Cobb Douglas Production Function
Calculate economic output using the Cobb-Douglas production function. This function models the relationship between capital, labor, and total output.
Formula
Q = A·K^α·L^(1-α)
- Q = total output
- A = productivity coefficient
- K = capital stock
- L = labor input
- α = capital elasticity (0-1)
Tech Startup Production
Inputs
- Capital (K): 100 $
- Labor (L): 50 units
- Total Factor Productivity (A): 1.5 coefficient
- Capital Elasticity (α): 0.3 0-1
A startup with 100 capital, 50 labor, 1.5 productivity, 0.3 alpha produces 42.46 output units.
Frequently asked questions
What does alpha represent?
Alpha is capital elasticity—how sensitive output is to capital changes. α=0.3 means 1% more capital increases output 0.3%.
When is this function used?
The Cobb-Douglas function models real economic relationships in industries. It's widely used in econometrics and growth modeling.