Course covers a limited subset of topics from mathematics for economists simon and blume 1994, and uses various definitions from the book. Twofactor cobbdouglas production function is given by where denotes the labor input, is the capital input, is the total. The estimation of the parameters of aggregate production functions is central to much of todays work on growth, technological change, productivity, and labor. The cobbdouglas production function is still today the most ubiquitous form in theoretical and empirical analyses of growth and productivity. Denote aggregate output by y, the input of capital by k, and the input of labour by l. For the case of two inputs, the ces production function takes the following form. Furthermore, this interpretation is applicable for both the cobbdouglas production function and the ces production function. Zhigang shen cobbdouglas production function was widely used in economics and productivity studies across many sectors. 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 inputs described. Algebraic production functions and their uses before cobbdouglas thomas m. A functional form, named after its originators, that is widely used in both theoretical economics and applied economics as both a production function and a utility function. The introduction of the cobb douglas regression and its adoption by agricultural economists jeff e. In particular we have f, l raised to the power alpha times k to the power of beta where these powers are positive numbers.
Such a form of the cobbdouglas production function assumes constant returns to scale of k and h, which can be thought of as combining two assumptions. The paper treats various aspects concernin g the cobbdouglas production function. On the one hand were highlighted conditions for the existence of. The transformed function is the equation for a simple two variable regression line in which all observations in the data set used. Profit maximization problem for cobbdouglas and ces. Humphrey fundamental to economic analysis is the idea of a production function. Applications of cobbdouglas production function in construction timecost analysis. The cobbdouglas production function department of economics.
During 19001947, charles cobb and paul douglas formulated and tested the cobbdouglas production function through various statistical evidence. In the 1920s the economist paul douglas was working on the problem of relating inputs. It has been argued that the cobbdouglas production function provides an acceptable representation of production technology taylor et al. It and its allied concept, the utility function, form the twin pillars of. Oaxaca university of arizona 1 cobbdouglas production function q aegtl. In general, a production function is a specification of how the quantity of output behaves as. On the cobbdouglas production function division of the. In economics and econometrics, the cobb douglas 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. Some aspects of the translog production function estimation. Cobbdouglas production functions 1 mathematical tricks the derivative of. A geometric characterization of ves and kadiyalatype.
The cobbdouglas production function economics discussion. We conclude that the formulas for the output elastisities and total factor productivitiy are compatible with the original 1928 data. The cobbdouglas production function is a simplified, yet accurate, means for calculating the impact of changes in the inputs, the relevant efficiencies, and the yields of a production activity. Let us begin with a simple form a production function first q fl, k the above mathematical equation tells us that q output is a function of two inputs. The cobbdouglas production function used and estimated by cobb and douglas 1928, and in each of the subsequent timeseries papers, takes the following form. The cobbdouglas functional form of production functions is widely used to represent the relationship of an output and two inputs. The mrs and the cobbdouglas consider a twogood world, xand y. In economics and econometrics, the cobbdouglas production function is a particular functional form of the production function, widely used to represent the. As we know, a production function explains the functional relationship between inputs or factors of production and the final physical output. Persamaan diatas sering disebut fungsi produksi cobbdouglas cobb douglas production function.
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. Lets consider a particular production function which is called cobbdouglas, cobbdouglas function. Preface second editionagricultural production economics second edition is a revised edition of the textbook agricultural production economics publi shed by macmillan in 1986 isbn 0023280603. The cobbdouglas production function is then given byy ak. Kautilya economics, commerce and finance 4,143 views. Cobbdouglas production function differentiation example youtube. The cobbdouglas production function y alk is still today the most ubiquitous form in theoretical and empirical analyses of growth and productivity felipe and adams, 2005. In economics, the cobb douglas functional form of pro duction functions is widely. The cobbdouglas production function, given by charles w. The sum of a and parameters shows the type of returns to scale in production. Pdf the complete theory of cobbdouglas production function. Algebraic production functions and their uses before cobb. While still being quite tractable, with a minimum of parameters, it is more. The cobbdouglas production function was not developed on the basis of any knowledge of engineering, technology, or management of the production process.
In other words, we do not impose an arbitrary parametric structure on aggregate production functions at the outset and instead derive their properties as a function of deeper structural microeconomic primitives. Special production functions cobb douglas, ces, ves, translog and their properties duration. Alternatively, we can always x a level of k and a level of l. Given the basic form of the cobbdouglas production function, well find the partial derivatives with respect to capital, k, and labor, l. They are a function of prices of inputs and the price of output. The microeconomic foundations of aggregate production. Again, since production function 1 is a cobbdouglas production function we can simply add the exponents together. Cost functions for given input prices r,w, and for a given output level q, nd. It was this body of work that yielded the cobb douglas production function that is used extensively in theoretical and applied. The cobbdouglas production function 173 the resulting equation is referred to as linear in the parameters or linear in the coefficients. An assessment of ces and cobbdouglas production functions 1 eric miller email. Our consumer, skippy, wishes to maximize utility, denoted ux,y.
How to use excel to estimate the cobbdouglas production function duration. Notes on labor demand under a cobbdouglas technology. Marginal cost derivations for a cobbdouglas 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 cobbdouglas function y t. On the one hand were h ighlighted conditions for the existence of the cobbdouglas function. The mrs and the cobbdouglas simon fraser university. Solow introduced a generalization of the cobbdouglas production function. Douglas used a special form of production function, which is known as the cobbdouglas production function. Notes on labor demand under a cobbdouglas technology r. It was instead developed because it had attractive mathematical characteristics, such as diminishing marginal returns to either factor of production. Untuk memudahkan pendugaan terhadap persamaan di atas maka persamaan tersebut diperluas secara umum dan diubah menjadi bentuk linier dengan cara. Marginal cost derivations for a cobbdouglas production. 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%. 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.
For example, agricultural production is not only dependent on labour and capital used but also on the use of other inputs such as land, fertilizers, irrigation. While discussing the production theory of the firm, economists c. Our findings also suggest that a failure to normalize the production function leads to a substantial upward bias in the estimated elasticity. This paper examines the nigerian economy from 1990 to 2009 and uses the. The cobbdouglas production function describes how output q depends on the capital k and labor l used in production. Over the following years, the cobbdouglas production function became a key concept of neoclassical economics1 for interesting updates and testing due to douglas himself, see 7. The weight of evidence accumulated in the empirical literature emphatically rejects the cobbdouglas specification. The introduction of the cobb douglas regression and its. Applications focus on two period borrowing and savings problems. In 1928, cobb and douglas introduced a famous twofactor production function, nowadays called cobbdouglas production function, in order to describe the distribution of the national income by help of production functions. One is that inputs other than physical capital k and human capital h as well as knowledge or technology, as captured by a are relatively unimportant. Notice that for the cobbdouglas function the factor demand for input 1 depends on w1 and pbut not on the price of the second input, w2. Explain the properties of cobbdouglas production function. Then mpl, is the derivative is taken at any point in the space of the factors of production, labor and capital.
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