Cost and Revenue Curves

A firm's decisions depend on what it costs to produce and what it earns. This unit builds the cost and revenue curves that Unit 5 uses to find the profit-maximising output in each market structure.

Accounting profit = revenue − explicit costs; economic profit = revenue − (explicit + implicit costs).

A shop-owner earning NPR 500,000 revenue with NPR 350,000 explicit costs has accounting profit 150,000; if she could have earned a 100,000 salary elsewhere and her capital could earn 30,000, economic profit is 150,000 − 130,000 = 20,000.

Zero economic profit means normal profit: the owner just covers all opportunity costs and stays in business.

4.2 Short-run cost curves

In the short run at least one input (plant, machinery) is fixed; in the long run all are variable.

Costs: Total fixed cost (TFC) does not change with output (rent, interest); total variable cost (TVC) rises with output (materials, wages); TC = TFC + TVC.

Per unit: AFC = TFC/Q (falls continuously, a rectangular hyperbola), AVC = TVC/Q, AC (ATC) = TC/Q = AFC + AVC, and marginal cost MC = ΔTC/ΔQ = ΔTVC/ΔQ, the extra cost of one more unit.

The shapes follow the law of variable proportions (diminishing returns): at first extra workers raise output a lot (MC falls), then crowding sets in (MC rises).

So AVC, AC and MC are U-shaped, and MC cuts AVC and AC at their minimum points (marginal below average pulls the average down; above, pulls it up).

4.3 Long-run cost curves

In the long run the firm can choose any plant size.

The long-run average cost (LAC) curve is the envelope of the short-run AC curves (SAC₁, SAC₂, SAC₃ …): for each output it shows the lowest achievable average cost when the plant can be chosen.

It is also U-shaped, but flatter, for reasons of scale: economies of scale (specialisation, bulk buying, spreading overhead, better technology) make LAC fall; at the minimum efficient scale it is flat (constant returns); diseconomies of scale (management and coordination problems) make it rise.

Long-run marginal cost (LMC) cuts LAC at its minimum.

At the minimum of LAC the firm's plant is operated at the minimum of its SAC (the optimal scale), and SMC = LMC; on the falling part of LAC the SAC touches it to the left of SAC's own minimum, on the rising part to the right.

Relationship: SAC ≥ LAC everywhere, with equality only at the one output where the plant is optimal; LAC is the envelope; LMC is not an envelope but passes through the points where SMC = LMC.

4.4 Concept of revenue

Total revenue TR = P × Q; average revenue AR = TR/Q = P (so the AR curve is the demand curve); marginal revenue MR = ΔTR/ΔQ, the extra revenue from one more unit.

Perfect competition: the firm is a price-taker; each extra unit sells at the market price, so AR = MR = P: a horizontal line; TR is a straight line from the origin.

Imperfect competition (monopoly, monopolistic competition, oligopoly): the firm faces a downward-sloping demand curve (it must cut price to sell more), so MR < AR and MR lies below AR.

TR rises, reaches a maximum where MR = 0 (the elasticity = 1 point), then falls.

For a linear demand AR = a − bQ: TR = aQ − bQ², MR = a − 2bQ, i.e. MR has the same intercept as AR and twice the slope, cutting the quantity axis at half the distance.

AR–MR–elasticity relation: MR = AR × (1 − 1/|e|) (so MR > 0 when demand is elastic, MR = 0 when |e| = 1, MR < 0 when inelastic: a monopolist never operates on the inelastic part).

Excel exercise: build the schedule in columns Q, TVC, then =TVC+100 for TC, =C3-C2 for MC, =C3/A3 for AC; chart AC and MC on one graph to see MC cut AC at its minimum, and =P*Q, =TR3-TR2 for revenue.

(a) Ford assembly line, Manchester, 1923

(b) Average cost against output, in thousand rupees

(a) Tea and sel roti, a street stall

(b) TR and TC lines, break-even at 116 cups

4.6 Eight uses of cost and revenue analysis

1. Deciding the price of a product. A firm must cover its average cost, so it never sells below the minimum of the AC curve for long. A Kathmandu printing press adds a margin to the unit cost of each job. Without knowing the cost curve the price would be a guess.
2. Choosing how much to produce. Output should rise as long as marginal revenue is above marginal cost. A bakery in Pokhara bakes extra batches only while the extra income covers the extra flour, gas and labour. This simple rule is the base of all profit decisions.
3. Deciding to shut down or to continue. In the short run fixed costs are sunk, so a firm keeps working if the price covers AVC even when it loses on AC. A hotel in the off-season may stay open on these grounds. If price falls below AVC, closing is the better choice.
4. Planning plant size and expansion. The long-run cost curve shows which factory size gives the lowest unit cost. A cement plant in Hetauda gains from economies of scale, while a very large unit may suffer from poor management. Banks study these curves before lending for expansion.
5. Understanding economies of scale in technology. Software has a high fixed cost to build and almost zero marginal cost per user. The average cost per user therefore falls steadily as the user base grows. This is why apps such as eSewa and Foodmandu fight to gain users quickly.
6. Separating accounting and economic profit. An owner who counts only cash costs may feel rich while earning less than a salary elsewhere. Economic profit includes the opportunity cost of own time and capital. A small shopkeeper uses it to decide whether the shop is worth running.
7. Understanding pricing power. A firm with a falling AR curve knows that MR is lower than price, so each extra unit sold earns less than the price shown. This is the basis of limited output and higher prices in monopolies. It also explains discounts that are offered only to some groups.
8. Controlling and budgeting costs. Splitting costs into fixed and variable lets a manager forecast the bill at any output. A college planning more students knows that rent stays the same but staff and electricity rise. Break-even analysis follows directly from TC and TR.

Formula and fact sheet

• TC = TFC + TVC; AFC = TFC/Q; AVC = TVC/Q; AC = AFC + AVC; MC = ΔTC/ΔQ.
• MC cuts AVC and AC at their minima; AFC always falls.
• LAC is the envelope of SAC; economies then diseconomies of scale.
• TR = PQ; AR = P; MR = ΔTR/ΔQ. Perfect competition: AR = MR = P. Otherwise MR < AR; linear: MR has twice the slope.
• MR = AR(1 − 1/|e|); TR maximum where MR = 0.

Chapter summary

• Economic cost includes implicit costs, so economic profit is lower than accounting profit; normal profit is a cost.
• Short-run cost curves are U-shaped because of diminishing returns; long-run curves are envelopes shaped by scale economies.
• Revenue curves are horizontal under perfect competition and downward-sloping with MR below AR otherwise.

Practice

1. Differentiate explicit and implicit, accounting and economic cost.
2. Given TFC = 60 and TVC = 20, 36, 48, 64, 90 for Q = 1–5, compute MC, AVC and AC.
3. Why does MC cut AC at its minimum?
4. Derive MR for AR = 60 − 2Q; at what output is TR maximum?
5. Explain the long-run average cost curve and economies of scale.
6. Why is MR below AR for a monopolist but equal to it in perfect competition?
7. A firm has revenue 800, explicit costs 500, and implicit costs 350. Find accounting and economic profit.

Answers and worked solutions

1. Explicit: paid to outsiders. Implicit: opportunity cost of owner's resources. Accounting cost = explicit; economic cost = explicit + implicit.

2. TC = 80, 96, 108, 124, 150. MC = 20, 16, 12, 16, 26. AVC = 20, 18, 16, 16, 18. AC = 80, 48, 36, 31, 30.

3. If the marginal cost is below the average, adding that unit lowers the average; if above, it raises it; so MC crosses AC where AC stops falling, at its minimum.

4. TR = 60Q − 2Q²; MR = 60 − 4Q. TR is maximum where MR = 0: Q = 15 (P = 30, TR = 450).

5. LAC is the envelope of short-run AC curves: the lowest cost of each output when the plant size can be chosen. It falls with economies of scale, is flat at the minimum efficient scale and rises with diseconomies of scale.

6. To sell one more unit a monopolist must lower the price on all units, so the extra revenue is less than the price; a price-taker sells every unit at the same fixed price, so MR = P.

7. Accounting profit = 800 − 500 = 300; economic profit = 800 − 850 = −50 (a loss compared with the best alternative).

Model answers: medium (5 marks) and long (10 marks) questions

Q1 (5 marks). Distinguish between explicit and implicit costs, and between accounting profit and economic profit, with a numerical example.

Introduction. To a business owner a cost is more than the cash paid out. Economists count every resource at what it could have earned elsewhere, its opportunity cost.

Explicit and implicit cost.

Point	Explicit cost	Implicit cost
Meaning	payments to outsiders for inputs	opportunity cost of the owner's own resources
Examples	wages, rent, raw material, electricity	own capital, own time, own building
Recorded in books	yes	no
Used in	accounting cost	economic cost (explicit + implicit)

Profit. Accounting profit = revenue − explicit costs. Economic profit = revenue − (explicit + implicit costs). The implicit costs include normal profit, the minimum reward that keeps the owner in the business.

Example. A shop earns revenue NPR 500,000 and pays explicit costs of 350,000. Accounting profit is 150,000. The owner could earn a 100,000 salary elsewhere and her capital could earn 30,000, so implicit cost is 130,000.

Economic profit = 150,000 − 130,000 = 20,000. Zero economic profit would mean exactly normal profit.

Conclusion. A business that shows an accounting profit may still be a poor choice if the owner's best alternative pays more.

Q2 (5 marks). Explain total, average and marginal revenue. Show how AR and MR are related in perfect competition and under imperfect competition.

Introduction. Total revenue TR = P × Q is the money received from sales. Average revenue AR = TR/Q = P, so the AR curve is the demand curve. Marginal revenue MR = ΔTR/ΔQ is the extra revenue from selling one more unit (Figure 4.3).

Perfect competition. The firm is a price-taker. Every unit sells at the market price, so AR = MR = P and both are one horizontal line. TR is a straight line through the origin.

Imperfect competition. The firm faces a downward-sloping demand curve and must cut the price to sell more. Therefore MR < AR. For AR = a − bQ, TR = aQ − bQ² and MR = a − 2bQ: the same intercept and twice the slope, so MR cuts the quantity axis at half the distance.

Numerical illustration. For AR = 60 − Q, MR = 60 − 2Q. At Q = 20, AR = 40 but MR = 20. TR = 60Q − Q² rises until MR = 0 at Q = 30, where TR = 900, and falls after that. At that point elasticity is exactly 1.

Conclusion. The price taker sees MR equal to price; every other firm sees MR below price, which is the root of monopoly power.

Q3 (10 marks). Explain the short-run cost curves and their relationships using a schedule. How is the long-run average cost curve derived, and why is it U-shaped?

Introduction. In the short run some input, such as plant, is fixed; in the long run all inputs can change. Costs are therefore divided into fixed and variable parts.

Cost concepts. TFC does not change with output; TVC rises with output; TC = TFC + TVC. Per unit: AFC = TFC/Q, AVC = TVC/Q, AC = AFC + AVC, and MC = ΔTC/ΔQ.

Schedule and curves (Figure 4.1), TFC = 100.

Q	1	2	3	4	5	6
TC	150	190	220	260	320	400
MC	50	40	30	40	60	80
AVC	50	45	40	40	44	50
AC	150	95	73.3	65	64	66.7

Relationships.

1. AFC falls throughout (a rectangular hyperbola), so AC and AVC come closer as output grows.
2. AVC, AC and MC are U-shaped because of the law of variable proportions: at first extra workers raise output a lot and MC falls; later crowding makes MC rise.
3. MC cuts AVC and AC at their minimum points. Here AVC is minimum (40) at Q = 3 to 4 and AC is minimum (64) at Q = 5. When MC is below the average, the average falls; when above, it rises.

Long-run curve (Figure 4.2). In the long run the firm may pick any plant size. Each plant has its own SAC curve.

For any output the firm chooses the plant with the lowest cost, so LAC is the lower envelope of the SAC curves, touching each at one output. LMC cuts LAC at its minimum.

Why U-shaped. Falling LAC comes from economies of scale: specialisation, bulk buying, spreading overhead and better technology. The flat part near the minimum efficient scale shows constant returns.

Rising LAC comes from diseconomies of scale: coordination, communication and management problems.

Feature	Short-run AC	Long-run AC
Fixed input	at least one	none
Shape cause	variable proportions	scale of operations
Curve	U, steeper	U, flatter envelope

Conclusion. Short-run curves guide daily output decisions; the long-run curve guides the choice of plant size.