explained with the economic theory. Secondly, when the variable input labor with a given level of Technical productivity is complemented with a once-and-for-all increase in the amount of physical capital input, the labor becomes more and more productive as the usage of labor increases. This clearly stands in contrast with the Law of Diminishing Marginal Returns. Finally, we find ever-increasing returns to ‘Technical productivity of labor’, keeping the amounts of labor and physical capital constant, which is again surprising. Key words : paradox; convex and concave marginal costs; Cobb-Douglas production function; increasing rate of return to Technical productivity of labor. JEL classification : D2, D3, D4. DOI : 10.7176/EJBM/11-1-12

The objective of the present study is to determine the status of technical efficiency for a sample of beekeepers in Malaysia. This is because determining the efficiency status of farmers are very important for policy purposes. Efficiency also is a very important factor of productivity growth. In an economy where resources are scarce and opportunities for new technologies are lacking, inefficiency studies will be able to show that it is possible to raise productivity by improving efficiency without the resource base or developing new technology. Estimates on the extent of inefficiency can help decide whether to improve efficiency or to develop new technologies to raise agricultural productivity. In this study, a Cobb-Douglas production function was employed to beekeeping data. Using the method of Maximum Likelihood Estimation (MLE) procedure, we derived the stochastic frontier production function. The technical efficiency index computed shows a mean efficiency ratio of 0.625 implying that substantial inefficiency exists among the Malaysian beekeepers in the sample under study. Our results indicate that there are great potentials for the beekeepers to further increase output using the available inputs and technology.

In the past, growth models have been constructed and analyzed with the help of a production function subject to certain restrictive features. For quite some time, the Cobb-Douglas production function (CD) with its input exponents adding upto unity and a unitary elasticity of substitution were mostly used by the economists for analysis. In recent times, the constant elasticity of substitution production function (CES) which includes CD, as well as Leontif production function as its special case has been widely used in various studies. One major limitation of this production function is that the elasticity of substitution parameter is not variable along an isoquant, though it can take different values for different values for different industries. We have made an attempt to test whether the estimated values of elasticity of substitution between labour and capital for a sector tend to change from one year to another and also whether it is CD or CES production function that characterizes a particular sector.

This paper estimates a series of production functions that explain the number of points a National Football League team will score during a season based on six measures of its offensive performance. The models that are estimated are linear and Cobb-Douglas production functions, using data for each team for each season from 2000 to 2018. Additionally, separate production functions are estimated for two sub-periods to determine whether the production functions vary over time and an accuracy check is performed at the end of the paper, where each team’s actual points are compared to its predicted points for the 2018 season.

Based on the analysis of the quantitative assessment of the influence of the factors of innovative activity on the dynamics of economic development and the endogenous determination of its contribution to the economic growth of the country, it is revealed that in foreign researches it is identified with the concept of the influence of scientific and technological progress. However, the impact of innovative factors on economic growth is not considered separately. Attempts of such a definition in Ukrainian researches are limited to well-known approaches: methods of integral assessment, methods of expert assessments, the method of multipliers, econometric models. Most of the approaches considered are focused on defining the innovative impact on economic development, rather than on economic growth. The main tool for assessing the role and innovative contribution to economic growth is the aggregate supply function model, usually based on the Cobb-Douglas production function. The analysis of the approaches used revealed a number of comments on econometric approaches. In contrast to this, an approach is proposed based on the neoclassical production function of Cobb-Douglas with a constant return to scale in the form of J. Tinbergen, with technical progress neutral according to J. Hicks, decreasing marginal productivity of macrofactors with limited interchangeability, which provides a causal functional (and not a statistical) relationship between input and output variables; does not require long time series. It is characterized by dynamic coefficients of elasticity, capital utilization rate and taking into account the innovation factor in each separate period. The innovation factor includes: the gross domestic expenditures on research and development, the expenditures on innovation, general expenditures on education. To define the contribution of formal innovation factor in economic growth applied "method of Solow residual", which by taking the logarithm and obtaining logarithmic derivatives in the production function, provides a formalized information about the contribution of each factor to economic growth and allows to develop the necessary regulatory measures. The method has been tested at the level of the country and old industrial regions of Ukraine: Dnepropetrovsk, Zaporozhye and Kirovograd regions of the Dnieper economic region of Ukraine. The role, importance and influence of the main factors of economic growth along with innovative ones on the part of the aggregate supply are considered and the cost-effectiveness of innovative factors is estimated.

Understanding Solow Residuals in Latin America Christian Daude (bio) Despite some improvements in recent years, long-term economic growth in Latin America and the Caribbean (LAC) has been rather disappointing over the past decades. Since 1960, gaps in the GDP per capita of LAC countries with respect to not only the United States but also their peers (“twin economies”) have widened steadily (see table 1). While the typical Latin American country1 was around 4.4 times poorer than the United States in 1960, as of 2008 it was 5.5 times poorer. The comparison with twin economies—countries that in 1960 had a GDP per capita comparable to that in Latin America2—is even more remarkable. The average LAC economy was just 20 percent poorer than its typical twin economy in 1960. In 2008, GDP per capita in Latin America was less than half that in the twin economies. [End Page 109] Click for larger view View full resolution Table 1. GDP per Capita in Latin America Relative to Benchmarksa This persistent decline in relative GDP per capita has been common to all countries in the region, with some exceptions. Of the nineteen LAC economies in my sample, five managed to grow faster than the United States during the 1960–2008 period: Brazil, Chile, Colombia, the Dominican Republic, and Panama. However, progress has been quantitatively modest. For example, if benchmarked to twin economies, only the Dominican Republic and Panama managed to grow faster over the same period. Furthermore, in several cases (for example, Brazil) progress was made mainly during the 1960s and 1970s, with growth being subpar from the debt crisis in the early 1980s onward. While the 2000s have been good years in terms of relative growth performance for the region, it will still take around 27 years to cut by 50 percent the GDP per capita gap with respect to the United States if the growth differential during 2000–08 of around 1.5 percent per year is to be maintained; with respect to the twin economies, it will take around 108 years. Therefore, low potential growth continues to be a significant challenge for the region. [End Page 110] This paper contributes to the understanding of what drives this poor performance by using new databases and analytical tools to explore the relative importance of productivity and factor accumulation across LAC countries. With regard to analytical tools, the paper provides new evidence from three viewpoints. First, I perform a careful analysis of different ways of decomposing GDP per capita levels into physical capital, human capital, and a residual—the “Solow residual,” often interpreted as a measure of total factor productivity (TFP), representing aggregate economic efficiency, but also often viewed as “a measure of our ignorance”—under different assumptions regarding the production function and measurement. Second, I present non-parametric estimations of efficiency based on a data envelope analysis that does not rely on the traditionally used Cobb-Douglas production function; instead, it recognizes that the relevant production possibilities frontier may be a function of factor endowments and thus differ across countries. With regard to new data sets, this paper uses three newly available sources. First, in contrast to previous studies focusing on Latin America, it uses the new version of the Barro and Lee (2010) data set on educational attainment, which addresses several concerns on data quality that arose over the previous version (see Cohen and Soto 2007 as well as De la Fuente and Domenech 2006). Second, I also use the latest version of the Penn World Tables (version 7.0), extending the analysis until 2008; doing so allows me to cover the 2000s, a decade that has been quite successful for the region in terms of economic growth compared with its past. Third, I use the PISA 2009 test scores from the Organization for Economic Cooperation and Development (OECD) to analyze the importance of cognitive skills and adjust human capital indicators for differences in quality. The paper focuses on the decomposition of GDP per worker into physical capital, human capital, and the Solow residual through the use of alternative methods, as policy recommendations might differ substantially according to the source of income disparities, in...

The Success of the Cobb-Douglas Production Function Is An Illusion

We directly observed a Cobb–Douglas symmetric plane using the index of surface openness, which is used in geography, and successfully identified it. Based on this observation, we measured the capital shares (capital elasticity) and labor shares (labor elasticity) and compared them with the results of multiple regression analysis used in economics. We confirmed consistent agreement in seven countries: Japan, Germany, France, Spain, Italy, the United Kingdom, and the Netherlands. Thus, we show that the Cobb–Douglas production function can be clearly captured in empirical data as a geometric entity with a quasi-inverse symmetry of variables. Based on the above discussion, we theoretically clarified why the Cobb–Douglas production function is better fit to empirical data in economics, because it uniquely derives the fact that their variables follow a power-law distribution.

Production function is the econometric model used to study the business relationship between input and output. In this paper, it uses Cobb-Douglas (C-D) production function as based model, and it uses regression analysis and Solow residual as the theoretical support. It simulates the production function model of railway transportation. Through the empirical study and quantify the railway transport enterprise production function analysis, the authors reveal factors affecting investment in the railway transport enterprise output volume. This research is helpful for future.

JN recent years, economists have presented empirical evidence that improvements in efficiency have accounted for most of the growth in aggregate output in the United States and many other countries during the past half century. Robert M. Solow has presented a Cobb-Douglas production function model in which he explicitly assumes that this increased efficiency (technical progress) is due to improvements which are embodied in new physical equipment.' The model is easily extended to the case in which improvements may be embodied in new physical equipment, or may be due to other causes (i.e., disembodied improvements).2 Furthermore, Solow has demonstrated that the explicit assumption that technical progress must be embodied in new physical equipment can be incorporated in a constant elasticity of substitution (CES) production function model.3 Such a model is more general than the embodied Cobb-Douglas model in that the latter implies that the elasticity of substitution is not only a constant, but also equal to one. Solow did not consider the case in which technical progress may also be disembodied, but again it is easy to incorporate this into the CES model. This will be done below. The purpose of this paper is to point out one striking difference between Solow's Cobb-Douglas, and his CES model, when it is assumed that technical progress may be either embodied or disembodied. Embodied technical progress in the Cobb-Douglas model has no influence on the elasticities of output with respect to labor and with respect to the net capital stock. In that model, it is not possible to isolate the influence of embodied technical progress from that of disembodied progress. In the case of the CES model, however, the elasticity of output with respect to capital relative to the elasticity with respect to labor is influenced by the rate of embodied progress. Another feature of the CES model is that it is possible to state output per labor unit as a function of the marginal product of labor, and of a time shift factor which is accounted for only by disembodied technical progress. Given these facts, given data on output, labor, and the net capital stock, and finally, given the assumption that labor and capital tend to be paid their marginal products, it is possible to obtain upper and lower bound estimates of the influence of embodied and disembodied progress on output. The procedure in this paper will be: first, to outline the derivation of the Cobb-Douglas model in which progress is assumed to be either embodied or disembodied; second, to describe the extension to the CES model; and third, to demonstrate how the CES model allows us to distinguish between the effects of embodied and disembodied progress on output, and to discuss some of the implications of the CES model.

In this study, contribution of education to economic growth in Turkey, between 1980 and 1990, was analyzed via the estimations of production function relationships. Firstly, Cobb-Douglas production functions were estimated by OLS, for panel data. Secondly, a difference model considering also the province-specific differences w as estimated. Finally, more flexible functional form of translog function was considered. lt w as concluded that the effect of education on output growth was positive, but not increasing during the decade, and also unchanging across regions. The output elasticity of capital increased over time and got lower for underdeveloped regions, while the reverse was true for the output elasticity of labor. lt was observed that the assumption of constant retums to scale, which was assumed for Cobb-Douglas production function held for the Turkish economy within the decade. The claims of difference forms were not supported for Cobb-Douglas production function, while they were supported for translog form. Translog function was found to be advantageous over Cobb-Douglas production function.

The manufacturing sector has been a major driver of GDP growth in Bangladesh. The sector recorded an impressive average annual growth during last a couple of decades. This study is an attempt to test empirically the Cobb-Douglas production function for manufacturing sector of Bangladesh. Data of total value of output, total asset, total liabilities, number of permanent workers etc. of about six major types of industries including Garments, Textiles, Food & Food Processing, Leather & Leather Products, Electronics and Chemicals& Pharmaceuticals have been used. Researchers use total value of output as Y, total liabilities as K, and number of permanent workers (including officials managers, personal) as L. Study finds that coefficient for K and L are 0.49 and 0.51 respectively for entire manufacturing sector. In case of Garments, coefficient for K is 0.30 and L is 0.61 implying that labor is more productive than capital. The statement is also true for Textile sector and Leather & leather products. Capital is, on other hand, more productive than labor in Food & food processing industries, Electronics, Chemicals & Pharmaceuticals sectors. The coefficients are significant and do not suffer from MC and also not from Autocorrelation. To correct heteroscedasticity, WLS method (weighted Least Square) has been adopted. Findings reveal that Cobb-Douglas production function is applicable and exhibits increasing returns to scale in the context of manufacturing sector of Bangladesh.

ABSTRACT. This study aims to determine the efficiency of a scale and intensit y of input use in laying chicken farming production phase II at Gowa. Results of this study are expected to provide additional information for further research, and for the improvement of poultry farm business management at the sites. Using survey method with data collection observation and interview. Some 30 farmers samples have been analyzed. The data collected is last 3 months include; (1) the number of population, (2) the amount of egg production per day or Henday, (3) the number of inputs used include DOC, feed, spacious cages, labor, and living cost. To determine the efficiency of a scale and intensity of input use analysts used the Cobb-Douglas production function. Results of this study concluded that the scale of production and the intensity of input use production phase II is a set of conditions that are not efficient or deccreasing return to scale (DRS). This is because the production phase II, aged 19-25 months biological production and reproductive capacity has decreased. The implications of this research is laying chicken breeders production phase II need to input a maximum of 39.80% reduction of the number of previous use.

Poultry production is one of the most important economic activities to the smallholder farmers of Kenya. However, constraints are evident which have resulted in low production of poultry and poultry products to meet population demand and for socio-economic sustainability of the livelihoods. The objective of the study was to determine resource use efficiency, optimal production levels, production systems of small-scale poultry farmers in Bureti district, Kenya. Primary data were obtained using a set of structured questionnaires from 300 representative farmers drawn from the study area using cross-sectional sampling techniques. Data were analyzed by Cobb-Douglas production function. The results showed that the resources used in poultry production were underutilized while others were over utilized. The efficiency indicators for poultry feeds (0.0603) showed that poultry feeds were inefficiently used. Labour efficiency indicator (-0.091) showed that farmers were not only grossly inefficient in the use of the resource but also over utilized it while the efficiency indicator (60.86) for poultry equipment implied the resource was inefficiently utilized. It is recommended that farmers should use inputs more efficiently (particularly feeds which were being inefficiently utilized) by reducing their levels of employment.