Production and Costs
Returns to scale
Decide the returns to scale of a production function.
Returns to scale is a long-run idea: all inputs are changed in the same proportion. What happens to output?
- Constant returns to scale (CRS): output rises in the same proportion. Doubling all inputs doubles output: f(tL, tK) = t × f(L, K).
- Increasing returns to scale (IRS): output rises by more. Doubling inputs more than doubles output.
- Decreasing returns to scale (DRS): output rises by less.
For the Cobb-Douglas production function, q = L^α K^β, the answer depends on the sum of the powers:
| α + β | Returns to scale |
|---|---|
| = 1 | constant |
| > 1 | increasing |
| < 1 | decreasing |
Example: q = L^0.3 K^0.5. Here α + β = 0.8, which is less than 1, so there are decreasing returns: doubling both inputs raises output by less than double.
Do not confuse this with the law of variable proportions, which is a short-run idea, with only one input changing.
Double the inputs, see what happens to output.
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