flowchart LR
AR[AR = P<br/>= a − bQ] --> MR[MR = a − 2bQ<br/>Twice the slope]
AR --> E[Mid-point of AR<br/>Unit elastic]
MR --> TR[TR maximum<br/>at MR = 0]
classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;
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22 Demand analysis: Law of demand; Elasticity of demand and its measurement; Relationship between AR and MR
22.1 Concept of Demand
In economics, demand is not merely a desire but a desire backed by willingness to pay and ability to pay — over a specified period, at a given price. Three elements must coexist: a wish for the good, the purchasing power to buy it, and the willingness to part with that money. The Law of Demand (Alfred Marshall, 1890) states that other things equal, the quantity demanded of a good varies inversely with its price.
TipDeterminants of Demand
- Own price of the good.
- Income of the consumer (positive for normal goods; negative for inferior).
- Prices of related goods — substitutes (positive cross-elasticity) and complements (negative).
- Tastes and preferences, fashion, advertising.
- Population and demographics.
- Expectations about future prices and income.
- Distribution of income.
- Climate, season, government policy.
22.2 The Law of Demand and the Demand Curve
Demand schedule and curve are downward-sloping for normal goods. The two reasons are the income effect and the substitution effect — when the price of a good falls, real income rises (income effect) and the relatively cheaper good is substituted for others (substitution effect).
TipExceptions to the Law of Demand
- Giffen goods — inferior goods whose income effect dominates the substitution effect (Sir Robert Giffen, 1880s).
- Veblen goods — conspicuous-consumption luxury goods (Thorstein Veblen, 1899).
- Expectations of future price rise — buy more now even though price has risen.
- Speculative assets — securities, bullion in a rising market.
- Necessities with no close substitute (e.g., salt) — demand insensitive to small price changes.
- Ignorance / Quality association — higher price taken as a signal of quality.
22.3 Elasticity of Demand
Elasticity of demand measures the responsiveness of quantity demanded to changes in a determinant. It was first formalised by Alfred Marshall (1890).
22.3.1 Four Major Elasticities
TipFour Elasticities
| Elasticity | Formula | Working content |
|---|---|---|
| Price (own) — Ed | \(E_d = \frac{\%\Delta Q}{\%\Delta P}\) (sign negative) | Responsiveness to own-price |
| Income — Ey | \(E_y = \frac{\%\Delta Q}{\%\Delta Y}\) | Positive for normal goods; negative for inferior |
| Cross — Exy | \(E_{xy} = \frac{\%\Delta Q_x}{\%\Delta P_y}\) | Positive — substitutes; Negative — complements; ≈ 0 — unrelated |
| Advertising / Promotional | \(E_a = \frac{\%\Delta Q}{\%\Delta A}\) | Responsiveness to advertising spend |
22.3.2 Degrees of Price Elasticity
TipFive Degrees of Price Elasticity of Demand
| Degree | Value | Demand-curve shape | Illustration |
|---|---|---|---|
| Perfectly inelastic | \(E_d = 0\) | Vertical | Insulin for a diabetic |
| Inelastic | \(0 < |E_d| < 1\) | Steep | Necessities (rice, salt) |
| Unit elastic | \(|E_d| = 1\) | Rectangular hyperbola | Mid-range goods |
| Elastic | \(|E_d| > 1\) | Flatter | Luxuries, branded apparel |
| Perfectly elastic | \(E_d = \infty\) | Horizontal | Firm’s demand in perfect competition |
22.3.3 Methods of Measuring Price Elasticity
TipFour Methods of Measuring Price Elasticity
- Total Outlay (TR test) — if price ↓ and TR ↑, demand is elastic; if TR unchanged, unit elastic; if TR ↓, inelastic.
- Proportionate / Percentage method — divide % change in Q by % change in P at a point.
- Geometric / Point method — at any point P on a linear demand curve, \(E_d = \frac{\text{lower segment}}{\text{upper segment}}\).
- Arc method — uses the average of two prices and two quantities for changes that are not infinitesimal: \(E_d = \frac{Q_2 - Q_1}{(Q_2 + Q_1)/2} \div \frac{P_2 - P_1}{(P_2 + P_1)/2}\).
22.3.4 Determinants of Price Elasticity
TipDeterminants of Price Elasticity of Demand
- Availability of substitutes — more substitutes, more elastic.
- Necessity vs luxury — luxuries more elastic.
- Proportion of income spent — bigger share, more elastic.
- Habit and brand loyalty — habits reduce elasticity.
- Time horizon — longer time, more elastic.
- Postponability of consumption — postponable goods more elastic.
- Number of uses — more uses, more elastic.
22.4 Relationship between AR, MR and Elasticity
For any firm: - Average Revenue (AR) = TR / Q = Price (P). - Marginal Revenue (MR) = \(\frac{dTR}{dQ}\).
The fundamental relation: \[MR = AR\left(1 - \frac{1}{|E_d|}\right) = P\left(\frac{E_d - 1}{E_d}\right)\]
This identity drives several important results.
TipAR-MR-Elasticity Identity in Action
| Elasticity | MR | TR behavior |
|---|---|---|
| \(|E_d| > 1\) (elastic) | MR > 0 | TR rises as Q rises |
| \(|E_d| = 1\) (unit elastic) | MR = 0 | TR is at maximum |
| \(|E_d| < 1\) (inelastic) | MR < 0 | TR falls as Q rises |
| \(|E_d| \to \infty\) (perfect comp) | MR = AR = P | Horizontal demand curve |
22.4.1 Linear Demand: AR and MR
For a linear demand curve \(P = a - bQ\): - AR = \(a - bQ\) - MR = \(a - 2bQ\) - AR and MR start at the same point on the price axis; MR’s slope is twice that of AR. - AR is unit elastic at the mid-point of the demand line; perfectly elastic at the price intercept; perfectly inelastic at the quantity intercept.
NoteDistractor warning
PYQ trap: When MR = 0, TR is maximum and demand is unit elastic. PYQs sometimes ask which value of MR coincides with maximum profit vs maximum revenue — MR = 0 maximises revenue; MR = MC maximises profit.
22.5 Income Elasticity and Engel’s Law
Engel’s Law (Ernst Engel, 1857) — as income rises, the proportion of income spent on food declines.
TipIncome Elasticity Categories
| Sign / Value | Type | Examples |
|---|---|---|
| \(E_y > 0\) | Normal good | Most goods |
| \(E_y > 1\) | Luxury (income-elastic) | Cars, foreign travel |
| \(0 < E_y < 1\) | Necessity (income-inelastic) | Food, salt |
| \(E_y < 0\) | Inferior good | Coarse cereals replaced by superior ones |
22.6 Cross Elasticity
TipCross Elasticity Categories
| Sign | Relationship | Example |
|---|---|---|
| \(E_{xy} > 0\) | Substitutes | Tea and coffee |
| \(E_{xy} < 0\) | Complements | Car and petrol |
| \(E_{xy} \approx 0\) | Unrelated | Salt and shoes |
22.7 Importance of Elasticity
TipWhy Elasticity Matters in Practice
- Pricing decisions — set price where elasticity supports the desired revenue effect.
- Tax policy — indirect tax on inelastic-demand goods (tobacco, alcohol) raises maximum revenue.
- Wage negotiation — labour-intensive firms with elastic product demand resist wage hikes more.
- International trade — devaluation works only if Marshall-Lerner condition (sum of elasticities > 1) holds.
- Monopoly profit-maximisation — choose price where MR = MC; with constant MR formula, choose price where elasticity > 1.
22.8 Practice Questions
Q 01
Law
Easy
The Law of Demand states that:
View solution
Correct Option: B
Inverse relation between own-price and quantity, ceteris paribus.
Q 02
Exceptions
Medium
Which good is **not** an exception to the law of demand?
View solution
Correct Option: D
Normal goods *obey* the law; the others are exceptions.
Q 03
Elasticity
Easy
A perfectly inelastic demand curve is:
View solution
Correct Option: B
$E_d = 0$ → **vertical**.
Q 04
Marshall
Medium
The concept of elasticity of demand was developed by:
View solution
Correct Option: B
Marshall — *Principles of Economics* (1890).
Q 05
Cross
Medium
A positive cross elasticity indicates that two goods are:
View solution
Correct Option: B
**Substitutes** — positive cross elasticity (tea and coffee).
Q 06
Income
Medium
A negative income elasticity indicates:
View solution
Correct Option: C
As income rises, demand falls → **inferior good**.
Q 07
Engel
Medium
Engel's Law states that as income rises:
View solution
Correct Option: B
Engel (1857): food share *declines* as income rises.
Q 08
Compute
Medium
Price falls from ₹10 to ₹9 (10 % cut); quantity rises from 100 to 120 (20 % rise). Price elasticity is:
View solution
Correct Option: C
$|E_d| = 20\% / 10\% = $ **2.0** — elastic.
Q 09
MR
Medium
When MR = 0 on a linear demand curve, the price elasticity is:
View solution
Correct Option: B
$MR = AR(1 - 1/|E|)$; MR = 0 ⇒ $|E| = 1$ ⇒ **unit elastic**.
Q 10
Linear
Hard
For a linear demand curve, MR:
View solution
Correct Option: B
AR = a − bQ, MR = a − 2bQ — **MR slope = 2 × AR slope**.
Q 11
Geometric
Hard
By the geometric method, the elasticity at a point on a linear demand curve equals:
View solution
Correct Option: B
At a point P, $E_d = \frac{\text{lower segment from P}}{\text{upper segment from P}}$.
Q 12
Perfect comp
Medium
In perfect competition, the demand curve facing the individual firm is:
View solution
Correct Option: B
Firm is a price-taker; demand is horizontal at the market price; AR = MR = P.
Q 13
Total Outlay
Medium
If price falls and total revenue rises, the demand is:
View solution
Correct Option: C
Marshall's TR test — price ↓ and TR ↑ → demand is **elastic**.
Q 14
Determinants
Medium
Which of the following will tend to make demand **less** elastic?
View solution
Correct Option: C
Necessities with no substitutes have *inelastic* demand.
Q 15
Giffen
Hard
A Giffen good has:
View solution
Correct Option: C
Giffen — strongly inferior good; **negative income effect** (price rise raises real income loss → more demand) outweighs the normal substitution effect.
Q 16
Veblen
Medium
Veblen goods are:
View solution
Correct Option: B
Thorstein Veblen (1899) — *The Theory of the Leisure Class*; conspicuous consumption.
Q 17
Maximize TR
Medium
A revenue-maximising firm should produce where:
View solution
Correct Option: B
TR is at maximum when **MR = 0**; profit-maximising condition is MR = MC.
Q 18
Tax
Hard
To maximise tax revenue with minimum loss of consumption, government should tax goods that are:
View solution
Correct Option: B
Inelastic-demand goods retain consumption despite tax — maximum revenue with least quantity loss.
Q 19
Income Elast
Medium
If income rises by 10 % and quantity demanded of a good rises by 20 %, income elasticity is:
View solution
Correct Option: B
$E_y = 20\%/10\% = 2.0 > 1$ → **luxury** good.
Q 20
AR-MR-E
Hard
If AR = ₹20 and price elasticity = 2, MR equals:
View solution
Correct Option: B
MR = AR(1 − 1/E) = 20 × (1 − 0.5) = **₹10**.
22.9 Quick Recall
ImportantQuick recall
- Demand = desire + ability + willingness to pay over a period.
- Law of Demand (Marshall 1890): own-price ↑ → Q ↓ (ceteris paribus).
- Exceptions: Giffen (inferior + dominant income effect), Veblen (conspicuous), speculative, expectations, necessities, ignorance.
- Elasticities: Price (\(E_d = \%\Delta Q / \%\Delta P\)), Income (\(E_y\)), Cross (\(E_{xy}\)), Advertising.
- Degrees: perfectly inelastic (vertical, 0), inelastic, unit elastic (rect. hyperbola, 1), elastic, perfectly elastic (horizontal, ∞).
- Methods: Total Outlay, Percentage, Geometric (lower/upper), Arc.
- AR–MR–E: \(MR = AR(1 − 1/|E|)\). Linear demand → MR slope = 2 × AR slope; AR is unit-elastic at mid-point; MR = 0 → TR maximum, E = 1.
- Engel’s Law (1857) — food share declines with income.
- Income types: normal (\(E_y > 0\)), luxury (\(E_y > 1\)), necessity (\(0 < E_y < 1\)), inferior (\(E_y < 0\)).
- Cross: substitutes (+), complements (−), unrelated (0).
- Tax inelastic-demand goods (sin taxes); tax elastic-demand goods discourages consumption.