(isoquant ).

Production Function With Substituable Factors

, continuous and twice derivable, , ,

Marginal Rate of Substitution

The differential of the production function :

along an isoquant and the Marginal Rate of Substitution (MRS) of Capital to Labor can be defined by

Elasticity of substitution

Elasticity of the substitution of Capital to Labor:

Hypothesis of the remuneration of factors to their marginal productivity,

nominal cost of capital,

nominal rate of wage,

level of prices

Returns to Scale

. Constant if

. Decreasing if

. Increasing if

Constant Returns to Scale

Euler theorem:

that means

Product Exhaustion Theorem

Zero-Profit

Reasoning per capita:

per capita product (or mean productivity of labor)

per capita capital

Frontier of the prices of factors

Cobb-Douglas Function

with

If , constant returns to scale. Then

and frontier of the prices of factors:

C.E.S Function

Function of Constant Elasticity of Substitution (CES)

with , ,

Constant returns to scale if , increasing if , decreasing if . is the scale elasticity. The per capita formulation of the CES function with constant returns to scale: