This paper examined the relationship between crude oil production and the nigerian economic performance using the cobbdouglas production function. The cobb douglas production function used and estimated by cobb and douglas 1928, and in each of the subsequent timeseries papers, takes the following form. Jul 26, 2016 during 19001947, charles cobb and paul douglas formulated and tested the cobbdouglas production function through various statistical evidence. Dec 01, 2012 cobb douglas production function, which defines the portion of labor and equipment needed based on the production rate, provides a muchneeded piece to modeling the cost functions in the. The cobbdouglas production of the nigerian economy 19742009. Feb 24, 2017 cobb douglas production function and the marginal rate of technical substitution. An assessment of ces and cobbsdouglas production functions. Special production functions cobb douglas, ces, ves, translog and their properties bse. Alternatively, the generalized leontief, generalized cobbdouglas and translog function all are sufficiently flexible. Cobbdouglas production function was widely used in economics and.
The cobbdouglas functional form of production functions is widely used to represent the relationship of an output and two inputs. Applications of cobbdouglas production function in construction. The cobbdouglas production function is based on the empirical study of the american manufacturing industry made by paul h. While still being quite tractable, with a minimum of parameters, it is more. What would be the interpretation of these coefficients in the regression is it just the change in output when the labor or capital share changes should the beta coefficients add up to 1, and if yes, are there. The cobbdouglas production function is a particular form of the production function. Cobbdouglas production function as an approach for. Cost functions for given input prices r,w, and for a given output level q, nd. Cobbdouglas production function contains the following useful. Anatomy of cobbdouglas productionutility functions in 3d. Finally, with combining both internal and external sources of uncertainty, the case is. Douglas studied the relationship of inputs and outputs and formed an empirical production function, popularly known as cobb douglas production function. In other words it is the sum of elasticities of output with respect to different inputs.
The anatomy of cobb douglas production utility functions in 3d, or any part thereof, may not be used as part of a document distributed for a commercial purpose. In our regression analysis, we will find out the effect of factors of production on output. Now combine x1 and x2 in a manner of ces to obtain z1 and similarly. Census bureau data, you can test for the three types of returns to scale based on the cobb douglas production function with both f tests and t tests. First of all, it is interesting to combine different sources that mention the cobb. Alternatively, we can always x a level of k and a level of l. Pdf the main objective of this paper is to propose and verify a time augmentation of the cobbdouglas production function parameters which. This thesis applies the cobbdouglas production function to explore the.
For the case of two inputs, the ces production function takes the following form. Explain the properties of cobbdouglas production function. Wh en app lying the cobbdouglas production function, dfhh as wel l as giorno et al. An assessment of ces and cobb douglas production functions 1 eric miller email. Anatomy of a cobb douglas type production utility function in three dimensions. Nov 04, 2017 maximize a cobb douglas production function using lagrange multipliers duration. Marginal cost derivations for a cobb douglas production function benedikt kolb 17th april 2016 imagine a producer wants to minimise costs from labour l tand capital k t, which come at factor prices w tand r t, respectively, subject to a production technology of the cobb douglas function y t a tl 1 k, where a tis total. Cobb douglas production functions 1 mathematical tricks the derivative of. Technology can be represented by a production function, such as cobb douglas and constant elasticity of substitution ces place a restriction on elasticity of substitution cobb and douglas 1928, arrow, et al.
Pdf cobbdouglas production functions daniel casarin. The cobbdouglas production function, given by charles w. A brief history of production functions munich personal repec. It is widely used because it has many attractive characteristics, as we will see below.
Humphrey fundamental to economic analysis is the idea of a production function. Douglas used a special form of production function, which is known as the cobbdouglas production function. Cobbdouglas production function, which implies a unitary elasticity of. It is a linear homogeneous production function of degree one which takes into account two inputs, labour and capital, for the entire output of the. In this case, the cobbdouglas production function has constant return to scale. The cobbdouglas production function economics discussion. This functional form, however, includes the assumption of a constant share of labor in output, which may be too restrictive for a converging country.
The cobbdouglas production function revisited arxiv. It and its allied concept, the utility function, form the twin pillars of neoclassical economics. The cobbdouglas production function 173 the resulting equation is referred to as linear in the parameters or linear in the coefficients. Example of cobb douglas production function the cobb douglas production function. While discussing the production theory of the firm, economists c. The estimate of returns to scale can be estimated from the cobbdouglas production function by taking the summation of the regression coefficients constant elasticities of various inputs. In other words, log y is a linear function of log x1 and log x2. The general form of cobbdouglas production function is. A production function, such as the translog transcendental logarithmic production function, can be used to model how a firm combines inputs to produce outputs. The model was fitted to nigerias data of crude oil production, labor input, capital input, oil domestic consumption and oil exports. Alternatively, the generalized leontief, generalized cobb douglas and translog function all are sufficiently flexible. Many details are omitted since this a repetition of the examples of utility functions. Special production functions cobbdouglas, ces, ves, translog and their properties bse.
On the cobbdouglas production function division of the. Algebraic production functions and their uses before cobbdouglas. The cobbdouglas production function is often used to analyse the supplyside performance and measurement of a countrys productive potential. The transformed function is the equation for a simple two variable regression line in which all observations in the data set used. In 1928, charles cobb and paul douglas presented the view that production output is the result of the amount of labor and physical capital invested. This gave birth to the original cobbdouglas production function. Y ta tkt l t 23 if technology is growing at a rate of 1% per year, the capital stock by 3%, and the labor supply by 2%. Testing for returns to scale in a cobbdouglas production. Originally, cd production function applied not to the production process of an individual firm but to the whole of the manufacturing production. For example, capital and labor can be used as a substitute of each other, but to a limited extent only. Marginal cost derivations for a cobbdouglas production function. Again, since production function 1 is a cobb douglas production function we can simply add the exponents together. Cobb douglas production function and the marginal rate of technical substitution.
Technology can be represented by a production function, such as cobbdouglas and constant elasticity of substitution ces place a restriction on elasticity of substitution cobb and douglas 1928, arrow, et al. Pdf applications of cobbdouglas production function in. The basic form of the cobbdouglas production function is as follows. The empirical results showed that crude oil output has a significant impact on nigerian economy because there was. Algebraic production functions and their uses before cobb.
Douglas is a linear homogeneous production function, which implies, that the factors of production can be substituted for one another up to a certain extent only. The cobb douglas is a simple production function that is thought to provide a reasonable description of actual economies. Maximize a cobb douglas production function using lagrange multipliers duration. Pdf the time augmented cobbdouglas production function. In economics, a production function is an equation that describes the relationship between input and output, or what goes into making a certain product, and a cobbdouglas production function is a specific standard equation that is applied to describe how much output two or more inputs into a production process make, with capital and labor being the typical. During 19001947, charles cobb and paul douglas formulated and tested the cobbdouglas production function through various statistical evidence. In the singleoutput case we can describe a production set z in two other waysthat are sometimes more convenient. Cobbdouglas production function refers to the production function in which one input can be substituted by other but to a limited extent. As samuelson 1979 conjectured, this explanation is that all the aggregate cobb douglas function regression captures is the path of the value added accounting identity according to which value added equals the sum of the wage. When, the cobb douglas function is homogeneous, meaning that a doubling of both of the two inputs at the same time results in a doubling of the output. The study and applications of the cobbdouglas production function in the. In economics and econometrics, the cobbdouglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs particularly physical capital and labor and the amount of output that can be produced by those inputs. Conducting an f test for constant returns to scale.
1402 219 21 149 700 310 707 1273 1480 805 901 361 1341 1100 547 1439 427 799 268 1365 529 264 386 444 681 328 865 1209 1187 253 1498 64 512 1149 1423 842