Unit 3: Theory of cost & revenue curves
Managerial Economics notes · PTU syllabus (BCOMGE 101-18)
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Unit summary
Cost and revenue decide profit. This unit covers cost concepts, short-run cost curves, long-run cost curves and economies of scale, and revenue concepts — total, average and marginal revenue — with the relationship between elasticity of demand and revenue.
After this unit you can
- Explain the various cost concepts used in decision-making
- Derive short-run cost curves and explain their shapes
- Explain the long-run average cost curve and economies of scale
- Explain revenue concepts and relate AR, MR and elasticity
PTU syllabus topics
- Cost concepts
- short and long run cost theory
- total/average/marginal revenue
- elasticity of demand and revenue
Average cost
AC = TC / Q
Marginal cost
MC = change in TC / change in Q
Average revenue
AR = TR / Q (equals price)
Marginal revenue
MR = change in TR / change in Q
Profit maximisation
MR = MC
And MC cuts MR from below
Topic 1
Cost concepts
Accounting vs economic cost
Explicit costs only vs explicit + implicit (opportunity) costs
Fixed vs variable
Do not change with output vs change with output
Sunk vs incremental
Already incurred, irrelevant vs additional cost of a decision
Private vs social
Borne by the firm vs borne by society (pollution)
Historical vs replacement
Original cost vs current cost to replace
Out-of-pocket vs book cost
Cash payments vs non-cash (depreciation)
- Normal profit is the minimum profit needed to keep the entrepreneur in the business — included in economic cost.
- Economic profit = Total revenue − (Explicit + Implicit costs).
Topic 2
Short-run cost theory
Total cost
TC = TFC + TVC
Average fixed cost
AFC = TFC ÷ Q
Average variable cost
AVC = TVC ÷ Q
Average total cost
ATC = AFC + AVC = TC ÷ Q
Marginal cost
MC = ΔTC ÷ ΔQ
| Output | TFC | TVC | TC | AFC | AVC | ATC | MC |
|---|---|---|---|---|---|---|---|
| 1 | 60 | 20 | 80 | 60 | 20 | 80 | 20 |
| 2 | 60 | 36 | 96 | 30 | 18 | 48 | 16 |
| 3 | 60 | 48 | 108 | 20 | 16 | 36 | 12 |
| 4 | 60 | 64 | 124 | 15 | 16 | 31 | 16 |
| 5 | 60 | 90 | 150 | 12 | 18 | 30 | 26 |
| 6 | 60 | 132 | 192 | 10 | 22 | 32 | 42 |
- AFC falls continuously (rectangular hyperbola).
- AVC, ATC and MC are U-shaped due to the law of variable proportions.
- MC cuts AVC and ATC at their minimum points — when MC < AC, AC falls; when MC > AC, AC rises.
Exam tip
Draw MC passing through the lowest points of AVC and ATC — this relationship is asked almost every year.
Topic 3
Long-run cost theory
- In the long run all costs are variable; the firm chooses the plant size.
- The long-run average cost (LAC) curve is the envelope of short-run average cost curves — touches each SAC at one point (planning curve).
- LAC is U-shaped (but flatter) due to economies and diseconomies of scale.
Source
Expansion of the firm itself
Expansion of the industry
Examples
Technical, managerial, marketing, financial, risk-bearing
Better infrastructure, skilled labour pool, ancillary industries, information
Control
Within the firm's control
Outside the firm's control
- Modern theory: LAC is often L-shaped — after minimum efficient scale, costs remain roughly constant.
- Long-run marginal cost (LMC) cuts LAC at its minimum.
Topic 4
Revenue concepts
Total revenue
TR = P × Q
Average revenue
AR = TR ÷ Q = Price
Marginal revenue
MR = ΔTR ÷ ΔQ
AR, MR and elasticity
MR = AR × (e − 1) ÷ e
| Q | Price (AR) | TR | MR |
|---|---|---|---|
| 1 | 10 | 10 | 10 |
| 2 | 9 | 18 | 8 |
| 3 | 8 | 24 | 6 |
| 4 | 7 | 28 | 4 |
| 5 | 6 | 30 | 2 |
| 6 | 5 | 30 | 0 |
| 7 | 4 | 28 | −2 |
- Under perfect competition, price is constant, so AR = MR — a horizontal line.
- Under imperfect competition, AR slopes downward and MR lies below AR (for a straight-line AR, MR falls twice as fast).
- TR is maximum when MR = 0.
Topic 5
Elasticity of demand and revenue
| Elasticity (e) | MR | Effect of price cut on TR |
|---|---|---|
| e > 1 | Positive | TR rises |
| e = 1 | Zero | TR unchanged (maximum) |
| e < 1 | Negative | TR falls |
Example
If AR = ₹20 and e = 2, MR = 20 × (2 − 1)/2 = ₹10. If e = 1, MR = 0. A monopolist therefore always produces on the elastic part of the demand curve (where MR > 0).
Key terms
- Opportunity (implicit) cost
- Value of the firm's own resources used, not paid in cash
- Marginal cost
- Addition to total cost from one more unit of output
- Envelope curve
- LAC curve enveloping short-run AC curves
- Economies of scale
- Fall in long-run average cost as output expands
- Marginal revenue
- Addition to total revenue from selling one more unit
Quick revision
- TC = TFC + TVC; AFC falls; AVC, ATC, MC U-shaped.
- MC cuts AVC and ATC at their minimum.
- LAC = envelope; economies and diseconomies of scale.
- Perfect competition: AR = MR; imperfect: MR < AR.
- MR = AR (e − 1)/e.
Important exam questions
Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).
Short-answer questions
- Q1.Distinguish explicit and implicit costs.
- Q2.What is sunk cost?
- Q3.Why is the AFC curve a rectangular hyperbola?
- Q4.Why is the LAC curve called an envelope curve?
- Q5.What are external economies?
- Q6.State the relationship between AR, MR and elasticity.
Long-answer questions
- Q1.Explain various cost concepts used in managerial decision-making.
- Q2.Explain short-run cost curves and the relationship between MC, AVC and ATC.
- Q3.Explain the long-run average cost curve and economies of scale.
- Q4.Explain revenue concepts and the relationship between AR, MR and elasticity of demand.
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