Fundamentals of Business Economics and Management · Cost of Production

Long-Run Cost Curves and Economies of Scale Explained

Updated 10 October 2026 · Fact-checked

The long-run average cost (LAC) curve shows the lowest possible average cost of producing each output when all inputs can be changed. It is an envelope of short-run average cost curves. It is U-shaped because economies of scale first lower cost, and diseconomies of scale later raise it.

Understand Long-Run Cost Curves and Economies of Scale

In the short run, at least one input, such as plant size, is fixed. In the long run, all inputs can be changed. A firm can build a bigger factory, buy more machines or shift to a new site. So in the long run there are no fixed costs.

Each plant size has its own short-run average cost (SAC) curve. A small plant has a SAC curve far to the left. A larger plant has a SAC curve further to the right. For any output, the firm chooses the plant size that gives the lowest average cost. The long-run average cost (LAC) curve joins these lowest cost points. It touches each SAC curve at one point and never goes above any of them, so it is called the envelope curve. It is also called the planning curve, because the firm uses it to plan the plant size for a target output.

The LAC curve is usually U-shaped, or more flatly dish-shaped. It falls at first because of economies of scale: as output grows, average cost per unit falls. It rises later because of diseconomies of scale: very large size makes the firm hard to manage, and average cost per unit rises.

Note one detail. The LAC touches each SAC at its lowest point only at the output where LAC is itself at its minimum. On the falling part of LAC, it touches each SAC to the left of that SAC's minimum point. On the rising part, it touches to the right of the SAC minimum. Only at the minimum of LAC do the two minimums coincide. This is a common exam point.

Economies of scale are of two kinds. Internal economies arise inside the firm because of its own growth. External economies arise outside the firm, because the whole industry grows. Diseconomies also come in the same two kinds.

Key formulas to remember

Long-run average cost: LAC = Long-run total cost ÷ Output; All inputs are variable, so there is no fixed cost in the long run.
Envelope rule: LAC ≤ SAC at every output level; LAC touches each SAC curve at one point and lies on or below all of them.
Tangency position: Falling LAC: tangent to the left of SAC minimum. Rising LAC: tangent to the right. At LAC minimum: SAC minimum.; Holds for U-shaped LAC with SAC curves of different plant sizes.
Scale and cost link: Economies of scale: LAC falls as output rises. Diseconomies: LAC rises as output rises.; Constant LAC means constant returns to scale in the cost sense.
Minimum efficient scale: Output at which LAC is lowest; This is the optimum size of the firm.

How to solve Long-Run Cost Curves and Economies of Scale questions

Use this method for any question on LAC or economies of scale.

1Read the key phrase: is it short run or long run? Long run means all inputs are variable and there is no fixed cost.
2If the question is about the LAC curve, recall the envelope idea: it touches every SAC curve and lies on or below all of them.
3If it asks why LAC is U-shaped, give the two causes: economies of scale on the falling part and diseconomies on the rising part.
4If it asks to classify an advantage, ask: does it arise inside the firm or from industry growth? Inside is internal; outside is external.
5Match the item to its type: technical, managerial, marketing, financial, risk-bearing for internal; localisation, information, shared services for external.
6For numerical cost questions, divide total cost by output, then compare the averages to see whether cost is falling or rising.
7Eliminate options with absolute words such as 'always' or 'only', and options that mention fixed cost in the long run.

Quickest way: Three-second classification check

When to use it: Use for MCQs that ask you to name a type of economy or diseconomy, or to identify the shape or role of the LAC curve.

Spot the word 'long run' and drop any option that mentions fixed cost.
For an economy or diseconomy, ask 'Is it the firm's own doing or the industry's?' to pick internal or external.
Remember: falling LAC means economies, rising LAC means diseconomies, and the minimum point is the optimum size.
For envelope questions, pick the option with 'tangent' and 'lower than or equal to SAC'.

Common mistakes in Long-Run Cost Curves and Economies of Scale

Saying the LAC is the sum of SAC curves or joins their minimum points.
Students think 'envelope' means connecting the lowest points of each curve.
Fix: LAC is tangent to each SAC at the output where that plant is the cheapest choice. It joins minimum points only at its own minimum.
Explaining the U-shape of LAC with the law of variable proportions.
The short-run SAC is U-shaped because of variable proportions, and students mix up the two.
Fix: Short-run U-shape comes from variable proportions. Long-run U-shape comes from economies and diseconomies of scale.
Mixing up internal and external economies.
Both lower cost, and the words sound alike.
Fix: Internal depends on the size of the firm. External depends on the size of the industry. A cheaper supplier base near an industrial cluster is external.
Assuming economies of scale continue forever.
Students remember that bigger is cheaper and ignore the later stage.
Fix: After a point, management problems and coordination delays cause diseconomies, and LAC rises.
Including fixed cost in long-run cost.
Students carry the short-run cost structure into the long run.
Fix: In the long run all costs are variable. There is no fixed cost.
Treating economies of scale and returns to scale as identical in every case.
Both deal with output growth and look similar.
Fix: Returns to scale concern the physical output response to inputs. Economies of scale concern the fall in cost per unit. They are related, but state which one the question asks.

Worked examples

Example 1

A firm's long-run total cost is ₹2,00,000 for 1,000 units, ₹3,00,000 for 2,000 units, ₹4,80,000 for 3,000 units and ₹8,00,000 for 4,000 units. Find the LAC at each output and state at which output the firm enjoys economies of scale and where diseconomies begin.

Show the solution

LAC = Total cost ÷ Output.
At 1,000 units: 2,00,000 ÷ 1,000 = ₹200.
At 2,000 units: 3,00,000 ÷ 2,000 = ₹150.
At 3,000 units: 4,80,000 ÷ 3,000 = ₹160.
At 4,000 units: 8,00,000 ÷ 4,000 = ₹200.
LAC falls from ₹200 to ₹150 as output rises from 1,000 to 2,000 units, so economies of scale operate here.
LAC rises from ₹150 to ₹160 and then ₹200, so diseconomies of scale begin after 2,000 units.

Answer: LAC is ₹200, ₹150, ₹160 and ₹200. Economies of scale operate up to 2,000 units, which is the minimum LAC. Diseconomies begin beyond 2,000 units.

Example 2

Which of the following is an external economy of scale? (a) A firm buys raw material in bulk at a discount (b) A firm hires a specialist production manager (c) A skilled labour pool and a supplier network develop around an industrial cluster where the firm is located (d) A firm uses a large machine that cannot be used in a small plant

Show the solution

Ask whether each benefit comes from the firm's own size or from the industry's growth.
Option (a) is a bulk-buying benefit from the firm's own large size. It is internal (marketing or purchasing).
Option (b) is a managerial economy from the firm's own growth. It is internal.
Option (d) is a technical economy from the firm's own large plant. It is internal.
Option (c) arises because many firms are located together and the industry has grown. It benefits all firms and is external.

Answer: Option (c).

Exam tips

Questions often ask for the reason behind the U-shape of LAC. Answer with economies first, then diseconomies of scale.
Memorise the one-line tests: internal means inside the firm, external means industry-wide. Most classification MCQs rely on this.
For the envelope curve, remember LAC is tangent to each SAC and never above it. Watch for options that say 'above' or 'intersects'.
There is no negative marking, so attempt every question. Eliminate options that mention fixed cost in the long run first.
Practise the types of internal economies as a list: technical, managerial, marketing, financial and risk-bearing.

Practice questions from Cost of Production

Long-Run Cost Curves and Economies of Scale in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Long-Run Cost Curves and Economies of Scale: frequently asked questions

Why is the long-run average cost curve U-shaped?

It falls at first because economies of scale reduce cost per unit as the firm grows. After the optimum size, diseconomies of scale such as management and coordination problems push cost per unit up. This produces the U-shape.

Why is the LAC curve called an envelope curve?

Each plant size has its own short-run average cost curve. The LAC curve touches each of them at one point and lies on or below all of them, so it wraps around them from below. This is why it is called the envelope.

What is the difference between internal and external economies of scale?

Internal economies come from the growth of the firm itself, such as better machines or bulk buying. External economies come from the growth of the whole industry, such as a skilled labour pool or better transport nearby. Internal gains belong to one firm, while external gains are shared by many.

Does the LAC curve touch each SAC curve at its lowest point?

Not usually. It touches the SAC at its lowest point only at the output where LAC is at its minimum. On the falling part of LAC, the tangency is to the left of the SAC minimum, and on the rising part it is to the right.