Finance

Cobb-Douglas Production Function Calculator

Calculate total output (Y) given labor (L), capital (K), and technology factor (A).

Technology / efficiency multiplier
Typically 0.6-0.8 (capital elasticity = 1−α)
Formula:
Y = A × L^α × K^(1−α)
Where α = labor's share of output
(1−α) = capital's share of output
If α + (1−α) = 1 → constant returns to scale

Understanding the Cobb-Douglas Function

The Cobb-Douglas production function is one of the most widely used models in economics. It describes the relationship between inputs (labor and capital) and output, and was developed by Charles Cobb and Paul Douglas in 1928.

Key Properties

  • Constant Returns to Scale: When α + β = 1, doubling both inputs doubles output
  • Diminishing Marginal Returns: Each additional unit of labor or capital produces less additional output
  • Factor Shares: α represents labor's share of income, (1−α) represents capital's share

Returns to Scale

ConditionTypeMeaning
α + β = 1ConstantDouble inputs → double output
α + β > 1IncreasingDouble inputs → more than double output
α + β < 1DecreasingDouble inputs → less than double output