Demand Analysis

Demand Analysis

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Demand = quantity of a good a consumer is willing and able to buy at various prices during a specific time period, ceteris paribus.

Law of Demand: Inverse relationship between price and quantity demanded — when price rises, quantity demanded falls, and vice versa. Graphically represented by a downward-sloping demand curve from left to right.

Key formulas to memorize:

• PED = % Change in Qd ÷ % Change in Price (where both Qd and Price are positive, PED is always negative; ignore the sign for interpretation — values >1 = elastic, <1 = inelastic, =1 = unitary)
• TR Test: When P falls, if TR rises → demand is elastic (|PED| > 1); if TR falls → demand is inelastic (|PED| < 1); if TR unchanged → unitary elastic (|PED| = 1)
• YED = % Change in Qd of Good X ÷ % Change in Income (positive for normal goods, negative for inferior goods)
• XED = % Change in Qd of Good A ÷ % Change in Price of Good B (positive = substitutes, negative = complements)

3 high-yield exam pointers for CS Executive:

1. Numerical problems on PED calculation are most frequent — always compute percentage changes correctly (use old base for denominator).
2. XED sign matters critically: a positive XED value indicates substitutes (e.g., tea and coffee), a negative value indicates complements (e.g., printers and ink cartridges).
3. The Total Revenue Test is a shortcut in elasticity questions — memorize the TR-P relationship table before the exam.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Definition and Scope

Demand in economics means the desire to purchase a commodity backed by willingness to pay and the ability to buy. The effective demand concept requires all three elements: desire, purchasing power, and willingness to spend. For CS Executive, the formal definition is: “The quantity of a commodity that a consumer wishes to purchase at a given price per unit of time, other things being equal.”

The Law of Demand states that, other factors (income, tastes, prices of related goods, expectations, number of buyers) remaining constant, as the price of a commodity falls, its quantity demanded rises, and as price rises, quantity demanded falls.

Types of Market Demand Determinants

Five key factors shift the entire demand curve (as opposed to movement along the curve caused by price changes):

| Factor | Effect on Demand Curve | |---|---|---| | Increase in consumer income (normal goods) | Rightward shift | | Rise in price of a substitute | Rightward shift | | Rise in price of a complement | Leftward shift | | Favorable change in taste/preference | Rightward shift | | Increase in population/market size | Rightward shift |

Movement along the curve occurs when the commodity’s own price changes (extension or contraction). Shift of the curve occurs when any determinant other than the commodity’s own price changes.

Price Elasticity of Demand (PED)

PED measures the degree of responsiveness of quantity demanded to a change in the commodity’s own price.

Formula: PED = (ΔQ/Q) ÷ (ΔP/P) = (ΔQ/ΔP) × (P/Q)

The midpoint method is preferred for accuracy: PED = (Q₂ − Q₁) ÷ [(Q₂ + Q₁)/2] ÷ (P₂ − P₁) ÷ [(P₂ + P₁)/2]

A PED value of −2.5 means a 1% increase in price causes a 2.5% decrease in quantity demanded — demand is elastic (more responsive than proportionately). A PED of −0.4 indicates inelastic demand.

Total Revenue (TR) Test for Elasticity

TR = P × Q

• When PED > 1 (elastic): A price cut increases TR
• When PED = 1 (unitary): Price change leaves TR unchanged
• When PED < 1 (inelastic): A price cut reduces TR

CS Executive frequently asks: “A firm lowers price from ₹50 to ₹45 and finds TR falls from ₹10,000 to ₹9,000. Find PED and comment.” The answer: revenue fell, so demand is inelastic.

Income Elasticity of Demand (YED)

YED = % Change in Qd ÷ % Change in Income

• YED > 0: Normal good (necessities have 0 < YED < 1; luxuries have YED > 1)
• YED < 0: Inferior good
• YED = 0: Necessity (income change does not affect quantity demanded)

Cross Elasticity of Demand (XED)

XED = % Change in Qd of Good A ÷ % Change in Price of Good B

This is where CS Executive exam-setters commonly test conceptual clarity:

• Positive XED → Goods are substitutes (rise in tea price makes coffee relatively cheaper, increasing coffee demand)
• Negative XED → Goods are complements (rise in petrol price reduces scooter demand)
• Zero XED → Unrelated goods

Exceptions to the Law of Demand

1. Giffen goods: Inferior goods where the income effect outweighs the substitution effect, producing a direct price-demand relationship. Classic example: cheap bread for a low-income household — as bread price falls, the household buys less bread (because they’re richer and can now afford better food).
2. Veblen goods: Luxury goods (diamonds, designer bags) where a higher price signals prestige, increasing demand.
3. Speculative demand: Stocks and real estate — people buy more when prices are rising expecting further increases.
4. Habitual consumption: Addictive goods (cigarettes, coffee) where consumers are insensitive to price changes.

Exam Question Patterns

CS Executive Economics typically tests this through:

• Numerical questions requiring PED calculation using the midpoint formula (4–6 marks)
• Diagram-based questions asking to identify elastic, inelastic, and unitary elastic segments on a linear demand curve (the same straight line has different elasticity at different points — the midpoint is unitary elastic, upper half is elastic, lower half is inelastic)
• Assertion-reason questions on XED sign and its implication for substitute/complement classification
• TR analysis questions where a change in price is given and students must determine the elasticity type

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Mathematical Foundations of Linear Demand Curve Elasticity

On a straight-line downward-sloping demand curve P = a − bQ, elasticity varies systematically along the curve even though the slope (−b) is constant. This is because the elasticity formula incorporates the P/Q ratio:

PED = (dQ/dP) × (P/Q)

Since dQ/dP is constant (the reciprocal of slope), elasticity is higher at higher prices and lower at lower prices. Specifically:

• At the midpoint of the curve: P = a/2, Q = a/(2b) → PED = −1
• At the upper segment (near price axis): P is high, Q is low → |PED| > 1 (elastic)
• At the lower segment (near quantity axis): P is low, Q is high → |PED| < 1 (inelastic)

This has a critical managerial implication for CS Executive students: a firm selling an inelastic product can raise prices to increase revenue, while an elastic product requires lowering prices to boost revenue. A monopolist optimally sets output where MR = MC, which requires understanding how revenue changes with output.

Edge Cases and Common Errors

Error 1 — Wrong sign convention: PED is technically negative due to the inverse relationship. However, exam answers should focus on the absolute value for elasticity classification. State “demand is elastic with |PED| = 2.5” rather than “PED = −2.5” unless the question explicitly asks for sign.

Error 2 — Confusing movement along vs. shift: A question stating “price of apples falls, quantity demanded rises” describes movement along the same demand curve. If the question says “income rises, quantity demanded of normal goods rises,” the entire demand curve shifts rightward. Mixing these up in theory questions loses marks.

Error 3 — YED sign misinterpretation: For a luxury good with YED = +3.5, a 10% rise in income increases quantity demanded by 35% — this is correct. But for an inferior good with YED = −2.1, a 10% income increase reduces quantity demanded by 21%. The sign must be interpreted correctly.

Relationship Between PED, AR, and MR

Average Revenue (AR) is simply the price per unit at each quantity — it is the demand curve itself. For a linear demand curve P = a − bQ:

• AR = P = a − bQ (the demand curve)
• TR = P × Q = aQ − bQ²
• MR = dTR/dQ = a − 2bQ (which is twice as steep as the AR curve)

The MR curve lies halfway between the origin and the AR curve at each output level. At Q = a/(2b) (the midpoint), MR = 0. This point separates profitable output (MR > 0, where TR is rising) from unprofitable output (MR < 0, where TR is falling).

Numerical Worked Example

Question: Demand function: Q = 100 − 2P. At P = ₹20, calculate: (a) PED (b) If price falls to ₹15, what is the new Q and new PED? (c) What happens to TR in each case?

Solution: (a) At P = 20: Q = 100 − 40 = 60 PED = (dQ/dP) × (P/Q) = (−2) × (20/60) = −2/3 ≈ −0.67 Since |PED| < 1, demand is inelastic at this price.

(b) New price = 15: Q = 100 − 30 = 70 Using midpoint method: ΔQ = 10, ΔP = −5 Average Q = 65, Average P = 17.5 PED = (10/65) ÷ (−5/17.5) = 0.154 ÷ (−0.286) = −0.54 Demand remains inelastic.

(c) At P = 20, TR = ₹1,200 At P = 15, TR = ₹1,050 TR falls because price cut increases quantity but the increase is proportionally smaller than the price reduction — consistent with inelastic demand.

Connections to Adjacent Topics

Demand Analysis forms the foundation for:

• Supply Analysis: Mirrors demand concepts but with a direct (positive) price-quantity relationship; both feed into equilibrium price determination
• Elasticity of Supply (ES): Uses the same percentage-change methodology but measures producer response to price changes
• Consumer’s Equilibrium: The demand curve is the individual’s marginal benefit curve, which directly connects to utility analysis and indifference curve theory (typically covered in the next chapter)
• Market Structures: Perfect competition relies on the firm’s perfectly elastic demand curve (a horizontal line at market price), while a monopoly faces the downward-sloping market demand curve — this is where elasticity determines the monopoly’s pricing power

Practice Prompts

1. From CS Executive past paper: “A commodity’s price falls from ₹8 to ₹7 per unit, and quantity demanded rises from 150 to 200 units. Calculate PED using the midpoint formula and classify the demand.” (Work through: ΔQ = 50, Average Q = 175, ΔP = −1, Average P = 7.5 → PED = 50/175 ÷ (−1/7.5) = 0.286 ÷ (−0.133) = −2.14 → Elastic)

2. Conceptual: “Two goods have XED = +4.2. If the price of Good A rises by 10%, by what percentage does the quantity demanded of Good B change? Are these goods substitutes or complements? If the cross elasticity were instead −0.8, what would this indicate?” (Answer: Good B demand rises by 42% → strong substitutes; negative XED indicates complements)

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