Estimation results support the cobbdouglas case and the estimated supplyside model accounts satisfactorily for the stylised features of the data, i. For example, for the cobb douglas production function q fl,k ala kb. Douglas used a special form of production function, which is known as the cobb douglas production function. With a cobb douglas production function, the share of output going to labor. Factor shares, the price markup, and the elasticity of substitution. Jul 26, 2016 during 19001947, charles cobb and paul douglas formulated and tested the cobbdouglas production function through various statistical evidence. Set up the problem for a profit maximizing firm and solve for the demand function for both inputs. For the time being, we are going to have just two inputs, k and l, and so we will write the production function as y fk,l.
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. A firm employs a cobbdouglas production function of the form. A quantitative survey of the capitallabor substitution elasticity. There can be other inputs, k and l are just examples. Does production function 1 have decreasing, constant, or increasing returns to scale. This twothirdsonethird split holds true empirically, at least as a fair approximation.
Pdf supplementary teaching note prepared for the labour economics and market analysis. We chose the euler formula of a simple homogeneous function of the first degree. 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. Although, a variety of functional forms have been used to describe production relationships, only the cobbdouglas production function is discussed here. We let the production technology in our model be represented by a cobbdouglas production function y. The cobb douglas production function, given by american economists, charles w. The labour demand and supply derivation by the cobbdouglas function. Notes on labor demand under a cobbdouglas technology. Pdf the cobbdouglas production function is often used to analyse the. In economics, a production function represents the relationship between the output and the combination of factors, or inputs, used to obtain it. A production function is a mathematical function that tells us how much output we get for given amounts of inputs. It has become known as the cobb douglas production function. Cobbdouglas production function sahand rabbani we will show that in the cobbdouglas production function model, the percentage of an economys income that is spent on labor and capital is constant. In economics and econometrics, the cobbdouglas production function is a particular.
Cobbdouglas production function differentiation example. The cobbdouglas production function is a special case of the constant elasticity of. Estimation of a ces production function with factor augmenting technology. The econometric model consists of cobbdouglas production function. Cobb and douglas estimated the value of k in the hypothesized relationship p blkc1k by using douglass laboriously compiled data to fit the linear regression logpc b. Humphrey fundamental to economic analysis is the idea of a production function. A firm employs a cobb douglas production function of the form. The figure given below captures how the production function looks like in case of increasingdecreasing and constant returns to scale. A cobb douglas production function is one of the famous statistical production function. For the period 19952005, the authors do not find significant difference between the calculation of the supply side of the czech economy by the cobbdouglas production function and a more.
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. What are the properties of the cobbdouglas production function. An assessment of ces and cobbsdouglas production functions. The authors apply a more general form of production function and allow labor share to. Oct 09, 2012 given the basic form of the cobb douglas production function, well find the partial derivatives with respect to capital, k, and labor, l. The cobbdouglas production function is a special case of the constant elasticity of substitution ces. For a given amount of labor and capital, the ratio q k is the average amount of production for one unit of. Marginal product of labor and capital assume q fl,k is the production function where the amount produced is given as a function of the labor and capital used. Marginal product of labor and capital assume q fl, k. The labour demand and supply derivation by the cobb douglas.
In its original form, this production function applies not to an individual firm but to the whole of manufacturing in the united states. L the quantity of labor applied to the production of q, for example, hours of labor in a month. For example, for the cobbdouglas production function q fl, k ala kb. This is a feature of the cobbdouglas production function the factor shares of income, as the payments to capital and labor are called, are equal to the cobbdouglas exponents, and is true regardless of how much capital or labor there is in the economy. 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. In this case, the output is manufacturing production and inputs used are labour and. Oaxaca university of arizona 1 cobb douglas production function q aegtl. Apr 23, 2018 in economics, aproduction function represents the relationship between the output and the combination of factors, or inputs, used to obtain it. An assessment of ces and cobbdouglas production functions 1 eric miller email. The cobb douglas production function is that type of production function wherein an input can be substituted by others to a limited extent. It has become known as the cobbdouglas production function. For example, for the cobbdouglas production function q fl,k ala kb. Notes on labor demand under a cobbdouglas technology r.
The cobb douglas function is widely used to represent production functions and also utility functions in economics. Conditional input demand functions are obtained from cost minimization. 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. As we know, a production function explains the functional relationship between inputs or factors of production and the final physical output. The cobb douglas form was developed and tested against. Q f l, k it is also called as production with two variable factor inputs, labour l and capital k in particular.
Problem set 1 the cobbdouglas production function suppose that the world is described by the solow model, and that the production function is. The transformed function is the equation for a simple two variable regression line in which all observations in the data set used. Algebraic production functions and their uses before cobb douglas thomas m. There are three main types of production functions. Oaxaca university of arizona 1 cobb douglas production function. The cobb douglas production function is a particular form of the production function. Cobbdouglas production function and perfect competition. H douglas, studies the relation between the input and the output.
Derivation of constant labor and capital share from the cobb. The cobb douglas production function 173 the resulting equation is referred to as linear in the parameters or linear in the coefficients. The introduction of the cobb douglas regression and its. Oaxaca university of arizona 1 cobbdouglas production function q aegtl. Cobb douglas cd production function is of the form q al. Algebraic production functions and their uses before cobbdouglas. Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus.
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. But question is what makes we nd the ces production function should look like this. The cobb douglas production function is a special case of the constant elasticity of substitution ces. The indirect utility function can be calculated by substituting the demand into the utility function. A commonly discussed form of long run production function is the cobbdouglas production function which is an example of linear homogenous production functions. Marginal cost derivations for a cobbdouglas production function. Euro area production function and potential output. 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. To calculate the output elasticity of a cobbdouglas production function, we must derive the total output with respect to the level of a production input. The cobbdouglas production function 173 the resulting equation is referred to as linear in the parameters or linear in the coefficients. Douglas used a special form of production function, which is known as the cobbdouglas production function. Derivation of constant labor and capital share from the cobb douglas production function sahand rabbani we will show that in the cobb douglas production function model, the percentage of an economys income that is spent on labor and capital is constant.
While discussing the production theory of the firm, economists c. 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%. Again, since production function 1 is a cobb douglas production function we can simply add the exponents together. Production functions linear vs leontief vs cobbdouglas. The output price is p and the input prices are r and w for k and l, respectively. In other words, log y is a linear function of log x1 and log x2. Lecture notes in macroeconomics growth, part 1 miscellaneous preliminaries what is a production function. Pdf the labour demand and supply derivation by the cobb. The cobbdouglas production function economics discussion. 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. Maximize a cobb douglas production function using lagrange. Apr 10, 2019 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 cobb douglas 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. The labour demand and supply derivation by the cobb douglas function. Recall that the golden rule level of the capital stock k gr maximizes consumption per worker in steadystate.
We know that the general form of production function is, q f k,l where, q output, k capital and l labour. Devesh raval november 15, 2010 abstract both the recent literature on production function identi. The cobb douglas production function, given by charles w. We chose the cobbdouglas specification for ease of.
Notes on labor demand under a cobb douglas technology r. Many details are omitted since this a repetition of the examples of utility functions. Cobb douglas output elasticity to calculate the output elasticity of a cobb douglas production function, we must derive the total output with respect to the level of a production input. It and its allied concept, the utility function, form the twin pillars of. The cobb douglas production function is based on the empirical study of the american manufacturing industry made by paul h. The general form of cobbdouglas production function is. For a given amount of labor and capital, the ratio. The cobbdouglas functional form of production functions is widely used to represent the relationship of an output and two inputs.
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