Constant returns to scale
Also called: CRS · Topic: Production Function, Returns and Costs · NCERT: Class 12, Ch 3 "Production and Costs"
Meaning
Constant returns to scale (CRS) means that when all inputs rise in the same proportion, output rises in exactly that proportion. Formally, f(tx₁, tx₂) = t·f(x₁, x₂). If inputs double, output doubles. Since all inputs must change, CRS is a long-run idea. Under CRS, long-run average cost stays constant. CRS holds at the lowest point of the U-shaped long-run average cost curve.
Example
In NCERT's Table 3.1, (3L, 3K) gives 30 units and (6L, 6K) gives 60 units, exactly double. In a Cobb-Douglas function, CRS means the powers add to 1, as in Q = 5L^½K^½.
Don't confuse with
- Diminishing marginal product: this is a short-run idea, where only one input rises. It can exist together with CRS. In Q = 5L^½K^½, the marginal product of labour falls if capital is fixed, yet the function shows CRS.
Related concepts
- Returns to scale
- Increasing returns to scale
- Decreasing returns to scale
- Cobb-Douglas production function