Production and cost functions
Production and cost functions: build the core model, apply it to evidence and qualify conclusions where outcomes depend on context.
9708 section 7.5; A Level. Checked against Cambridge's 2026–2028 Version 2 (latest version published December 2025) and 2029 Version 1 (published September 2026). Cambridge states that neither version has significant changes affecting teaching. Always follow the syllabus for the candidate's examination year.
Before you begin
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What distinguishes the long run from the short run in production theory?
What you will learn
- Calculate total, average and marginal product
- Explain diminishing returns in the short run
- Calculate fixed, variable, total, average and marginal costs
- Explain short-run cost curves
- Distinguish short-run from long-run production
- Explain returns to scale and long-run average cost
- Analyse scale economies and diseconomies
Core model and terms
In the short run at least one factor is fixed. Total product is output; average product is output per variable input; marginal product is the extra output from an additional input. Diminishing marginal returns occur when extra units of a variable factor add progressively less output alongside fixed factors. Fixed cost does not vary with output in the short run; variable cost does. TC = FC + VC, average cost is total cost per unit and marginal cost is the change in total cost from extra output.
Apply and evaluate
In the long run all factors can vary. Returns to scale compare the percentage change in output with a proportional change in all inputs. The long-run average-cost curve can fall with economies of scale, flatten near minimum efficient scale and rise with diseconomies. Internal economies arise within a firm; external economies arise from industry or location. Growth can reduce costs, but coordination and congestion can reverse the effect.
Pause and explain
Which statement best applies production and cost functions?
Worked example
A firm uses 4 workers to produce 48 units; 5 workers produce 55. Find average product at 5 workers and marginal product of the fifth worker.
Show the worked solution
- Average product = 55 ÷ 5 = 11 units per worker
- Marginal product = 55 − 48 = 7 units
- The fifth worker adds 7 units
Answer Average product = 55 ÷ 5 = 11 units per worker → Marginal product = 55 − 48 = 7 units → The fifth worker adds 7 units
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A firm uses 4 workers to produce 48 units; 5 workers produce 55. Find average product at 5 workers and marginal product of the fifth worker.
Give me a hint
Use output divided by labour for average product and the output difference for marginal product.
Compare my reasoning
- Average product = 55 ÷ 5 = 11 units per worker
- Marginal product = 55 − 48 = 7 units
- The fifth worker adds 7 units
Average product = 55 ÷ 5 = 11 units per worker Marginal product = 55 − 48 = 7 units The fifth worker adds 7 units
Look for these in your work
- Average product = 55 ÷ 5 = 11 units per worker
- Marginal product = 55 − 48 = 7 units
- The fifth worker adds 7 units
Fixed cost is $200 and variable cost is $360 at 30 units. Calculate total cost, average total cost and average variable cost.
Give me a hint
Add costs, then divide each relevant total by output.
Compare my reasoning
- TC = 200 + 360 = $560
- ATC = 560 ÷ 30 = $18.67
- AVC = 360 ÷ 30 = $12
TC = 200 + 360 = $560 ATC = 560 ÷ 30 = $18.67 AVC = 360 ÷ 30 = $12
Look for these in your work
- TC = 200 + 360 = $560
- ATC = 560 ÷ 30 = $18.67
- AVC = 360 ÷ 30 = $12
A marginal product falls as a bakery adds workers to one fixed-size kitchen. Explain the likely short-run mechanism.
Give me a hint
Relate the variable input to the fixed factor.
Compare my reasoning
- More workers share the same kitchen and equipment
- Coordination or crowding can limit each extra worker’s contribution
- Marginal product can fall
More workers share the same kitchen and equipment Coordination or crowding can limit each extra worker’s contribution Marginal product can fall
Look for these in your work
- More workers share the same kitchen and equipment
- Coordination or crowding can limit each extra worker’s contribution
- Marginal product can fall
An industry cluster lowers each firm’s transport and training costs. Is this an internal or external economy of scale? Explain.
Give me a hint
Ask whether the saving comes from the individual firm’s own expansion or the surrounding industry.
Compare my reasoning
- The saving comes from the industry cluster
- It can benefit multiple firms in the area
- This is an external economy of scale
The saving comes from the industry cluster It can benefit multiple firms in the area This is an external economy of scale
Look for these in your work
- The saving comes from the industry cluster
- It can benefit multiple firms in the area
- This is an external economy of scale
Common mistakes
- Applying diminishing returns when all factors vary or confusing internal economies with savings available to an entire industry.
What can you explain now?
What distinguishes the long run from the short run in production theory?
Compare with the explanation
In the long run all factors of production can vary
The short run has at least one fixed factor; the long run permits adjustment of all factors.
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Make it stick
Before moving on, explain the central idea in production and cost functions and state one condition that could change its effect.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.