Three Paradoxes with The 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 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.

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.

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.

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.

Croatian agriculture stagnates over the last quarter of the century. Although it is heavily subsidized and the investment in mechanization was high, Croatian agriculture did not improve its production level, not even after the accession to the European Union. The project of green and blue Croatia, which aim is to connect agricultural production and tourism, did not show significant results import substitution. In this paper non-perennial crops agriculture is analyzed since it forms more than 40% of total agricultural production in Croatia. In order to distinguish the contribution of capital, labour and total factor productivity, a Cobb-Douglas production function is estimated on a panel data set for Croatian non-perennial agriculture in the period of 2008 – 2014. It was discovered that production elasticities do not correspond to the shares of expenditures on labour and capital which is a common production function assumption. Also, it is shown that total factor productivity declines over time, a disinvestment and labour decline caused stagnation of this sector of Croatian economy. A further analysis is made to determine the impact of subsidies and export orientation on TFP and it is found that Croatian agricultural production is affected by export orientation and subsidies, but their impact is almost irrelevant.

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.

Predictive models are used in an attempt to anticipate future transitions, mitigate losses, and maximize economic gains. In today’s market, companies look for high reliability and quality of products due to great market competition. Hence warranty data is of considerable interest to companies. Warranty shows the ability of a system or component to perform its functions within a given customer usage. Many statistical and data mining methods are available to predict the warranty data. This study focuses on analyzing the predictive efficiency of the T-method and Cobb-Douglas production function on warranty data by comparing their prediction capability. The T-method, developed by Genichi Taguchi, is founded upon the fundamentals of the Taguchi System of Quality Engineering which is used to calculate an overall prediction based on signal-to-noise ratio. Using this method, the required parameters are calculated to obtain an overall estimate of the true value of the output for each signal member. The Cobb-Douglas production function is then applied on the same dataset. In economics, the Cobb-Douglas functional form of production function is widely used to represent the relationship of the output to inputs. The strength of the relationship is then assessed using the R-squared and adjusted R-squared values.

In this paper, we present a function for the share of factors of output, which is in complete agreement with primary production theories in microeconomics. We follow some assumptions for production function, and also payment to each factor equals their marginal products, and we create a new production function which is called the efficient production function. We then try not only to remove the significant defects in Cobb-Douglas production function but also by accept the presented theory. We conclude that the need for most previous approaches have caused problems and even the developed functions have not been able to solve the problem. The presented model in complete agreement is also supported by the empirical findings for the United States (U.S.) economy.

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.

This paper assesses the validity of the constant elasticity of substitution (CES) and the Cobb‐Douglas (CD) production functions in modelling the aggregate production function and computing the total factor productivity (TFP) in South Africa for the period 1970‐2006. The CES function is estimated with Nerlove's two‐step procedure using the autoregressive distributed lag (ARDL) cointegration and the Kalman filter estimation techniques, while the CD production function is estimated using the Kalman filter technique. The results of the forecast performance of the two model specifications show that the CD specification outperforms the CES for the period 1970‐2006, although the CD specification may be too restrictive.

In an economy where recourses are scarce and opportunities for a new technology are lacking, studies will be able to show the possibility of raising productivity by improving the industry’s efficiency. This study attempts to measure the status of technical efficiency of tea-producing industry for panel data in Bangladesh using the stochastic frontier production function, incorporating technical inefficiency effect model. It was observed that Translog Production Function is more preferable than Cobb-Douglas Production Function. The study estimates that the average technical efficiency of tea producing industries in Bangladesh is 59%. Therefore, the results indicated that there is a great potential exists for tea industry to further increase the value added by 41% using the available input, technology and efficiency improvement, thereby reducing the cost of production. The study identifies that the mean efficiency of tea industries for value added vary among the regions and year-wise mean efficiency seems to be unstable during the study period and therefore, continued efforts to update technologies and equipment are required in pursuit of efficiency in tea industry.