When does a production function satisfy constant returns to scale?
A production function satisfies constant returns to scale (CRS) when a proportional increase in all inputs results in an increase in output by the same proportion.
Mathematically, consider a production function q = f(x₁, x₂). If both factors are increased by t times (where t > 1), then CRS holds when f(tx₁, tx₂) = t·f(x₁, x₂). This means the new output level is exactly t times the previous output level.
For example, if all inputs get doubled and the output also gets doubled, the production function exhibits CRS. This situation occurs in the long run when both factors are scaled up by the same proportion.
Explanation
The textbook clearly defines CRS in Section 3.6 'Returns to Scale'. The key points are: (1) CRS occurs when proportional input increase leads to same proportional output increase, (2) The mathematical condition is f(tx₁, tx₂) = t·f(x₁, x₂), and (3) The example of doubling inputs leading to doubled output illustrates CRS. This is a 3-mark question requiring definition, mathematical expression, and an example.