Constant Elasticity Of Substitution Demand Function

A rm uses two inputs aka factors of production to produce a single output. The constant elasticity of substitution ces function is popular in several areas of economics but it is rarely used in econometric analysis because it cannot be estimated by standard linear regression techniques.

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Specifically it arises in a particular type of aggregator function which combines two or more types of consumption goods or two or more types of production inputs into an aggregate quantity.

Constant elasticity of substitution demand function. Functions featuring constant elasticity of substitution ces are widely used in applied economics and finance. α distribution parameter or capital intensity factor coefficient concerned with relative factors in the total output. The elasticity of substitution is most often discussed in the context of production functions but is also very useful for describing util ity functions.

First i derive a number of conditions such as the optimal demand schedule when aggregation technology is ces. Total output yis given by a concave twice dierentiable function y f x 1 x. U x y αxρ 1 α yρ 1 ρ it is a tedious but straight forward application of lagrangian calculus to demonstrate that the associated demand functions are.

Constant elasticity of substitution ces preferences u x xρ 1 x ρ 2 xρ n 1 ρ where ρ 1 and ρ 6 0 marginal utilities u x i 1 ρ xρ 1 x ρ 2 xρ n 1 ρ 1ρxρ 1 i typeset by foiltex 1. Second i show how the ces function nests some particular functional forms as special cases. These have come to be known as ces production functions.

Constant elasticity of substitution in economics is a property of some production functions and utility functions. In this note i do two things. In many economic textbooks the constant elasticity of substitution ces utility function is defined as.

This aggregator function exhibits constant elasticity of substitution. The constant elasticity of substitution production function shows that any change in the technology or organizational aspects the production function changes with a shift in the efficiency parameter. It must be that the elasticity x 1 x 2 of the function gsatis es the equations 1 w 1 w 2 dln f 1 x x 2 f 2 x 1 x dln x 1 x 2 13 constant elasticity of substitution a very interesting special class of production functions is those for which the elasticity of substitution is a constant.

X p x p y m α p x σ m α σ1 1 y and y p x p y m 1 α p y σ m α σ1 x 1.

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