Introduction — why cost and revenue matter
Cost and revenue are the two accounting “stories” every firm watches. Cost tells us what it takes to produce goods (resources used, money spent, sacrifices made). Revenue tells us what the firm receives from selling output. The interaction between cost and revenue determines profit, survival, pricing, output decisions, and long-run strategy. For WAEC, students must be able to:
- define and distinguish many cost types (TC, TFC, TVC, AC, MC, opportunity cost, sunk cost, etc.),
- calculate and draw short-run and long-run cost curves,
- explain revenue measures (TR, AR, MR, MRP), and
- use the MR = MC rule to show profit-maximizing output and the break-even/shut-down analysis.
This chapter explains concepts, shows calculations, and gives classroom-ready examples.
10.1 Basic cost concepts (definitions + classroom formulas)
Total Cost (TC) = total economic cost of producing a given output.
TC = TFC + TVC
- Total Fixed Cost (TFC): costs that do not change with output (rent, insurance, some managers’ salaries in short run).
- Example: A bakery pays ₦200,000 per month in rent regardless of loaves baked.
- Total Variable Cost (TVC): costs that vary with output (raw materials, hourly wages, fuel).
- Example: Flour costs increase with number of loaves.
Average (per-unit) measures
- Average Total Cost (ATC or AC) =
TC / Q(cost per unit) - Average Fixed Cost (AFC) =
TFC / Q(falls as Q rises) - Average Variable Cost (AVC) =
TVC / Q
Note: AC = AFC + AVC
Marginal Cost (MC) = the extra cost of producing one more unit.
MC = ΔTC / ΔQ (or ΔTVC / ΔQ, since TFC does not change with Q)
Important teacher point: Emphasize that MC is a flow concept (change in cost) and is central to decisions. Also show algebraic examples (below).
10.2 Accounting cost vs Economic cost (opportunity cost)
- Accounting (money) cost: explicit payments recorded in books (wages, rent, interest expense).
- Economic cost: accounting cost plus opportunity costs of all resources (what owner could earn elsewhere).
- Example: If the owner uses his building instead of renting it out, the forgone rent is an economic cost (opportunity cost), though not an accounting expense.
Sunk cost: cost already incurred and irrecoverable (e.g., research spent on a failed product). Sunk costs should not affect current production decisions.
Exam tip: WAEC often tests the distinction — always define opportunity cost and give a local example (e.g., a farmer keeping land fallow to store for expected price increase — forgone current crop revenue).
10.3 Short run vs Long run costs
- Short run: at least one input is fixed (typically capital). Firms can only vary variable inputs (labour, raw materials). Cost curves are shaped by that constraint.
- Long run: all factors are variable; firms can adjust plant size. Long-run cost curves (LRAC) show the lowest possible AC for each output when the firm can choose the optimum scale.
Envelope property: LRAC is the lower envelope of short-run AC curves (each short-run AC corresponds to a particular plant size). Draw and explain in class.
10.4 Typical shapes of cost curves and their relationship
What to draw and why (graphical rules for class):
- TFC is a horizontal line (constant) — draw it on Y-axis but usually show its per-unit AFC falls as Q rises.
- TVC is upward sloping (starts at zero).
- TC starts at TFC (intercept) and rises — same shape as TVC shifted upward by TFC.
- AFC declines continuously (hyperbolic).
- AVC is U-shaped (falls then rises due to diminishing marginal returns).
- AC (ATC) is U-shaped and lies above AVC; AC cuts its minimum where MC = AC.
- MC is U-shaped and cuts AVC and AC at their minima. MC intersects AC at AC’s minimum — crucial exam fact.
Economic intuition: at low output, average costs fall (spreading fixed cost and increasing returns); beyond some point, diminishing returns raise MC and push AC up.
10.5 Worked numerical example — cost schedule (teacher model)
Use this in class as demonstration. Suppose:
| Q (units) | TFC (₦) | TVC (₦) | TC (₦) = TFC+TVC |
|---|---|---|---|
| 0 | 1000 | 0 | 1000 |
| 1 | 1000 | 200 | 1200 |
| 2 | 1000 | 360 | 1360 |
| 3 | 1000 | 510 | 1510 |
| 4 | 1000 | 680 | 1680 |
| 5 | 1000 | 870 | 1870 |
Compute:
AFC = TFC / Q(for Q>0)AVC = TVC / QAC = TC / QMCfor each additional unit = ΔTC / ΔQ
Sample calculations:
- For Q = 2:
- AFC = 1000 / 2 = 500
- AVC = 360 / 2 = 180
- AC = 1360 / 2 = 680
- MC from Q=1 to Q=2: ΔTC = 1360 − 1200 = 160 → MC = 160
(You can construct full table in class; students must practice computing MC and AC and observing where MC rises and AC’s minimum.)
10.6 Marginal and average relationships — core rules
- If
MC < AC⇒ AC is falling. - If
MC > AC⇒ AC is rising. MC = AC⇒ AC is at minimum.
Same applies to AVC: MC cuts AVC at AVC’s minimum.
Class activity: give students a partial table and ask them to fill MC, AFC, AVC, AC and identify AC and AVC minima.
10.7 Cost classification by time and behavior — summary
- By behavior: Fixed vs variable; direct vs indirect; explicit vs implicit; average vs marginal.
- By time: Short-run vs long-run cost.
- Special types: Sunk cost (past, irrecoverable), avoidable vs unavoidable costs.
Exam tip: define each, give examples, and explain decision relevance (e.g., sunk costs are irrelevant for optimization).
10.8 Revenue concepts (definitions + formulas)
- Total Revenue (TR) = Price (P) × Quantity (Q)
TR = P × Q - Average Revenue (AR) =
TR / Q= P (in perfect competition)
AR = TR / Q - Marginal Revenue (MR) = change in TR from selling one more unit
MR = ΔTR / ΔQ
Interpretation: AR is revenue per unit (the demand curve). MR is additional revenue from an extra unit and is crucial for pricing decisions. In perfect competition MR = AR = P (horizontal demand). In imperfect competition (monopoly, monopolistic competition), MR lies below AR and falls as Q rises.
10.9 Marginal Revenue Product (MRP) — link to factor demand
Marginal Revenue Product (MRP) of a factor (labour) = MP × MR
- Where MP = marginal product (extra output from one more worker), MR = marginal revenue from selling extra output.
- Firms hire labour up to the point where
MRP = wagein competitive factor markets.
Teacher note: connect MRP to derived demand for factors and to wage determination.
10.10 Profit, profit maximization and break-even analysis
Profit = TR − TC
Profit maximization rule: produce where MR = MC (provided MC is rising at that point). Explain with graphs:
- For competitive firm: price (P) is given, so produce Q where
P = MC; since P = MR, condition reduces toMR (=P) = MC. - For monopolist: set
MR = MC, then use demand curve to set price.
Break-even point: level of output where TR = TC (profit = 0). Firms want to be above break-even in long run.
Shutdown rule (short run): if TR < TVC (i.e., price < AVC at optimum), the firm should shut down in short run because it cannot cover variable costs; if TR ≥ TVC, it can continue (cover part of fixed costs).
Exam examples: Students must explain and compute break-even and shut-down using TR and cost schedules or graphs.
10.11 Relationship between cost curves and revenue curves (graphical intuition)
- Draw cost curves (AC, AVC, MC) and revenue line(s).
- For a competitive firm: horizontal price (P) line = MR = AR. The firm’s supply in short run is the portion of MC above AVC (i.e., MC curve truncated below AVC).
- For a monopolist: MR lies below AR; profit maximization at MR = MC; price read off demand (AR) at that Q (usually P > MC).
Class activity: sketch both cases and highlight profit/loss areas (rectangle TR – TC or show shaded profit area).
10.12 Long-Run cost curves and economies/diseconomies of scale (revisited)
- Long-Run Average Cost (LRAC): U-shaped due to economies then diseconomies of scale.
- Economies of scale (technical, managerial, financial, risk-bearing, marketing).
- Diseconomies of scale (coordination problems, bureaucracy, worker alienation).
Exam tip: relate LRAC movements to firm size decisions and industry structure.
10.13 Common algebraic examples (teacher-ready, copy-paste safe)
- Cost functions example: Suppose
TFC = 500, andTVC = 20Q + 2Q^2. Then:TC = 500 + 20Q + 2Q^2AC = TC / Q = (500 / Q) + 20 + 2QAVC = TVC / Q = 20 + 2QMC = dTC/dQ = 20 + 4Q(use Δ when discrete)- To find minimum AC set
d(AC)/dQ = 0or equateMC = AC.
- Revenue example: If demand
P = 100 − 2Q, then:TR = P × Q = (100 − 2Q)Q = 100Q − 2Q^2MR = dTR/dQ = 100 − 4Q- Profit max: set
MR = MCand solve for Q.
(When using derivatives in class, note WAEC typically prefers discrete Δ calculations but understands algebraic rules.)
10.14 Classroom problems (practice — teacher can assign)
- Given: TFC = 200; TVC = 30Q + 5Q^2. Make a table for Q = 0 to 6 showing TFC, TVC, TC, AFC, AVC, AC, MC (use ΔTC). Identify AC minimum and MC behavior.
- Given demand
P = 120 − 3Q. Find TR and MR. If MC = 20 + 2Q, find profit-maximizing Q and P. - A firm’s price in perfect competition is ₦50. Given the MC schedule: Q=1→MC=30; Q=2→MC=40; Q=3→MC=50; Q=4→MC=60. Determine output level and explain.
(Leave these as exercises; provide full solutions later if the student requests.)
10.15 Key Points to Master (Exam-focused)
- Know and write definitions of TC, TFC, TVC, AC, AVC, AFC, and MC — with formulas:
TC = TFC + TVCAC = TC / QAVC = TVC / QAFC = TFC / QMC = ΔTC / ΔQ
- Understand accounting vs economic cost; define opportunity cost and sunk cost; use local examples.
- Be able to compute cost schedules, draw AC, AVC and MC, and show:
- MC cuts AVC and AC at their minima.
- AFC falls as Q rises.
- Understand short run vs long run; LRAC as envelope of SRAC curves; explain economies/diseconomies of scale.
- Know revenue definitions and formulas:
TR = P × Q,AR = TR / Q,MR = ΔTR / ΔQ.
- Apply profit maximization rules:
MR = MC(and check second-order condition MC rising). - Be able to compute and interpret break-even point (TR = TC) and shutdown rule (P < AVC → shut down).
- Explain MRP = MP × MR and how it determines factor demand (especially labour).
- Practice numerical problems (tables and algebraic). WAEC often asks computation + graphing questions.
Closing teacher notes
- Use the worked numerical table and algebraic examples in class; ask students to draw graphs from the numbers (TC, AC, MC).
- Emphasize the decision rule MR = MC repeatedly — it’s the cornerstone for firms’ output decisions across market structures.
- Show real-world Nigerian cases (e.g., how rising fuel costs increase TVC for transport firms, shifting short-run supply; minimum wage implications for small firms’ MC and employment).
- Prepare short quizzes with cost tables and simple revenue functions — students must be comfortable switching between tabular, graphical, and algebraic representations.
-
Section A: Objective Questions (30 WAEC-Style)
Instruction: Answer all questions. Each carries 1 mark.
- Which of the following is a fixed cost?
A. Wages of factory workers
B. Rent of a factory building
C. Cost of raw materials
D. Transport expenses - The cost that changes with the level of output is called:
A. Fixed cost
B. Variable cost
C. Average cost
D. Marginal revenue - If total cost is ₦12,000 and total fixed cost is ₦5,000, what is the total variable cost?
A. ₦17,000
B. ₦7,000
C. ₦5,000
D. ₦12,000 - The addition to total cost resulting from producing one extra unit of output is:
A. Average cost
B. Marginal cost
C. Fixed cost
D. Revenue - Which of the following best describes Average Fixed Cost (AFC)?
A. TFC/Q
B. TVC/Q
C. TC/Q
D. MC × Q - In the short run, fixed costs:
A. Increase with output
B. Decrease with output
C. Remain constant
D. Depend on demand - Which curve is U-shaped due to the law of variable proportions?
A. Total cost curve
B. Average fixed cost curve
C. Average variable cost curve
D. Average total cost curve - When marginal cost is less than average cost, the average cost will:
A. Rise
B. Fall
C. Remain constant
D. Be infinite - The revenue a firm receives from selling one additional unit of output is:
A. Total revenue
B. Average revenue
C. Marginal revenue
D. Net revenue - If a firm sells its output at a fixed price of ₦500 per unit, its average revenue curve will be:
A. Downward sloping
B. Vertical
C. Horizontal
D. U-shaped - At output level of 10 units, TR = ₦2000. What is AR?
A. ₦20
B. ₦200
C. ₦100
D. ₦2,000 - The break-even point is reached when:
A. TR = TC
B. AR = MR
C. TC = 0
D. TR > TFC - If TC = ₦100 and TR = ₦120, then profit is:
A. ₦120
B. ₦20
C. ₦220
D. ₦80 - Which of the following costs falls continuously as output rises?
A. Total fixed cost
B. Average fixed cost
C. Marginal cost
D. Average variable cost - The revenue curve under perfect competition is:
A. Downward sloping
B. U-shaped
C. Horizontal straight line
D. Vertical straight line - If TR = ₦6000 and output = 300 units, what is AR?
A. ₦6000
B. ₦300
C. ₦20
D. ₦18 - Which of the following shows the relationship between output and total expenditure on inputs?
A. Revenue curve
B. Cost curve
C. Production function
D. Demand curve - In the short run, marginal cost intersects the average cost curve at its:
A. Lowest point
B. Highest point
C. Midpoint
D. Origin - Normal profit is said to occur when:
A. TR = TC
B. TR > TC
C. TR < TC
D. TR = TFC - Which of these is an implicit cost?
A. Wages of hired labour
B. Rent paid to landlord
C. Interest on own capital forgone
D. Cost of electricity - Economies of scale occur when:
A. Average cost rises as output increases
B. Average cost falls as output increases
C. Marginal cost rises
D. Total cost falls - Diseconomies of scale occur when:
A. Output falls
B. Average cost rises with increased output
C. Marginal cost falls
D. Fixed cost rises - If TFC = ₦100 and TVC = ₦400, then TC = ?
A. ₦500
B. ₦400
C. ₦300
D. ₦100 - Which of these is true under perfect competition?
A. AR = MR = Price
B. AR > MR
C. AR < MR
D. AR = TC - The slope of the total cost curve gives:
A. Average cost
B. Marginal cost
C. Fixed cost
D. Total revenue - Which of the following will cause a downward shift in the cost curves?
A. Increase in wages
B. Reduction in taxes
C. Increase in raw material cost
D. Rise in transportation cost - If MC > AC, then AC will:
A. Rise
B. Fall
C. Remain constant
D. Be zero - Which cost concept is most relevant for decision-making?
A. Sunk cost
B. Marginal cost
C. Fixed cost
D. Implicit cost - If TR = ₦2,500 and TC = ₦2,500, then the firm is:
A. Making supernormal profit
B. Making normal profit
C. Making a loss
D. Facing diseconomies - The point where TR and TC curves intersect is called:
A. Equilibrium point
B. Break-even point
C. Shut-down point
D. Optimum point
Section B: Essay Questions (15 WAEC-Style)
Instruction: Answer any number as directed by your teacher/examiner.
- Define cost of production and explain the distinction between fixed cost, variable cost, and total cost.
- With the aid of diagrams, explain the shapes of Average Cost, Average Variable Cost, and Marginal Cost curves.
- Explain the relationship between marginal cost and average cost.
- Discuss five differences between short-run and long-run costs.
- Using examples, distinguish between implicit and explicit costs.
- Explain the concept of opportunity cost in production decision-making.
- With the aid of diagrams, describe economies and diseconomies of scale.
- Distinguish between accounting cost and economic cost, giving examples.
- Define revenue and explain the relationship between Total Revenue, Average Revenue, and Marginal Revenue.
- Show with the aid of a diagram the TR, AR, and MR curves under perfect competition.
- Explain the concept of break-even point and its importance to producers.
- Discuss five differences between perfect competition and monopoly in terms of revenue curves.
- Explain the profit position of a firm in the short run: (i) supernormal profit, (ii) normal profit, (iii) loss. Illustrate with diagrams.
- With the aid of graphs, explain the relationship between cost and revenue in determining the equilibrium of a firm.
- Discuss the roles of cost and revenue analysis in business decision-making.
Answer Key & Model Solutions — Theory of Cost and Revenue
Part A: Objective Questions (30)
Q1. C — Total Fixed Cost (TFC)
- TFC never changes with output.
Q2. A — Average Cost (AC)
- AC = TC ÷ Q.
Q3. B — Total Variable Cost (TVC)
- TVC = TC − TFC.
Q4. C — TC = TFC + TVC
- Always true.
Q5. A — Diminishing marginal returns
- Explains rising MC.
Q6. B — Short-run cost
- AVC and AFC are short-run concepts.
Q7. C — Constant marginal returns
- U-shaped AVC means diminishing then increasing returns.
Q8. A — Opportunity cost
- Economists use opportunity cost, not accountants’ historical costs.
Q9. C — Marginal Cost (MC)
- Defined as ΔTC/ΔQ.
Q10. B — Marginal Revenue (MR)
- Change in TR ÷ change in Q.
Q11. D — Total Revenue = P × Q.
Q12. C — MR = MC
- Profit maximization rule.
Q13. A — Perfect competition
- MR = AR = P.
Q14. D — Monopoly
- Firm is price maker, MR < AR.
Q15. C — Price discrimination
- Selling at different prices for same product.
Q16. A — AFC falls continuously
- “Spreading effect.”
Q17. B — Economies of scale
- Long-run AC falls.
Q18. C — Diseconomies of scale
- Long-run AC rises.
Q19. D — MC curve
- Always cuts AC and AVC at minimum points.
Q20. B — Total Revenue curve
- In monopoly, TR curve rises then falls as demand is downward sloping.
Q21. A — Normal profit
- Included in cost in economics.
Q22. C — Supernormal profit
- Occurs when TR > TC.
Q23. B — Break-even point
- TR = TC.
Q24. D — Shutdown point
- TR just equals TVC, firm covers variable costs only.
Q25. A — Fixed cost
- Insurance, rent = fixed.
Q26. B — Variable cost
- Wages, raw materials = variable.
Q27. C — Long run
- All costs variable.
Q28. D — Short run
- At least one factor fixed.
Q29. B — AR curve
- Demand curve is same as AR curve.
Q30. A — Decreasing cost industry
- LR supply curve slopes downward.
Part B: Essay Questions (15)
Q1. Define total cost, average cost, and marginal cost with examples.
- Total Cost (TC): Sum of TFC + TVC. Example: If TFC = ₦100, TVC = ₦50, then TC = ₦150.
- Average Cost (AC): TC ÷ Q. If TC = ₦150 and Q = 10, AC = ₦15/unit.
- Marginal Cost (MC): Change in TC ÷ Change in Q. If TC rises from ₦150 to ₦170 when output rises from 10 to 11, MC = ₦20.
Q2. Explain the difference between fixed cost and variable cost with five examples each.
- Fixed Cost (unchanged with output): Rent, salaries of permanent staff, insurance, depreciation, property tax.
- Variable Cost (changes with output): Raw materials, wages of casual workers, electricity/fuel, transport, packaging.
Q3. With the aid of a diagram, explain the relationship between AC, AVC, AFC, and MC.
- AFC: Always falls.
- AVC: U-shaped due to law of variable proportions.
- AC: Sum of AFC + AVC, also U-shaped.
- MC: Cuts AVC and AC at their minimum points.
Q4. Distinguish between economist’s and accountant’s view of cost.
- Accountant’s cost: Explicit costs (wages, rent, materials).
- Economist’s cost: Explicit + Implicit (opportunity cost, normal profit).
- E.g., ₦50,000 foregone salary by entrepreneur is included by economist, ignored by accountant.
Q5. Define and illustrate the concepts of total, average, and marginal revenue.
- TR = P × Q.
- AR = TR ÷ Q = P.
- MR = ΔTR ÷ ΔQ.
- In perfect competition, AR = MR = P.
- In monopoly, MR < AR.
Q6. Discuss the concept of normal profit and supernormal profit.
- Normal profit: Minimum return required to keep entrepreneur in business (TR = TC).
- Supernormal profit: Excess of TR over TC (TR > TC).
Q7. Define marginal revenue product (MRP). Why is it important in factor pricing?
- MRP: Change in TR from employing one more unit of a factor.
- Importance: basis for demand for factors of production, explains wage determination, guides employment decisions.
Q8. With examples, explain economies and diseconomies of scale.
- Economies of scale: Unit cost falls as output rises (bulk buying, specialization, financial advantages).
- Diseconomies: Unit cost rises as firm becomes too large (bureaucracy, coordination problems, labour unrest).
Q9. Explain why the short-run average cost curve is U-shaped.
- Due to law of diminishing returns: initially specialization lowers cost, then congestion raises cost.
Q10. Explain, with a diagram, how a competitive firm determines output and price.
- Price = MR = AR.
- Firm chooses output where MR = MC.
- AC determines profit/loss. If P > AC → profit, if P = AC → normal profit, if P < AC → loss.
Q11. Distinguish between short-run and long-run cost curves.
- Short run: At least one factor fixed, U-shaped SAC curve.
- Long run: All factors variable, LAC derived as envelope of SACs.
Q12. State and explain four factors that can cause economies of scale.
- Technical (specialized machines).
- Managerial (division of management).
- Financial (easier access to loans).
- Marketing (bulk purchase and distribution).
Q13. Explain the break-even point using cost and revenue curves.
- Break-even point is where TR = TC.
- Diagram: TR curve intersects TC curve.
- At this point, firm earns normal profit.
Q14. Explain three reasons why AFC always declines with output.
- TFC constant, so more units spread the cost.
- Mathematically, AFC = TFC ÷ Q, so as Q increases, AFC falls.
- Graph approaches zero but never touches the axis.
Q15. Discuss four limitations of using cost and revenue analysis in real-life decision-making.
- Assumes perfect knowledge.
- Measurement difficulties (e.g., opportunity cost hard to quantify).
- Uncertainty in future demand and costs.
- Ignores non-monetary objectives of firms (e.g., social goals).
- Which of the following is a fixed cost?