Definition: The Constant Elasticity of Substitution Production Function or CES implies, that any change in the input factors, results in the constant change in the output. In CES, the elasticity of substitution is constant and may not necessarily be equal to one or unity.
The constant elasticity of substitution production function can be shown algebraically as:
Q = A [ α K – Φ + ( 1 – α ) L – Φ ] -1/ Φ
Where, Q = output, K = Capital and L = Labor
A = efficiency parameter that shows the organizational aspects of production and the state of technology.
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.
α= distribution parameter or capital intensity factor coefficient concerned with relative factors in the total output.
Φ = substitution parameter, that determines the elasticity of substitution
The homogeneity of the production function can be determined by the value of the substitution parameter (Φ), if it is equal to one, then it is said to be linearly homogeneous i.e. the proportionate change in the input factors results in the increase in the output in the same proportion.
In constant elasticity of substitution production function, all the input factors are taken into the consideration such as raw material, technology, labor, capital, etc. The marginal product of one factor increases with the increase in the value of the other factors of production. Also, the marginal product of labor and capital will be positive in case of constant returns to scale.