Cobb-Douglas Production Function Calculator
Compute total production output using the Cobb-Douglas function Q = A × Lᵅ × Kᵝ. Adjust total factor productivity, labor, capital and the output elasticities to see output, returns to scale (IRS/CRS/DRS) and marginal products.
workers
units
Total output from the Cobb-Douglas function Q = A × Lᵅ × Kᵝ
- 1
Labor contribution (Lᵅ)
100 ^ 0.7 = 25.1189 - 2
Capital contribution (Kᵝ)
50 ^ 0.3 = 3.2336 - 3
Production output (Q)
1 × 25.1189 × 3.2336 = 81.23Q = A × Lᵅ × Kᵝ — the Cobb-Douglas production function.
How does this calculator work?
Q = A × L^α × K^β. For A=1, L=100 workers, K=50 units, α=0.7, β=0.3: Q = 1 × 100^0.7 × 50^0.3 ≈ 68. Returns to scale equal α + β (>1 increasing, =1 constant, <1 decreasing). Marginal products MPL = α·Q/L and MPK = β·Q/K show extra output per additional input unit.
Formula
How this is calculated
The Cobb-Douglas production function, introduced by Charles Cobb and Paul Douglas in 1928, expresses total output Q as a function of two primary inputs — labor (L) and capital (K) — scaled by a productivity multiplier A. The exponents α and β represent the output elasticities of labor and capital: a 1% increase in L, holding K fixed, raises output by approximately α%.
The sum α + β determines returns to scale. If α + β = 1, doubling all inputs exactly doubles output (constant returns to scale — the most common empirical finding). If the sum exceeds 1, output more than doubles (increasing returns, consistent with economies of scale); if less than 1, returns are diminishing. Empirically, for many developed economies α ≈ 0.7 and β ≈ 0.3, implying roughly constant returns.
Marginal products (MPL = α·Q/L and MPK = β·Q/K) measure the extra output from one additional unit of each input. They decline as inputs increase, reflecting diminishing marginal returns. The function assumes inputs are substitutable but complementary — neither alone produces output — and abstracts away dynamics such as capacity constraints, externalities and skill heterogeneity within the labor force.
Frequently asked questions
It means the firm or sector exhibits increasing returns to scale: doubling all inputs more than doubles output. This is common in industries with strong network effects, large fixed costs (high-tech, pharmaceuticals) or significant learning economies.
A captures everything that affects output beyond raw labor and capital inputs — technology, management quality, institutions, and efficiency. Growth in A (called TFP growth or Solow residual) is a key source of long-run economic growth and is often measured as output growth not explained by growth in L and K.
Yes. L and K are measured in consistent units of your choice (worker-hours, machine-hours, currency value of capital stock). The function is scale-neutral as long as you use the same units throughout and compare ratios rather than absolute magnitudes across different measurement systems.
TG we-Calculate Editorial Team. (2026). Cobb-Douglas Production Function Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cobb-douglas-production-function-calculator
TG we-Calculate Editorial Team. "Cobb-Douglas Production Function Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/cobb-douglas-production-function-calculator.
TG we-Calculate Editorial Team, "Cobb-Douglas Production Function Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cobb-douglas-production-function-calculator
@misc{wecalculate_cobb_douglas_production_function_calculator, title = {Cobb-Douglas Production Function Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cobb-douglas-production-function-calculator}}, year = {2026}, note = {TG we-Calculate} }
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