In our regression analysis, we will find out the effect of factors of production on output. Contoursof a cobbdouglas production function 5 10 15 20 25 30 5 10 15 20 25 30 notice that the function. An application of non linear cobbdouglas production. The cobbdouglas functional form of production functions is widely used to represent the relationship of an output and two inputs. The cobbdouglas production function and the steady state. Neoclassical onesector growth model state university of. Using the economic data published by the government, cobb and douglas took the year 1899 as. Algebraic production functions and their uses before cobb douglas thomas m. Cobbdouglas production function 5 10 15 20 x1 5 10 15 20 x2 0 10 20 fhx1,x2l figure 3. While still being quite tractable, with a minimum of parameters, it is more. How to derive a per capita production function from a. Cobbdouglas production function contains the following useful. 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.
We chose the cobbdouglas specification for ease of. Consider a production function with two inputs given by y fx1,x2. As samuelson 1979 conjectured, this explanation is that all the aggregate cobbdouglas function regression captures is the path of the value added accounting identity according to which value added equals the sum of the wage. Furthermore, this interpretation is applicable for both the cobbdouglas production function and the ces production function. Cobbdouglas cd production function is of the form q al. Y k l1 y l k l y k c 1 sy c l 1 s y lc 1 sy i sy i l s y li sy 1. An assessment of ces and cobbsdouglas production functions. A study on the cobbdouglas production function huscap. In other words, log y is a linear function of log x1 and log x2. Production function estimation in stata using inputs to. The effect of infrastructure and human resources on the higher. Algebraic production functions and their uses before cobbdouglas.
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. This section will discuss the discovery of the production formula and how partial derivatives are used in the cobbdouglas model. The value of a reflects the state of technology as well as the skill and education level of the workforce. If the production function is denoted by p p l,k, then the partial derivative. An application of non linear cobbdouglas production function. It and its allied concept, the utility function, form the twin pillars of. Derive the equation describing the dynamics of k kal, that is, the k equation. The three main methods of estimation discussed in the paper are.
Neoclassical onesector growth model consider the solow neoclassical onesector growth model with cobbdouglas production function y f k, l k 1 3 l 2 3. Model of cobb douglas production function in onion production in sakuru village, monta district, bima regency is the maximum production can be a chieved with a land area of. This concept can be applied at the level of individual. Dreze in this paper we consider the specification and estimation of the cobbdouglas production function model. Second, technological change is purely laboraugmenting in the long run. Problems with regional production functions and estimates of. The production function model was applied to the study of growth problems by robert solow american economist, massachusetts institute of technology, nobel prize 1990. The cobb douglas production function and the steady state. A macroeconomic production function is a mathematical expression that describes a sys tematic relationship between inputs and output in an economy, and the cobbdouglas and constant elasticity of substitution ces are two functions that have been used ex tensively. 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. On the origin of the cobbdouglas production function.
Deriving a per capita production function from a general production function. The cobbdouglas production of the nigerian economy 1974. The model was fitted to nigerias data of crude oil production, labor input, capital input, oil domestic consumption and oil exports. However, radhu 15, showed the positive correlation between indirect tax rates and prices of the commodities. Pdf the cobbdouglas production function is often used to analyse the. So for today we will think about a very useful one, the cobbdouglas production function. Estimates of a cobbdouglas production function, us manufacturing, state. The cobbdouglas production function 1 introduction in general, a productionfunctionis a speci. Solow began with a production function of the cobbdouglas type. It is not observed by the econometrician, and it can impact the choices of. During 19001947, charles cobb and paul douglas formulated and tested the cobbdouglas production function through various statistical evidence. 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.
What is the savings rate associated with our cobbdouglas production function where we. In choosing this very function, they referred to the theory due to j b clark. The introduction of the cobb douglas regression and its adoption by agricultural economists jeff e. Neoclassical onesector growth model consider the solow neoclassical onesector growth model with cobb douglas production function y f k, l k 1 3 l 2 3.
Algebraic production functions and their uses before cobbdouglas thomas m. A famous case is the well known cobb douglas production function introduced by charles w. L 1, where k measures aggregate capital and l aggregate labor in efficiency units. Golden rule steady state 1 if y k l1, then thegoldenrule savings ratein the economy is equal to, the share of capital income in total. 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. In the case of a cobbdouglas production function, neutral and laboraugmenting technological progress are equivalent. Since the publication of the article in 1928, the term cobb douglas production function has been used to refer to nearly any simple multiplicative production function. The cobbdouglas production function is a particular form of the production function. Thus, for a cobbdouglas production function y k l1, the share of labor and capital costs in total income are constant, and equal to 1 and, respectively. The original production function contained only two inputs, capital k and labor l. A cobbdouglas 4 5 represention of technology has the followingform.
Econ 464 example of cobb douglas production function the cobb douglas production function. Students run into it over and over again in problem sets and economists. The basic form of the cobbdouglas production function is as follows. 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. Jul 26, 2011 deriving a per capita production function from a general production function. The general form of cobbdouglas production function is.
Suppose the production function takes the cobbdouglas form, f k, al k al 1. The cobb douglas production function is the widely used function in econometrics. Pdf the utilization of the cobbdouglas production function for. This problem is based on the material in the chapter appendix. The cobbdouglas production function used and estimated by cobb and douglas 1928, and in each of the subsequent timeseries papers, takes the following form. While discussing the production theory of the firm, economists c. An application of nonlinear cobbdouglas production. It is widely used because it has many attractive characteristics, as we will see below. The cd production functions possess a number of important properties which have made it widely useful in the analysis of economic theories.
The cobb douglas production function marcoecomics youtube. In one way or another economists and students of economics are all familiar with this paper. Douglas used a special form of production function, which is known as the cobbdouglas production function. The cobbdouglas production function, given by charles w. Marginal cost derivations for a cobbdouglas production function. It is well known that the study of the shape and the properties of the production possibility frontier is a subject of great interest in economic analysis. Suppose that the economys production function is given by y kan1a and assume that a.
Pdf optimization of cobbdouglas production functions. An assessment of ces and cobbdouglas production functions 1 eric miller email. Rewrite production function y k l 2 3 in perworker terms. In economics and econometrics, the cobbdouglas production function is a particular functional form of the production function, widely used to represent the. Chapter 2 the solow growth model and a look ahead 2. 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. In particular, it is wellknown that for a neoclassical growth model to exhibit steady state growth, either the production function must be cobbdouglas or technical change must be laboraugmenting in the long run. 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. For the purposes of this note, the production technology is assumed to be cobb douglas yt. All being well, wed expect a to be gradually increasing over. In other words, an assumption kortum 1997 suggests we make if we want a model to exhibit steady state growth leads to important predictions about the shape of production functions and the direction of technical change. Profit maximization problem for cobbdouglas and ces. The introduction of the cobb douglas regression and its. The empirical results showed that crude oil output has a significant impact on nigerian economy because there was.
In the case of a cobb douglas production function, neutral and laboraugmenting technological progress are equivalent. The most significant areas of difficulty related to intermediate and longterm planning are identified, and the techniques for the macroeconomic analysis and forecasting of resource support for the armed forces based on the cobbdouglas production function are proposed. Since were doing macroeconomics we will be considering. Jul 26, 2016 during 19001947, charles cobb and paul douglas formulated and tested the cobbdouglas production function through various statistical evidence. Intermediate macroeconomics lecture 4 growth models. Production function estimation in stata using inputs to control for unobservables amil petrin. We let the production technology in our model be represented by a cobbdouglas production function y. The shape of production functions and the direction of. The cobb douglas production function 173 the resulting equation is referred to as linear in the parameters or linear in the coefficients. Some characterizations of the cobbdouglas and ces production. Nov 04, 2014 a theory of production charles cobb and paul douglas a copy of the paper can be found here. The cobb douglas production function, given by charles w.
What is the savings rate associated with our cobb douglas production function where we assume that capital. A theory of production charles cobb and paul douglas a copy of the paper can be found here. Explain the properties of cobbdouglas production function. Humphrey fundamental to economic analysis is the idea of a production function. L is the rate at which production changes with respect to the amount of labor. It has become known as the cobbdouglas production function. For the case of two inputs, the ces production function takes the following form. Cobbdouglas production function as an approach for better. Suppose the production function takes the cobb douglas form, f k, al k al 1.
For other neoclassical production functions this is not the case. 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. Production functions generally take the form of yfk,l so it would be interesting to find what the per capita form. This paper examined the relationship between crude oil production and the nigerian economic performance using the cobbdouglas production function. Algebraic production functions and their uses before cobb. In economics, the cobbdouglas functional form of pro. Oct 18, 2015 the cobb douglas production function marcoecomics.
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