Business Economics · Theory of Production and Cost

Long-Run Costs and Revenue Concepts for CA Foundation Business Economics

Q: Why is the long-run average cost curve called an envelope curve?

It wraps around all the short-run average cost curves from below. It touches each one at a single point and never lies above any of them. It shows the lowest cost for each output when the firm can choose its plant size.

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

Internal economies come from the growth of the firm itself, such as technical or managerial gains. External economies come from the growth of the whole industry, such as better transport or a skilled labour pool. External economies help all firms in the industry.

Q: How do you find marginal revenue from a table?

Subtract the TR of the previous quantity from the TR of the current quantity. If quantity rises by more than one unit, divide the change in TR by the change in quantity.

Q: What is the break-even point in Business Economics?

It is the output where total revenue equals total cost, so profit is zero. Beyond it, the firm earns a profit if price and cost per unit stay as assumed.

Updated 1 October 2026 · Fact-checked

In the long run all inputs are variable, so the long-run average cost (LRAC) curve is a U-shaped envelope of short-run average cost curves. Revenue concepts are TR = P × Q, AR = TR ÷ Q and MR = change in TR ÷ change in Q. Break-even is where TR equals TC.

Understand Long-Run Costs and Revenue Concepts

In the long run, a firm can change every input: land, plant, machinery and labour. So there are no fixed costs in the long run. All costs are variable.

Each plant size has its own short-run average cost (SAC) curve. The long-run average cost (LRAC) curve shows the lowest cost of producing each output when the firm is free to choose the best plant size. It touches each SAC curve at one point and does not go above any of them. This is why LRAC is called the envelope curve or planning curve.

LRAC is usually U-shaped. It falls at first because of economies of scale, then may stay flat, then rises because of diseconomies of scale. Internal economies arise inside the firm as it grows, such as technical, managerial, marketing, financial and risk-bearing economies. External economies arise from the growth of the whole industry, such as better transport, skilled labour pools and supplier networks. They lower costs for all firms in the industry.

Now revenue. Total revenue (TR) is the total money a firm earns from sales: price × quantity. Average revenue (AR) is revenue per unit sold, which equals price. Marginal revenue (MR) is the extra revenue from selling one more unit.

The break-even point is the output at which TR = TC, so profit is zero. Below it the firm makes a loss. Above it the firm makes a profit, provided the price stays the same and costs behave as assumed. A firm maximises profit where MR = MC, with MC cutting MR from below.

Key formulas to remember

Total revenue: TR = P × Q; P is price per unit and Q is quantity sold.
Average revenue: AR = TR ÷ Q = P; AR is the same as price. The AR curve is the demand curve.
Marginal revenue: MR = ΔTR ÷ ΔQ = TRn − TRn−1; Use TRn − TRn−1 when quantity rises by one unit.
Long-run average cost: LRAC = LTC ÷ Q; LTC is long-run total cost. The curve is the envelope of SAC curves.
Break-even condition: TR = TC (profit = 0); Profit = TR − TC. Profit is positive above break-even output, if price and costs stay unchanged.
Profit-maximising condition: MR = MC, with MC rising through MR; MC must cut MR from below.
Revenue under constant price (perfect competition): AR = MR = P; The firm is a price taker, so each extra unit sells at the same price.

How to solve Long-Run Costs and Revenue Concepts questions

Use this method for any MCQ on long-run cost or revenue.

1Read the question and decide: is it about long-run cost, economies of scale, or revenue and break-even?
2For theory questions, check whether the cost is internal (inside the firm) or external (industry-wide), and whether the stage is falling, flat or rising LRAC.
3For revenue numbers, write TR = P × Q for each output level first.
4Find AR = TR ÷ Q and MR = change in TR between successive units.
5For break-even, set TR = TC, or compare TR and TC in the table, and find where they are equal.
6For profit-maximising output, find where MR = MC, or where the gap TR − TC is largest.
7Match your result to one option and check that the other three values differ for a clear reason.

Quickest way: Table-first elimination

When to use it: Use this for numerical revenue and break-even MCQs when time is short.

Write a small two-row table of Q and TR. Do not compute everything in your head.
Get MR by subtracting adjacent TR values. Check that the MR values add up to the last TR.
If the price is constant, AR = MR = P. Skip all the work and read the price directly.
For theory, remember: falling LRAC means economies, rising LRAC means diseconomies, and LRAC touches but never cuts the SAC curves.
Eliminate options that confuse internal and external economies or that claim fixed costs exist in the long run.
If a question needs more than about 90 seconds of calculation, skip it and return later. A wrong answer costs 0.25 marks.

Common mistakes in Long-Run Costs and Revenue Concepts

Saying fixed costs exist in the long run.
Students mix short-run and long-run ideas.
Fix: In the long run all inputs are variable, so all costs are variable.
Thinking the LRAC curve passes through the minimum points of all SAC curves.
The envelope idea is remembered loosely.
Fix: LRAC is tangent to each SAC curve. Where LRAC is falling, the tangency is to the left of that SAC's minimum point. Where LRAC is rising, it is to the right. Only at the minimum of LRAC (optimal scale) do the minimum points of LRAC and that SAC coincide.
Mixing up internal and external economies.
Both words describe lower costs from growth.
Fix: Internal comes from the firm's own size. External comes from the growth of the industry or its surroundings.
Calculating MR as TR ÷ Q.
It gets confused with AR.
Fix: AR = TR ÷ Q. MR is the change in TR from one extra unit.
Believing AR and MR are always equal.
Perfect competition is the example studied first.
Fix: AR = MR only when price is constant. If the firm must cut price to sell more, MR is below AR.
Taking break-even as the point of maximum profit.
The word 'point' suggests an optimum.
Fix: Break-even means zero profit (TR = TC). Maximum profit is where MR = MC.

Worked examples

Example 1

A firm sells at a constant price of ₹40 per unit. It sells 5 units, then 6 units. What is the marginal revenue of the 6th unit? (a) ₹40 (b) ₹200 (c) ₹240 (d) ₹6.67

Show the solution

TR at 5 units = 40 × 5 = ₹200.
TR at 6 units = 40 × 6 = ₹240.
MR = 240 − 200 = ₹40.
Price is constant, so MR = AR = P = ₹40, which agrees.

Answer: (a) ₹40

Example 2

A firm's TR and TC at output 10 units are ₹500 and ₹500. At 12 units TR is ₹600 and TC is ₹560. Which statement is correct? (a) The firm makes a loss at 10 units (b) 10 units is the break-even output (c) The firm makes a loss at 12 units (d) The firm makes a profit at 10 units

Show the solution

At 10 units, TR = TC = ₹500, so profit = 0. This is break-even.
Option (a) is wrong because profit at 10 units is zero, not a loss.
Option (d) is wrong for the same reason: profit at 10 units is zero, not a positive amount.
At 12 units, profit = 600 − 560 = ₹40, a profit, so (c) is wrong.
Only option (b) is correct.

Answer: (b) 10 units is the break-even output

Example 3

Which of the following is an external economy of scale? (a) Bulk purchase discount obtained by one firm (b) Better roads and a skilled labour pool developed in an industrial cluster (c) Hiring specialist managers within the firm (d) Using larger machines that cut the firm's cost per unit

Show the solution

External economies come from the growth of the industry or area, not from one firm's own size.
Option (a) is a marketing economy that arises inside the firm, so it is internal.
Option (c) is a managerial economy, which is internal.
Option (d) is a technical economy, which is internal.
Option (b) benefits all firms in the cluster, so it is external.

Answer: (b) Better roads and a skilled labour pool developed in an industrial cluster

Exam tips

Theory MCQs often test the definition of the envelope curve, the absence of fixed costs in the long run, and internal versus external economies. Learn these three well.
For numerical questions, build a TR table first. MR is the difference between successive TR values.
Remember AR = MR = P under perfect competition, and MR < AR when price falls as output rises.
Do not confuse break-even (zero profit) with profit maximisation (MR = MC).
If two options sound alike, check the key word: 'firm' points to internal, 'industry' points to external.

Practice questions from Theory of Production and Cost

Long-Run Costs and Revenue Concepts: frequently asked questions

Why is the long-run average cost curve called an envelope curve?

It wraps around all the short-run average cost curves from below. It touches each one at a single point and never lies above any of them. It shows the lowest cost for each output when the firm can choose its plant size.

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

Internal economies come from the growth of the firm itself, such as technical or managerial gains. External economies come from the growth of the whole industry, such as better transport or a skilled labour pool. External economies help all firms in the industry.

How do you find marginal revenue from a table?

Subtract the TR of the previous quantity from the TR of the current quantity. If quantity rises by more than one unit, divide the change in TR by the change in quantity.

What is the break-even point in Business Economics?

It is the output where total revenue equals total cost, so profit is zero. Beyond it, the firm earns a profit if price and cost per unit stay as assumed.