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. The cobbdouglas production function is a special case of the constant elasticity of substitution ces. Cobb douglas function demand theory discusseconomics. Recall from 103 that elasticity is the ratio of two variables percentage change. The cobbdouglas production function is a particular form of the production function. Elasticity of demand concepts price elasticity of demand. This form is called a cobbdouglas utility function. The microeconomic foundations of aggregate production. Compared to standard flexible functions such as the translog function, this framework has several advantages. The introduction of the cobb douglas regression and its. Some economists believe that the more general ces may be a more 1although cobb douglas does restrict the elasticity of substitution between the demand for labor. Find expressions for income elasticity of demand ii. One of the limitations of cobbdouglas production function is the unitary elasticity of substitution between labour and capital. 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.
Lecture notes on elasticity of substitution ted bergstrom, ucsb economics 210a october 26, 2015 todays featured guest is \the elasticity of substitution. By defining the variable output elasticities cobbdouglas function, this article shows that a large class of production functions can be written as cobbdouglas function with nonconstant output elasticity. He noted that the output curve lay between the two curves for the factors, and tended to be approximately one quar. Algebraic production functions and their uses before cobbdouglas thomas m. For most consumer goods and services, price elasticity tends to be between. Review of microeconomics algebraic formulation of mrs. Cobbdouglas, some income elasticities can be effectively zero at any. Lecture notes on elasticity of substitution ted bergstrom, ucsb economics 210a march 3, 2011 todays featured guest is \the elasticity of substitution. We consider a consumer with cobbdouglas preferences. Algebraic production functions and their uses before cobbdouglas. It is a tedious but straightforward application of lagrangian calculus to demonstrate. Cobbdouglas production function handout jae wook jung. Relative demand function y x fp x p y the elasticity of this function is the elasticity of substitution in consumption.
In this article we will discuss about the constant elasticity of substitution production function. With very large and increasing per capita income, ultimately the utility function becomes indistinguishable from cobbdouglas. Unitary elasticity of substitution in cobb douglas production function. Cobbdouglas preferences are easy to use and therefore commonly used. 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. Course covers a limited subset of topics from mathematics for economists simon and blume 1994, and uses various definitions from the book. The elasticity of substitution in the cobbdonglas production function is unity can be proved below. The graphical derivation of demand described above is useful for understanding what it means to derive demand from a consumers utility and budget, but an analytical technique is helpful since the demand is then known for many different income levels and for different prices of the other commmodity y. Intermediate microeconomics dirk bergemann, spring 2012 week of 122 128 1 lecture 5. In the early 1960s and 70s economists began to relax the restrictions imposed by cobb douglas.
The mid point forumula for price elasticity of demand. Applications focus on two period borrowing and savings problems. The ownprice elasticity of demand is defined as the percentage change in. In economics, aproduction function represents the relationship between the output and the combination of factors, or inputs, used to obtain it. 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. Elasticities for empirically estimated demand function. With very large and increasing per capita income, ultimately the utility function becomes indistinguishable from cobb douglas. The cobb douglas production function has been the most widely used production function in empirical work. Oaxaca university of arizona 1 cobbdouglas production function. Calculating elasticities from a translog cost function. To see this, note that the optimal capitallabor ratio may be expressed in logs as ln k l ln. The ces function shares the cobb douglas functions homogeneity of degree one. The elasticity of production, also called the output elasticity, is the percentage change in production divided the percentage change in the quantity of an input used for that production.
The mrs and the cobbdouglas simon fraser university. The two panels a and b show estimates based on the crosssectional dimension. December 12, 2016 discusseconomics microeconomics leave a comment. Review of microeconomics algebraic formulation of mrs in. By defining the variable output elasticities cobb douglas function, this article shows that a large class of production functions can be written as cobb douglas function with nonconstant output elasticity. Here we get analytic solutions for the marshallian demands for cobb douglas and perfect complement utility functions own price, income, and cross price link to mother of all elasticity handouts. Dec 12, 2016 in the past installments from discusseconomics on demand theory, now were venturing into the graphical and mathematical expressions of the cobb douglas demand function. Price elasticity of demand is greater, the greater the availability of substitutes, and the more similar the substitutesthe more important the item as a share of the consumers budget, the greater is the income effect of a change in price, so the more elastic is the demand. The mrs and the cobbdouglas consider a twogood world, xand y. Mar 07, 2009 this should be easy but for some reason i dont know where to go with it. When derived demand systems are obtained from a cost function, it is possible to estimate several elasticities of substitution along with price elasticities. It is also called the partial output elasticity, because it refers to the change in the output when only one output change that is, its the partial derivate of the production function, as opposed to the total derivative.
In the 2input case the own price demand elasticity is a. Unitary elasticity of substitution in cobbdouglas production function. Find the income elasticity of demand for the demand curve where. 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. Dec 18, 2010 this video introduces the cobb douglas utility function for two goods and demonstrates some of its properties. Cobbdouglas functions are typically difficult for optimisation problems. The introduction of the cobb douglas regression and its adoption by agricultural economists jeff e. 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. However, the cobb douglas is extremely restrictive as it sets the elasticity of substitution between factors to one.
An assessment of ces and cobbsdouglas production functions. Humphrey fundamental to economic analysis is the idea of a production function. In the early 1960s and 70s economists began to relax the restrictions imposed by cobbdouglas. Intro mathematics for economists mathematics for economists. Production functions linear vs leontief vs cobbdouglas. In a competitive product market a rise in a factor price raises cost, and eventually product price, by that factors share. Input demand functions under longrun pro t maximization with decreasing returns to scale can be derived. The ces function shares the cobbdouglas functions homogeneity of. I demonstrate how to compute marginal rate of substitution for cobb douglas utility.
If the production function has only one input, the elasticity of production. In the past installments from discusseconomics on demand theory, now were venturing into the graphical and mathematical expressions. Rejected the cobbdouglas form viton 1981, berechman 1993, and others. A monotonic transformation which preserves the ordinal properties of the function can be used.
Try out yourself which case is correct for cobbdouglas. It and its allied concept, the utility function, form the twin pillars of. This is a rigid assumption of cobbdouglas production function. This is a workinprogress course website for mathematics for economists, produced by fan. Cobbdouglas function that allows for any nonnegative constant elasticity of substitution. Algebraic production functions and their uses before cobb. The cobbdouglas production function has been the most widely used production function in empirical work. He began by plotting the series of output day index of physical production, labor workers employed, and fixed capital on a log scale. Lecture notes on elasticity of substitution ucsb economics.
Total demand elasticity increase in the wage rate increases cost of producing a given output. This should be easy but for some reason i dont know where to go with it. This video introduces the cobbdouglas utility function for two goods and demonstrates some of its properties. Graphically expressed utility maximizing with the assumption wellbehaved preferences. 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. Find expressions for the own price elasticity of demand. Cobbdouglas is one of the easiest ces utility functions to work with. Ux,yxa yb where a and b are positive numbers not necessarily integers. 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. This functional form has become very popular in programming models e. Algebraic production functions and their uses before cobb douglas thomas m. 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. However, the cobbdouglas is extremely restrictive as it sets the elasticity of substitution between factors to one.
An assessment of ces and cobbdouglas production functions 1 eric miller email. I thought considering cobb douglas with ces just tells me they arent perfect complements or perfect substitutes. Calculating elasticities from a translog cost function overview elasticities of substitution are an important measure of production relationships. Notes on labor demand under a cobbdouglas technology r. One of the limitations of cobb douglas production function is the unitary elasticity of substitution between labour and capital. 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. Assume that consumers utility function is of cobbdouglass form. One of the most common applications of the notion of elasticity of demand is to monopoly theory, where a monopolist is selling a good and the quantity of the good that is demanded is a function dp of the monopolists price p. Our consumer, skippy, wishes to maximize utility, denoted ux,y. Lecture notes on constant elasticity functions thomas f. 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. 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. Econometric estimation of the constant elasticity of.
Finally, consider the most general cobbdouglas form. There are three main types of production functions. Notes on labor demand under a cobbdouglas technology. The cobb douglas production function is a special case of the constant elasticity of substitution ces.
May 25, 2014 elasticity of substitution in production. For example, if a firm increases the number of workers by 10%, and the number of products produced per month increases by 20%, the elasticity of production will be. Notes on labor demand under a cobb douglas technology. Constant elasticity of substitution production function. What are the properties of the cobbdouglas production. For the case where that partial is exactly zero, the elasticity of substitution is zero. Others involve more complicated calculus that we will not. The cobbdouglas production function is a special case of the constant elasticity of substitution ces production technology. It is part of a larger category called constant elasticity of substitution ces utility functions. The cobbdouglas output elasticity is constant and equal to. Mar 14, 2019 a production function is an equation that establishes relationship between the factors of production i. 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. Elasticity of demand concepts free download as powerpoint presentation.
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