What this calculator does
Cobb-Douglas Production Function works out total output from labour and capital inputs given their productivity and output elasticities. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
The inputs explained
| Field | What to enter |
|---|---|
| Total factor productivity (A) | A number. Starts at 1.5. |
| Labour input (L) | A number. Starts at 100. |
| Capital input (K) | A number. Starts at 50. |
| Output elasticity of labour (β) | A number. Starts at 0.65. |
| Output elasticity of capital (α) | A number. Starts at 0.35. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with total factor productivity (a)
Every other input is held at the calculator’s starting values while total factor productivity (a) varies. Select any row to load that scenario into the calculator.
| Total factor productivity (A) | Total output (Y) | Returns to scale (α + β) | Scale type |
|---|---|---|---|
| 0.75 | 58.84 | 1.000 | Constant returns to scale |
| 1.13 | 88.66 | 1.000 | Constant returns to scale |
| 1.5 | 117.69 | 1.000 | Constant returns to scale |
| 2.25 | 176.53 | 1.000 | Constant returns to scale |
| 3 | 235.38 | 1.000 | Constant returns to scale |
| 4.5 | 353.06 | 1.000 | Constant returns to scale |