Long-run costs and economies of scale
Learning goals
After this page, you can:
- Read economies of scale, constant returns and diseconomies of scale off a long-run average cost curve or a table of cost per unit at different sizes.
- Explain the learning curve — cost per unit falls with cumulative output — and tell it apart from economies of scale.
- Recognize economies of scope in one line, and write a two-year cost-per-unit sentence as evidence for or against scale economies.
The idea
The pie shop opens a second shop. Then it builds a central kitchen that bakes for ten shops and buys fruit by the truckload. Cost per pie falls. At forty shops, the delivery vans cross the whole region, and there are three layers of managers. Cost per pie creeps back up.
This page is about that path: what happens to cost per unit when a company chooses how big to be.
The long run: choose your plant size. On the last page, the oven and the kitchen were fixed. That is the short run. In the long run, every input can change, including the size of the kitchen and the number of shops. So the long-run question is: if I could pick any size, what is the lowest cost per unit I could reach at each level of output?
Each possible size has its own short-run average cost curve (the U-shape from the last page). The long-run average cost curve (LRAC) traces the lowest of those curves at every output. Think of it as a menu: for each output, it shows the cost per unit you get if you pick the best size for that output. Economists call it the “lower envelope” of the short-run curves.
Three zones along the LRAC.
- Economies of scale: LRAC falls as the company grows. Each unit gets cheaper.
- Constant returns to scale: LRAC is flat. Growing neither helps nor hurts cost per unit.
- Diseconomies of scale: LRAC rises. The company has grown past its best size.
Why bigger can be cheaper. Three common reasons:
- Big, indivisible inputs. A large oven, a delivery truck, an accounting system or a brand ad campaign costs about the same whether it serves 2 shops or 20. Spread over more pies, each pie carries less of it.
- Specialization. A big operation can have one person who only decorates, one who only buys, one who only schedules. Each gets very good at one job.
- Bulk buying. Fruit by the truckload costs less per pound than fruit by the box.
Why bigger can become dearer. Past some size, new problems appear. Delivery routes get long. Managers need managers to coordinate them. Information moves slowly up and down the chain, and mistakes take longer to fix. These coordination costs push cost per unit back up.
Our pie company’s table of cost per pie by number of shops: 1 shop $16.84, 2 shops $15.60, 5 shops $14.30, 10 shops $13.50, 20 shops $13.40, 40 shops $14.10, 80 shops $15.20. Cost falls steeply up to 10 shops (economies of scale), is nearly flat from 10 to 20 (roughly constant), and rises after 20 (diseconomies of scale).
The learning curve: practice, not size. Here is a different way costs fall. A decorator’s first wedding cake takes 10 hours. By the 8th cake, she takes about 7.3 hours, with the same kitchen and the same tools. She has simply learned. A learning curve says that cost (or time) per unit falls by a steady percent each time cumulative output — the total ever made — doubles. With a 90% learning curve, each doubling cuts time per unit to 90% of what it was: 10 hours, then 9, then 8.1, then 7.29.
Do not confuse the two ideas:
- Economies of scale depend on size per period: how many pies a month you make right now.
- The learning curve depends on cumulative experience: how many pies you have ever made.
A small shop that has been open for twenty years can be far down its learning curve. A brand-new giant factory starts at the top of its learning curve, even though it has big scale economies.
Economies of scope: two products, one set of inputs. Economies of scope exist when producing two products together costs less than producing them separately. The same counter and staff that sell pies in the afternoon can sell coffee and breakfast in the morning. The rent is paid once. Scope is about variety, not volume.
Testing it with your company: the two-year sentence. You cannot see a company’s LRAC curve. But you can check one piece of evidence. Take cost of revenue (or another cost) and divide by units sold (stores, subscribers, seat-miles…) for two years. Then compare:
% change in cost per unit = (c₂ − c₁) ÷ c₁, read next to the % change in units.
If volume rose and cost per unit fell, that is consistent with economies of scale. It is not proof: input prices, product mix or learning could explain it too. If volume fell and cost per unit fell, scale cannot be the reason. Look for another explanation.
LRAC = lowest cost per unit at each output when every input, plant size included, can change (the lower envelope of the short-run ATC curves)
Falling LRAC = economies of scale · flat = constant returns · rising = diseconomies of scale
Learning curve: time per unit × (learning rate) each time cumulative output doubles · Two-year check: % change in cost per unit = (c₂ − c₁) ÷ c₁, next to the % change in units
Try it
Part 1: the scale curve. The thick orange line is the LRAC. The dashed U-curves are three plant sizes (1, 10 and 40 shops). Each touches the LRAC at its own best size.
- Move the slider from 1 to 80 shops. Where does the zone change from economies of scale to roughly constant? Where do diseconomies begin?
- Read the cost per pie at 1, 10 and 40 shops. By what percent does it fall from 1 to 10 shops?
Part 2: the learning curve.
- Set the learning rate to 80%. How many hours does the 8th cake take now? What does a 100% rate mean?
Part 3: your company’s two-year sentence. Type cost of revenue (or cost per unit) and units for the last two years from your company’s 10-K. Then press Copy sentence.
Worked example
Problem. A growing pie company’s cost per pie is $16.84 with one shop, $13.50 with a central kitchen serving 10 shops, and $14.10 at 40 shops. (1) Describe each move. (2) A decorator’s first wedding cake takes 10 hours. With a 90% learning curve, how long do the 2nd, 4th and 8th cakes take? (3) Year 1 cost of revenue is $3.00 million on 250,000 pies; year 2 is $3.42 million on 300,000 pies. Write the two-year sentence.
Step 1. From 1 to 10 shops. (13.50 − 16.84) ÷ 16.84 = −19.8%. Cost per pie falls by about a fifth: bulk fruit, one big oven run all day, one bookkeeper for all the shops. Economies of scale.
Step 2. From 10 to 40 shops. (14.10 − 13.50) ÷ 13.50 = +4.4%. Cost per pie rises: longer delivery routes and more managers. Diseconomies of scale.
Step 3. Learning. Each doubling multiplies the time by 0.9. Cake 2: 10 × 0.9 = 9 hours. Cake 4: 9 × 0.9 = 8.1 hours. Cake 8: 8.1 × 0.9 = 7.29 hours. Same kitchen, same tools — just practice. This is a learning curve, not a scale economy.
Step 4. Scope. The same counter and staff that sell pies in the afternoon sell coffee and breakfast in the morning. One rent, two product lines: economies of scope.
Step 5. The two-year sentence. Year 1: 3,000,000 ÷ 250,000 = $12.00 a pie. Year 2: 3,420,000 ÷ 300,000 = $11.40 a pie. Change: (11.40 − 12.00) ÷ 12.00 = −5.0%. Volume: (300,000 − 250,000) ÷ 250,000 = +20%. The sentence: “Cost per pie fell 5.0% (from $12.00 to $11.40) while volume rose 20%.” That is consistent with economies of scale — one piece of evidence, not proof.
Check yourself
A bakery chain’s cost per loaf is $2.10 with 1 store, $1.80 with 10 stores and $1.85 with 40 stores. Between 10 and 40 stores, the chain shows:
Falling cost per unit with size = economies of scale; rising = diseconomies.
Which of these is a source of economies of scale for a bakery chain?
Scale economies come from spreading big inputs, specialization and bulk buying over more output.
A decorator’s time per wedding cake falls from 10 hours on the first cakes to 7 hours after 200 cakes, with the same tools and the same kitchen. This is:
Learning curve: cost falls with cumulative experience; economies of scale: cost falls with size.
A bakery that already runs its counter and staff all afternoon adds a morning coffee and breakfast line, and running both lines together costs less than running two separate shops. This is an example of:
Economies of scope: making two products together costs less than making them apart.
A company’s cost per unit was $12.40 on 20,000 units in year 1 and $11.16 on 26,000 units in year 2. By what percent did cost per unit fall?
% change in cost per unit = (year 2 − year 1) ÷ year 1; read it next to the % change in volume.
Video
Video coming soon.