coefficient technique de production

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TITLE: ON THE COEFFICIENTS OF PRODUCTION

coefficients of production: \"In order to obtain one unit of a product certain quantities of other products and the service of capital are used These quantities are what is called the coefficients of production \" (Pareto Manuel p 304) It must however be mentioned that in some other cases

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A Review of Input-Output Analysis

coefficients) are assumed constant so that for every man-hour of labor output a fixed amount of each consumer good is required as input; that is consumers are treated as a technologically determined production process and not as choice-making organisms 2 In the open input-output models the assumption of constant

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The Cobb-Douglas Production Function

The input cost function is C = v1x1 + v2x2 The dual cost function for a Cobb Douglas type of production function is found using the following procedure First the equation for the expansion path is found by partially differentiating the production function with respect to x1 and x2 to find the marginal products

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The Cobb–Douglas Production Function

In general a production function is a specification of how the quantity of output behaves as a func-tion of the inputs used in production This concept can be applied at the level of individual firms industries or entire economies Since we’re doing macroeconomics we will be considering an ag-gregate production function applying at the economy-

Who invented the production function?
Various specific mathematical forms have been put forward for the production function, but the most commonly used is that developed by Charles Cobb and Paul Douglas in the second quarter of the 20th century. Here’s their specification:
Can technical coefficients still be viewed as if it consisted of two components?
technical coefficients may still be viewed as' if it consisted of the two components described. The reason for so viewing it is to show how unlikely it is that all elements of A are off in the same direction. .157
What is an example of a production function?
For example, suppose that the production function is †10.42 y = x1x2 The individual partial elasticities of production for each input is 1, and the function coefficient is 2. Despite its strange appearance, this is a production function of the Cobb Douglas type. Suppose that the price of both x1 and x2 is $1 per unit.
Which Isoquants are convex to the origin of a production function?
The isoquants generated by a Cobb!Douglas type of production function are convex to the origin if the partial elasticities of production are positive, and as a result, points of tangency that meet second order conditions are easy to find. For example, suppose that the production function is †10.42 y = x1x2

1 Introduction

In general, a production function is a specification of how the quantity of output behaves as a func-tion of the inputs used in production. This concept can be applied at the level of individual firms, industries, or entire economies. Since we’re doing macroeconomics we will be considering an ag-gregate production function, applying at the economy-

D AK N1 0 1 <

Here Y represents aggregate output, K the capital input, and N the labor input (capital and labor being the two “factors of production” in this function). The A term represents Total Factor Produc-tivity (TFP for short); you can think of this as a “quality” factor—as opposed to K and N which are just quantitative. The value of A reflects the state

3 Cross partials

A further point relevant for macroeconomic analysis: what (if anything) happens to the marginal product of labor when the capital input is increased? And conversely, what happens to the MPK when N increases? In mathematical terms, we’re talking about the so-called “cross-partial” deriva-tives, dMPN dK and dMPK d N. = = dMPN D 1 dK . users.wfu.edu

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