Production Function

Cobb Douglass Production Function

$Y=A{K}^{\alpha }{N}^{\beta }$

$Y:$ real output produced in a given period of time

$K:$ quantity of capital used in period

$N:$ number of worker or labor hours

$A:$ total factor of productivity

• effectiveness of capital and labor
• affected by tech, gov reg, management

$MPK=\frac{\partial Y}{\partial k}$; this is also the slope of the production function assuming diminishing marginal product of capital: as we increase $K$ it increases $Y$ but at a decreasing rate

Returns to scale (ALL INPUTS by SAME FACTOR)

• determined by sum of exponents
  • $=$ 1 constant
  • $<$ 1 decreasing
  • $>$ 1 increasing

Output Elasticity JUST LOOK TO EXPONENT

Output Elasticity of Capital $\frac{\Delta Y/Y}{\Delta K/K}=\frac{\partial \log (Y)}{\partial \log (K)}=\alpha$

Output Elasticity of Labor

$$\frac{\Delta Y/Y}{\Delta N/N}=\frac{\partial \log (Y)}{\partial \log (N)}=\beta$$

Shifts of Production Function

Supply Shocks e.g. Weather change, gov reg, management