Short on time? This page is the recap. For explanations, graphs and worked examples, use the full study guide.
Recap
- A production function shows the maximum output from each combination of inputs, with given technology. It is measured in units of output, not money.
- Short run: at least one input (usually capital) is fixed. Long run: all inputs can change.
- Total product (TP) is total output. Marginal product (MP) is the extra output from one more unit of the variable input. Average product (AP) is output per unit of the input.
- As workers are added to fixed capital, MP usually rises at first (specialisation), then falls (diminishing marginal returns) and may become negative (overcrowding).
- Diminishing marginal returns are caused by the fixed input being shared among more workers, not by worse workers.
Key relationships
| Relationship | How to use it |
|---|---|
| MP = ΔTP ÷ ΔL | A change between two rows; plot it halfway between them |
| AP = TP ÷ L | A ratio in one row |
| TP = sum of the MPs so far | Rebuild TP from an MP table |
| TP = AP × L | Rebuild TP from an AP table |
| MP > AP → AP rises; MP < AP → AP falls | So MP crosses AP at the maximum of AP |
| MP > 0 → TP rises; MP = 0 → TP at its maximum; MP < 0 → TP falls | Slope of TP = MP |
| Change | Effect |
|---|---|
| More of the fixed input (more capital or land) | TP shifts up; MP higher at most levels of labour |
| Better technology or training | TP, and usually MP and AP, shift up |
| Loss of capital (breakdown, damage) | TP shifts down |
Assumptions behind the model
- Identical units of the variable input (every worker equally skilled).
- Technology and the fixed inputs do not change while you read one table.
Mistakes to avoid
- Saying diminishing marginal returns means TP is falling.
- Saying diminishing returns begin where MP is negative. They begin where MP starts to fall.
- Dividing TP by L to get MP, or subtracting to get AP.
- Applying diminishing marginal returns to the long run, when no input is fixed.
- Saying AP falls as soon as MP falls. AP falls only once MP is below it.
- Blaming falling MP on less able workers.
Quick self-check
- TP is 60 with 3 workers and 72 with 4 workers. What is the MP of the fourth worker, and the AP of 4 workers? (72 − 60 = 12; 72 ÷ 4 = 18)
- AP of 4 workers is 18. The fifth worker’s MP is 13. Does AP rise or fall? (Falls, because 13 < 18: AP becomes 85 ÷ 5 = 17)
- Why can’t diminishing marginal returns happen in the long run? (There is no fixed input: every input can change.)
Next: practice questions.