Why Does Production Function Take the Cobb–Douglas Form?

To explore the internal driving force of the growth of rice yield per unit area in China, a model based on varying-coefficient production function is proposed in this study, which comes from the idea that the constant elasticity parameters in the Cobb-Douglas production function can be extended to functional forms. Applying such model to economic growth analysis, on the one hand, the dynamic contribution rate of each input factor can be measured, and, on the other hand, the contribution rate of the input factor can be decomposed into net factor contribution rate and interaction factor contribution rate, thus expanding the explanatory ability of growth rate equation. Using such model, the output elasticity of capital and labor in China’s rice yield growth are calculated from 1978 to 2020, and the dynamic characteristics of the contribution rate of capital, labor and generalized technological progress are analyzed. Next, the capital contribution rate is decomposed according to the composition of the total capital. The results show that: (1) The capital elasticity and labor elasticity are indeed not constant in different years. In China, from 1978 to 2020 the value of capital elasticity was between 0.3209 to 0.3589, with a mean of 0.3437, and the value of labor elasticity was between −0.1759 to −0.1640, with a mean of −0.1730. (2) Natural disasters do affect capital elasticity and labor elasticity in rice production. (3) When the annual proportion of crop disasters increases, the contribution rate of interaction between capital and natural disaster (KDR) value is negative, whereas the contribution rate of interaction between labor and natural disaster (LDR) value is positive. (4) Compared with 1978, the generalized technological progress contribution rate (GTPR) of the rice yield growth in China from 1979 to 2020 shows a declining trend in fluctuations, whereas the total capital contribution rate (TKR) shows a rising trend in fluctuations and the total labor contribution rate (TLR) is relatively stable in the same period. Since 2000, capital investment has become the main factor for the rice yield growth per unit area in China, of which machinery, chemical fertilizer, seed and pesticide are the four most important input factors.

Οικονομική της χαρτογράφησης των φυσικών πόρων - η περίπτωση του δασολογίου

The analysis used in this experiment was is the the analysis of Cobb-Douglas production function and elasticity of production. The results obtained were F test results stating that all variable number of cages, seed, feed, and labor simultaneously significant effect on the production of carp. Based on the coefficient of determination showed that 89% variation amount of production can be explained by a variable number of cages seed, feed and labor. While 11% is influenced by other variables not included in the regression model. T test results stated that the factor of seed and feed real and significant effect on the production of carp while the number of cages and a factor of labor is not significant and not significant to the production of carp. The elasticity of the production number cages, seed, feed, and labor respectively (-0.983), (0.600) (0.221) (0.441) which means elastsitas number of cages in the region of production III and elasticity of seed, feed and energy working in the region of production II. Suggestions in this study were (1) should farmers carp determine the factors of production that significantly affect the production of carp so that farmers can see the production factors which need to be considered both quantity and quality, (2) should need counseling for farmers on the use of factors of production enterprises an efficient carp cages primarily on the number of cages in a single use of cages without reducing the use of seeds. Keywords: Goldfish, Regression Model, Elasticity Production

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.)

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 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.

There considered the approach of the linear econometric dependences parameters estimating for the case of combining a set of special conditions arising in the simulation process. These conditions address the most important problems met in practice when implementing a series of classes of mathematical models, for the construction of which the matrix of explanatory variables can be used. In most cases the vectors that make up the matrix have a close correlation relationship; this leads to the need of performing calculations using a rank deficient matrix. There are also take place violations of the Gauss-Markov theorem condition. The list of above mentioned special conditions is augmented by the additional model parameters constraints. Cobb-Douglas's production function and the Solow model are known economic problems of this type. In this research the need to impose additional constraints on the model parameters is extended to a wider range of tasks. In general, the economic formulation of the problem with the specified features is presented.Known ways to solve these tasks are discussed. The authors’ approach proposed takes into account the whole spectrum of these features. This approach is based on the application of pseudorandom matrices and the use of singular matrix decomposition. The use of proposed mathematical tools makes it possible to improve the quality of estimating model parameters while using real economic processes data. The analytical definition is found for the parameter evaluating vector of a linear econometric model with all the above mentioned features. Analysis of the used definition provides determination of the conditions that the matrix must satisfy; this describes additional model parameters constraints. The term was also obtained to estimate the variance of a linear econometric model parameters vector.The results obtained can be used in machine learning systems in the implementation of problems of econometric dependencies or discriminant models.

This study was conducted in 2020 to determine the profitability and productivity of organic turmeric production in the Surkhet district of Mid-western Nepal. Face-to-face interviews were conducted with 60 farmers and two focus group discussions were held in four different communities. Turmeric is commonly utilized among Nepalese households in the preparation of curries and is considered one of Nepal’s top five major spice crops. Despite being one of the top five-spice crops, Nepal’s dependency on imported turmeric has been growing every year to meet domestic demand due to the gradual decline in domestic production. The simple descriptive and statistical tools including the Cobb-Douglas production function and benefit-cost analysis were used to analyze the result. The benefit-cost ratio was found to be 1.20, indicating that organic turmeric production was a low profitability sub-sector with a productivity of only 9.06 metric tons per hectare. The Cobb- Douglas production function showed that the cost on seed had a non-significant effect on gross returns and other costs like human labour cost, organic manure cost, ploughing cost, and other costs (agriculture equipment, thread, sack/doko, and rhizome treatment) were found statistically significant. Return to scale was calculated using the Cobb- Douglas production function and it was found to be 0.363, indicating that a 10% increase in the cost of production increases the rate of return by 3.63%, which is a diminishing rate of return. As a result, replacing human labour with agricultural machinery, lowering seed costs, and ensuring appropriate market prices are required to boost the productivity and profitability of organic turmeric production in the research area.

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.

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.

Cassava farming in Salatiga City is a food-crop commodity farming business that has good opportunities because the demand for cassava in the market is increasing. However, some obstacles hinder cassava farming, namely cassava productivity which has not reached the target and limited production factors. This indicates that the use of production factors is still not efficient. Production factors that directly affect the productivity of cassava are land area, seeds, fertilizers, and labor. The aims of this study were: (1) to analyze the influence of production factors on cassava production, (2) to analyze the level of elasticity of cassava production factors, and (3) to analyze the level of technical efficiency and economic efficiency in cassava farming activities in Salatiga City. The analytical method used is the Cobb-Douglas production function with thehelp of the SPSS program to examine the influence of factors on cassava production and production elasticity. Technical efficiency is analyzed using the stochastic frontier production function. The results showed that the factors of seeds, manure, and labor were thought to affect cassava farming. The results of the elasticity analysis of all factors of production are in the rational area (Region II) with a positive value. The results of the technical efficiency analysis show that only the seed variable has a positive and significant value. Based on the results of the calculation of economic efficiency analysis, it shows that the input use of the land area, seeds, manure, and labor is not efficient.

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.