Definition
Long-run production function: the relationship showing how a firm's output changes when all factors of production are varied together, with no factor held fixed.
No fixed factors
- Because all factors change together, the firm can alter its whole scale of production.
- The law of diminishing returns does not apply in the long run, because no factor is held fixed.
- How long the long run lasts depends on the industry, so it is longer where plant takes years to build than where it can be rented quickly.
Key Idea
- The long run is a planning horizon in which the firm can change plant size and all other inputs.
- With no fixed factor, output responds to changes in the scale of all inputs, not to diminishing returns.
Returns to scale
Definition
Returns to scale: the relationship between a proportional change in all inputs and the resulting change in output in the long run.
- Increasing returns to scale occur when doubling all inputs more than doubles output, so long-run average cost falls.
- Constant returns to scale occur when doubling all inputs exactly doubles output, so long-run average cost stays constant.
- Decreasing returns to scale occur when doubling all inputs less than doubles output, so long-run average cost rises.
Example
- A firm doubles all inputs, a 100% rise, from 10 workers and 5 machines to 20 workers and 10 machines.
- Output rises from 100 to 250 units.
- Output is 2.5×, more than the 2× rise in inputs, so the firm has increasing returns to scale.
- Had output only doubled to 200 it would be constant returns, and a rise to just 160 would be decreasing returns.
Effect on long-run costs
- Increasing returns underlie falling long-run average cost and economies of scale.
- Constant returns give a flat section of the long-run average cost curve.
- Decreasing returns underlie rising long-run average cost and diseconomies of scale.
- The full shape of the long-run average cost curve is examined in the long-run cost function.
Example
- A brewery doubles its inputs and output rises more than in proportion, so average cost falls from £1.20 to £0.90 a bottle.
- A very large brewery can become hard to coordinate, so decreasing returns push average cost back up.
Exam technique
- Stress that all factors vary, so returns to scale is a long-run idea.
- Link each case directly to the slope of the long-run average cost curve.
Common Mistake
- Do not treat returns to scale as a short-run idea, because in the long run all factors vary at once.
- Do not confuse returns to scale with the short-run law of diminishing returns.
Self review
- Why does the long run have no fixed factors of production?
- What is returns to scale and what are its three types?
- How does each type of returns to scale affect long-run average cost?
- Why does the law of diminishing returns not apply in the long run?
