Basing our understanding of the function above, we can now define a more specific production function the cobb douglas production function. Econ cobb douglas elasticity of substitution duration. The cobbdouglas production function is a particular form of the production function. Third, we compare the results of the generally used cobbdouglas utility function a special case of the constant elasticity of substitution function, the formula for which is q al a k b, to those of the constant elasticity of substitution function.
Cobbdouglas form which persists almost as a paradigm in modern. The elasticity of substitution is the elasticity of the ratio of two inputs to a production or utility function with respect to the ratio of their marginal products or utilities. In most empirical studies relating to either industry or agriculture, the ces production function is used to know the extent of substitution possibilities between labour and capital. Lecture notes on elasticity of substitution ucsb department of. Cobbdouglas preferences are easy to use and therefore commonly used. Sep 24, 2012 cobb douglas elasticity of substitution. When the elasticity of substitution equals unity then the ces production function nests the. Lecture notes on constant elasticity functions thomas f. D24, e23, o14 1 introduction a key parameter in economics is the elasticity of substitution between capital and labor. While still being quite tractable, with a minimum of parameters, it is more. Elasticity of substitution is the elasticity of the ratio of two inputs to a production or utility function with respect to the ratio of their marginal products or utilities. On the basis of the value of a, the form of production function cobbdouglas or constant elasticity ces production function can be selected for the analysis. Pdf this paper proposes to estimate the elasticity of substitution resulting from the ces production function.
Substitution elasticities in a ces production framework. Recent literature provides estimates of the elasticity of substitution well below 1 thus rejecting the traditional cobb douglas production function though there is no particular value on which consensus converges. From cobbdouglas, textbooks and surveys then proceed to the more exotic ces, or constant elasticity of substitution, function p kl. The linear production function is the simplest form of a 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%. The different types of production function as shown in figure16. Cobb douglas production function can be expressed as follows. These inputs are l amount of labour and k hours of capital. May 25, 2014 econ cobb douglas elasticity of substitution duration.
Isoelastic elasticity of substitution production functions. What are the properties of the cobbdouglas production. How can i obtain leontief and cobbdouglas production. Identifying the elasticity of substitution with biased technical change. It measures the curvature of an isoquant and thus, the. Algebraic production functions and their uses before cobb. For example, capital and labor can be used as a substitute of each other, but to a limited extent only. It is a tedious but straightforward application of lagrangian calculus to demonstrate. The cobb douglas s major strengths are its ease of use and its seemingly good empirical.
In cobbdouglas production function, only two input factors, labor, and capital are taken into the consideration, and the elasticity of substitution is equal to one. The proofs i will present are based on techniques relevant to the fact that the ces production function has the form of a generalized weighted mean. The ces function shares the cobb douglas function s homogeneity of degree one. What are the properties of the cobbdouglas production function. In cobb douglas production function, only two input factors, labor, and capital are taken into the consideration, and the elasticity of substitution is equal to one. Isoelastic elasticity of substitution production functions kolegia sgh. On the basis of the value of a, the form of production function cobb douglas or constant elasticity ces production function can be selected for the analysis. Review of microeconomics algebraic formulation of mrs. Review of microeconomics algebraic formulation of mrs in. The ces function shares the cobbdouglas functions homogeneity of. Lecture notes on elasticity of substitution ted bergstrom, ucsb economics 210a march 3, 2011 todays featured guest is \the elasticity of substitution. Relative demand function y x fp x p y the elasticity of this function is the elasticity of substitution in consumption. An early alternative to the cobbdouglas production function is the constant elasticity of substitution ces production function 1.
Cobbdouglas production function can be expressed as follows. The elasticity of substitution in the cobbdonglas production function is unity can be proved below. Elasticity of a function of a single variable before we meet this guest, let us spend a bit of time with a slightly simpler notion, the elasticity of a a function of a single variable. For the cobbdouglas function the elasticity of substitution between the input variables is always equal to 1 for a proof see, e. How do we get cobbdouglas and leontief functions from ces. We show that the large elasticity of substitution between capital and labor estimated in the literature on average, 0. 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. Deriving shortrun cost functions from a cobb douglas production function duration. Third, we compare the results of the generally used cobb douglas utility function a special case of the constant elasticity of substitution function, the formula for which is q al a k b, to those of the constant elasticity of substitution function. Although the format and coverage remains similar to the first edition, many small revisions. Elasticity of substitution between labor and capital nbp. The above mathematical equation tells us that q output is a function of two inputs assumption. 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.
Thus the elasticity of substitution of a constant returns to scale production function can be expressed as the elasticity of output per capita with respect to the marginal product of labor. This is a rigid assumption of cobbdouglas production function. The estimation of the elasticity of substitution of a ces production. Explain the properties of cobbdouglas production function.
By defining the variable output elasticities cobbdouglas function, this. It is also assumed that, if any, of the inputs, is zero, the output is also zero. Constant elasticity of substitution ces production function. In the extreme case of leontief nosubstitution technology, where the l. This paper introduces two formal equivalent definitions of the cobb douglas function for a continuum model based on a generalization of the constant elasticity of substitution ces function for a.
Cobb douglas production function and the marginal rate of technical substitution cost minimisation duration. Cobbdouglas production function refers to the production function in which one input can be substituted by other but to a limited extent. This was used in the original paper where the ces function was introduced, arrow, k. Where there are two factors and a homogeneous production function, the elasticity of substitution. If the cobbdouglas production function is ql,k a l. One of the limitations of cobbdouglas production function is the unitary elasticity of substitution between labour and capital. The cobbdouglass major strengths are its ease of use and its seemingly good empirical.
Econ cobbdouglas elasticity of substitution youtube. Contents a measuring substitutability b elasticity of substitution under constant returns to scale c cobbdouglas production functions d constant elasticity of substitution ces production functions e elasticities of substitution in multiinput cases a measuring substitutability let us now turn to the issue of measuring the degree of substitutability between any pair of factors. Most lectures teach the relationship between the ces, cobbdouglas, and leontief functions using the value of elasticity of substitution, namely, in the discrete object model. Lecture notes on elasticity of substitution ted bergstrom, ucsb economics 210a october 26, 2015 todays featured guest is \the elasticity of substitution. The two panels a and b show estimates based on the crosssectional dimension. This lecture note aims at being a reference for algebraic computations of the leontief and cobb douglas functions by taking limits of ces functions both in discrete and. L ql 2 the first part of 2 the dividend is the marginal product of. A growth framework using the constant elasticity of. 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. An assessment of ces and cobbsdouglas production functions. Cobb douglas production function refers to the production function in which one input can be substituted by other but to a limited extent. The cobb douglas production function is a particular form of the production function. This lecture note aims at being a reference for algebraic computations of the leontief and cobbdouglas functions by taking limits of ces functions both in discrete and. Intermediate microeconomics dirk bergemann, spring 2012 week of 122 128 1 lecture 5.
This paper introduces two formal equivalent definitions of the cobbdouglas function for a continuum model based on a generalization of the constant elasticity of substitution ces function for a. They observe that the ces function includes cobbdouglas as a special case when the elasticity, or. Because of this unit elasticity of substitution between two factors in the production function, isoquants are convex to the origin shown in fig. In a competitive market, it measures the percentage change in the ratio of two inputs used in response to a percentage change in their prices. Constant elasticity of substitution production function. The cobbdouglas output elasticity is constant and equal to. The mean elasticity conditional on the absence of publication bias, disaggregated data, and inclusion of information from the firstorder. In economics, aproduction function represents the relationship between the output and the combination of factors, or inputs, used to obtain it. The constant elasticity of substitution ces production function, first introduced to economics by arrow, chenery, minhas, and solow 1961, is probably the.
We consider a consumer with cobbdouglas preferences. Pdf a production function with variable elasticity of factor. The elasticity of substitution back contents a measuring substitutability b elasticity of substitution under constant returns to scale c cobb douglas production functions d constant elasticity of substitution ces production functions e elasticities of substitution in multiinput cases a measuring substitutability. Pdf the main aim of this paper is to prove the existence of a new production function with variable elasticity of factor substitution. The estimation of the elasticity of substitution of a ces. Mar 09, 2010 most lectures teach the relationship between the ces, cobb douglas, and leontief functions using the value of elasticity of substitution, namely, in the discrete object model. Under a quasiconcave production function the elasticity attains any. A key parameter in economics is the elasticity of substitution between capital and labor. Algebraic production functions and their uses before cobbdouglas. Find the partial derivatives of the cobb douglas production function duration. Basing our understanding of the function above, we can now define a more specific production function.
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