Cobb-Douglas Production function:
Firms, according to the Neo Classical Theory, earn zero economic profit.
Y = +
Y = Real GDP.
= Total Capital income
= Total Labour income.
= Capital’s Share of National Income.
= Labour’s Share of National Income.
Cobb Douglas Production Function is a neo classical production function with a unique feature.
It gives us constant factor shares Such that:
= Capital’s Share of National Income =
= Labour’s Share of National Income = 1-
is a constant between 0 and 1.
We write the C-D production function as:
( ) .
A is a parameter reflecting the level of technology.
Why does the C-D function look like this?
1. It exhibits constant returns to scale. Without which we do not have competitive market.
2. It ensures that the MPL and MPK diminish with L and K, respectively. Otherwise we do
not have downward sloping factor demand curves.
3. It generates the Euler’s equation.
CRTS: ( ). in other words,
( ) = Y ( ) ( ) ( ) .
( ) = zY.
MPK and MPL
MPK = F ( ) ( ).
Therefore MPK is nothing but the contribution of an additional unit of capital towards
output/national income. Note that L stays the same.
Suppose, ( ) .
Find the Marginal Product of Capital:
Numerical (tedious/time consuming) way:
Assume the initial values for K, L and some constant values for A and
Suppose K = 10, L =10, A = 1, .
( ) ( ) ( ) = 10
( ) ( ) ( ) = 10.5
MPK = 10.5 – 10 = 0.5
What Happens to MPK when K changes? In other wo