(isoquant
).
,
continuous and twice derivable,
,
,
and the Inada conditions:
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 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
. 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
with
If
,
constant returns to scale. Then
and frontier of the prices of factors:
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: