Microeconomics guide, Unit 3, step 13 of 28Previous step Next step

Step 13: Production and Costs

By the EconTutorials team. 10-minute read with 6 practice questions.

SyllabusAP Micro 3.1–3.3 · Cambridge 7.5

In 30 seconds

In the short run at least one input (like the size of the factory) is fixed; in the long run every input can change.
The Law of Diminishing Marginal Returns: adding more workers to a fixed input eventually adds less and less output, which makes marginal cost rise.
Key cost formulas: $ TC = FC + VC $, $ ATC = TC/Q $ and $ MC = \Delta TC/\Delta Q $. When MC is below ATC, ATC falls; when MC is above ATC, ATC rises.
In the long run, economies of scale lower average cost as a firm grows and diseconomies raise it; minimum efficient scale helps decide how many firms an industry can support.

Video lesson coming soonA short animated lesson for this step will appear here.

Short run and long run

A coffee shop can hire an extra barista tomorrow. It cannot build a bigger shop overnight. In the short run it is stuck with its current space and machines. Given enough time, it can move to a larger site, buy better equipment or open more branches. In economics, that difference is what separates the short run from the long run. It is not about a number of months; it is about which inputs can change.

Key termShort run: a period in which at least one factor of production is fixed, usually capital such as the building or equipment.

Key termLong run: a period in which all factors of production are variable, so the firm can change its size, technology and workforce.

Fixed inputs cannot be changed in the short run (a bakery’s oven). Variable inputs can (the number of bakers hired this week). This split matters because costs behave very differently in the two periods.

The Law of Diminishing Marginal Returns

In the short run, the only way to make more is to add more of the variable input, usually labour, to the fixed input. The book’s example is a pizza restaurant with one oven:

Cooks	Pizzas per hour	Marginal product (MP)
1	20	20
2	45	25
3	65	20
4	80	15
5	90	10

The second cook helps a lot. After that, each extra cook adds fewer pizzas because they all share one oven. By the fifth cook, people are mostly waiting. That is diminishing marginal returns.

Key termMarginal product (MP): the extra output produced by one more unit of a variable input, $ MP = \Delta TP / \Delta L $, where TP is total product and L is labour.

Key termLaw of Diminishing Marginal Returns: in the short run, as more of a variable input is added to a fixed input, the marginal product of the variable input will eventually fall.

This law is the reason marginal cost eventually rises. Each extra cook costs the same wage but adds fewer pizzas, so the cost of each extra pizza goes up. The link is inverse: when MP is rising, MC is falling; when MP is at its maximum, MC is at its minimum; when MP falls, MC rises.

Short-run costs

Short-run costs come in two types.

Fixed costs (FC) do not change with output and must be paid even if output is zero: rent, insurance, loan repayments, salaries of permanent staff.
Variable costs (VC) rise and fall with output: raw materials, hourly wages, electricity used in production, packaging.

Add them together and you get total cost, then divide to get the averages:

\[ TC = FC + VC \qquad ATC = \frac{TC}{Q} = AFC + AVC \qquad MC = \frac{\Delta TC}{\Delta Q} \]

Average fixed cost, $ AFC = FC/Q $, falls all the time as the same fixed cost is spread over more units.
Average variable cost, $ AVC = VC/Q $, falls and then rises: a U shape caused by diminishing returns.
Average total cost, ATC, is also U-shaped and always sits above AVC. The gap between them is AFC.
Marginal cost, MC, is the cost of one more unit. It falls then rises, and it cuts both AVC and ATC at their lowest points.

Worked example

A small T-shirt printer has these total costs: Q = 0: $100; Q = 1: $150; Q = 2: $190; Q = 3: $240; Q = 4: $300; Q = 5: $380. Find FC, then MC and ATC at each output, and the output where ATC is lowest.

Step 1$ FC = TC \text{ at } Q = 0 = \$100 $

Step 2$ MC: 150-100 = 50,\; 190-150 = 40,\; 240-190 = 50,\; 300-240 = 60,\; 380-300 = 80 $

Step 3$ ATC: \tfrac{150}{1} = 150,\; \tfrac{190}{2} = 95,\; \tfrac{240}{3} = 80,\; \tfrac{300}{4} = 75,\; \tfrac{380}{5} = 76 $

Step 4Lowest ATC is $75 at Q = 4. MC of the 4th unit ($60) is below ATC; MC of the 5th unit ($80) is above it.

While each extra T-shirt costs less than the current average, the average falls. Once the 5th shirt costs $80, more than the $75 average, it pulls the average up to $76. MC crosses ATC at its minimum.

Think of your exam average. If your next test score is below your average, your average falls. If it is above, your average rises. MC and ATC work exactly the same way.

Common mistakeThinking that ATC is rising because MC is rising. MC can be rising while ATC is still falling, as long as MC is below ATC. What matters is whether MC is above or below the average, not which way MC is moving. Also remember that a change in fixed cost does not change MC at all, because MC comes only from the extra cost of one more unit.

Long-run costs and economies of scale

In the long run, the firm can choose its scale: a small workshop or a giant factory. The long-run average cost (LRAC) curve shows the lowest possible average cost at each output when all inputs can vary. It is usually U-shaped, with three zones:

Economies of scale: LRAC falls as the firm grows.
Constant returns to scale: LRAC stays flat.
Diseconomies of scale: LRAC rises because the firm has become too big to run well.

Key termEconomies of scale: the fall in long-run average cost as a firm increases its output, from causes such as specialisation, bulk buying, bigger machines, cheaper finance and spreading marketing over more units.

Key termDiseconomies of scale: the rise in long-run average cost when a firm grows too large, from communication breakdowns, management complexity, worker alienation and co-ordination failures.

Key termMinimum efficient scale (MES): the smallest output at which LRAC reaches its minimum.

MES explains the shape of whole industries. Where MES is huge compared with the market (aircraft, semiconductors), only a few giant firms can survive. Where MES is small (restaurants, hairdressers), many small firms can all produce at low cost. The book’s case study is Tesla: as it built very large factories, its estimated cost per car fell sharply, but managing operations across several continents later brought signs of diseconomies.

Do not mix up the two “limits” in this step. Diminishing returns is a short-run idea caused by a fixed input. Diseconomies of scale is a long-run idea caused by the difficulty of managing a very large organisation.

Exam tipTwo links are tested almost every year: (1) MP and MC move in opposite directions, so diminishing returns makes MC slope upward; (2) MC cuts AVC and ATC at their minimum points. On any cost diagram, draw MC passing through the lowest point of both U-shaped average curves, and draw the gap between ATC and AVC getting narrower as output rises.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. A firm has FC = $500 and VC = $1,500 when it produces 100 units. Calculate ATC. Show worked answer

$ TC = 500 + 1{,}500 = \$2{,}000 $
$ ATC = 2{,}000 / 100 = \$20 $ per unit

EasyQ2. Which of these is a fixed cost for a restaurant in the short run: food ingredients, monthly rent, or takeaway packaging? Show worked answer

Monthly rent. It has to be paid however many meals are served. Ingredients and packaging rise and fall with output, so they are variable costs.

MediumQ3. MC is currently $12 and ATC is $15. Is ATC rising or falling? Explain. Show worked answer

ATC is falling. The next unit costs $12, which is less than the current average of $15, so it pulls the average down. ATC will keep falling until MC rises to meet it at the minimum of ATC.

MediumQ4. A firm has FC = $100. At Q = 20, VC = $400. Producing the 21st unit raises TC to $518. Find AFC, AVC and ATC at Q = 20, the MC of the 21st unit, and say whether ATC rises or falls. Show worked answer

$ TC = 100 + 400 = \$500 $
$ AFC = 100/20 = \$5 $; $ AVC = 400/20 = \$20 $; $ ATC = 500/20 = \$25 $
$ MC = (518 – 500)/1 = \$18 $
MC ($18) is below ATC ($25), so ATC falls. Check: $ 518/21 \approx \$24.67 $, which is lower than $25.

MediumQ5. A firm has FC = $3,000 a month and a constant variable cost of $4 per unit. (a) Write TC and ATC as functions of Q. (b) Find ATC at 500 and 1,500 units. (c) If FC rises to $4,500, what happens to MC? Show worked answer

(a) $ TC = 3{,}000 + 4Q $; $ ATC = 3{,}000/Q + 4 $
(b) At 500: $ 3{,}000/500 + 4 = 6 + 4 = \$10 $. At 1,500: $ 3{,}000/1{,}500 + 4 = 2 + 4 = \$6 $. ATC falls because fixed cost is spread over more units.
(c) MC stays at $4. A change in fixed cost does not affect the cost of one more unit. (ATC rises, though: at 1,500 units it becomes $ 4{,}500/1{,}500 + 4 = \$7 $.)

ExamQ6. A car wash has one washing bay (fixed). Output per day with 1 to 5 workers is 25, 60, 85, 100 and 105 cars. (a) Calculate the marginal product of each worker. (b) Identify where diminishing marginal returns begins. (c) The bay costs $150 a day and each worker is paid $90 a day. Calculate ATC per car with 4 workers. (d) Explain why diminishing returns makes MC rise. [7 marks] Show worked answer

(a) MP: 1st = 25; 2nd = 60 − 25 = 35; 3rd = 85 − 60 = 25; 4th = 100 − 85 = 15; 5th = 105 − 100 = 5. [2 marks]
(b) Diminishing returns begins with the 3rd worker, when MP falls from 35 to 25. [1 mark]
(c) $ TC = 150 + 4 \times 90 = \$510 $. Output = 100 cars. $ ATC = 510/100 = \$5.10 $ per car. [2 marks]
(d) Each worker costs the same $90 but adds fewer cars as MP falls, so the cost of each extra car rises. For example, the 2nd worker’s cars cost about $ 90/35 \approx \$2.57 $ each, while the 4th worker’s cost $ 90/15 = \$6 $ each. Falling MP means rising MC. [2 marks]

Check yourself

1. As output increases, average fixed cost:

The same fixed cost is spread over more and more units.

2. If MC is below ATC, then ATC is:

A unit that costs less than the average pulls the average down.

3. Economies of scale refer to:

Economies of scale are a long-run idea about the size of the whole operation.

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The short version

Short run: at least one input is fixed. Long run: all inputs can change.
Diminishing marginal returns (short run) makes MP fall and MC rise.
$ TC = FC + VC $; $ ATC = TC/Q $; $ MC = \Delta TC / \Delta Q $. AFC always falls; AVC, ATC and MC are U-shaped.
MC cuts AVC and ATC at their minimums: below the average pulls it down, above pulls it up.
LRAC falls with economies of scale and rises with diseconomies; a large MES means few firms, a small MES means many.

This guide covers the core of the chapter. For the full Chapter 10, with cost-curve diagrams, the Tesla Gigafactory case study and 15 exam-style questions with a complete answer key, see the book Economics Made Simple.

Step 13: Production and Costs

Short run and long run

The Law of Diminishing Marginal Returns

Short-run costs

Long-run costs and economies of scale

Practise: 6 questions

Check yourself

The short version

Further reading on EconTutorials

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