### Basic Reminders about Production Function

#### Production Function With Complementary Factors (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: 