Price elasticity of demand: measurement, determinants and expenditure

Detail

1. What price elasticity of demand means

• Price elasticity of demand (eD) measures how strongly the quantity demanded of a good reacts when its own price changes.
• Formula: eD = % change in quantity demanded ÷ % change in price = (ΔQ/Q) × (P/ΔP)
• ΔQ = change in quantity. ΔP = change in price.

• Q and P = the starting (initial) quantity and price.

• It is a pure number. It has no unit.

• Both the top and the bottom are percentages, so the units cancel.

• So you can compare the elasticity of rice (kg), milk (litres) and cars (numbers).

• Its sign is negative.

• The law of demand says that when price rises, quantity demanded falls, so the two changes have opposite signs.

• By convention it is quoted in absolute value, written |eD|. So "eD = −0.5" is read as "elasticity of 0.5".

• WHO gives an equivalent definition: the % change in quantity consumed when the price changes by 1% [2].

2. Measuring it: the percentage (point) method

Example 2.2 (Class 12): bananas

• Price rises from ₹5 to ₹7 (P₁ = 5). Quantity falls from 15 to 12 (Q₁ = 15).
• %ΔQ = (12 − 15)/15 × 100 = −20%
• %ΔP = (7 − 5)/5 × 100 = +40%
• |eD| = 20/40 = 0.5. Demand is inelastic, because quantity changed less than price in % terms.

Exercise 22 (Class 12)

• Price rises from ₹4 to ₹5 (+25%). Quantity falls from 25 to 20 units (−20%).
• |eD| = 20/25 = 0.8. Demand is inelastic.

3. Degrees of elasticity

Type	Value of |eD|	Meaning	Curve / typical case
Perfectly inelastic	0	Quantity does not change at all	Vertical curve
Inelastic	< 1	%ΔQ < %ΔP	Essentials (food, salt, medicine)
Unitary elastic	= 1	%ΔQ = %ΔP	Rectangular hyperbola
Elastic	> 1	%ΔQ > %ΔP	Luxuries
Perfectly elastic	∞	At any price above P̄, quantity falls to zero	Horizontal curve

• Elastic demand: |eD| > 1. Buyers react strongly to price.
• Inelastic demand: |eD| < 1. Buyers react only a little.
• Unitary elastic demand: |eD| = 1. The % changes are equal, so total spending does not change.
• Key point: elasticity belongs to a point on the curve, not to the good itself. The same good can be elastic at one price, unitary at another and inelastic at a third.

Real-world estimates for India (beyond NCERT)

• Petrol, diesel and kerosene demand in India is inelastic, but it still responds to price. An IMF working paper (Kapur and Mohan, April 2014) estimated [4]:
• petrol: −0.66
• diesel: −0.36

• kerosene: −0.54

• For comparison, surveys of other countries put the long-run elasticity of gasoline (petrol) demand at −0.6 to −0.9 [4].

• Worked example from the same paper: diesel was under-priced by about ₹11 per litre in 2011-12 and 2012-13, which was about 25% of the actual price [4].
• If the price had been raised by 25%, the fall in quantity ≈ 0.36 × 25% ≈ 9% [4].

• With less diesel used, oil imports and the current account deficit (the amount by which a country's payments to the rest of the world exceed its receipts) would each have been about 0.5% of GDP lower in each of those years [4].

• Tobacco: cigarette elasticities are "nearly always" between 0 and −1 [2].

• In high-income countries they cluster around −0.4 [2].
• In low- and middle-income countries they range from −0.2 to −0.8 (IARC, 2011) [2].

4. Elasticity along a linear demand curve

• Take a straight-line demand curve q = a − bp. Here a and b are positive constants.
• Its slope is fixed: Δq/Δp = −b.
• Elasticity along a linear demand curve: eD = (Δq/Δp) × (p/q) = −bp/q = −bp/(a − bp)
• Elasticity changes as you move along the line, because p/q changes:
• At p = 0 (the point where the line meets the quantity axis): eD = 0.
• Between p = 0 and p = a/2b: |eD| < 1 (inelastic).
• At the midpoint p = a/2b: |eD| = 1 (unitary).
• Above a/2b: |eD| > 1 (elastic).

• At q = 0 (the point where the line meets the price axis): eD = ∞.

• Rule to remember: a straight line has a constant slope but not a constant elasticity. Slope and elasticity are different things.

Exercise 23 (Class 12)

• D(p) = 10 − 3p. At p = 5/3, q = 10 − 5 = 5.
• eD = −3 × (5/3) / 5 = −1. Demand is unitary.
• Check: a/2b = 10/6 = 5/3. So this price is exactly the midpoint.

Extra practice on the same curve

• At p = 1: q = 7, so eD = −3 × 1/7 = −0.43 (inelastic, below the midpoint).
• At p = 2: q = 4, so eD = −3 × 2/4 = −1.5 (elastic, above the midpoint).

5. Geometric measure of elasticity

• Geometric measure of elasticity: a way to read elasticity straight from a diagram by measuring lengths, without doing any calculation with numbers.
• Draw a straight-line demand curve that meets the quantity axis at A and the price axis at B. Take any point D on the line.
• eD = lower segment ÷ upper segment = DA/DB

• The proof uses similar triangles (triangles that have the same shape but different sizes).

• Reading it:

• At A: DA = 0, so eD = 0/DB = 0.
• At B: DB = 0, so eD = DA/0 = ∞.

• At the midpoint: DA = DB, so eD = 1.

• Example: if D divides the line so that DA = 3 cm and DB = 6 cm, then |eD| = 3/6 = 0.5 (inelastic).

6. Constant-elasticity curves (Fig 2.20)

• Vertical demand curve. Demand is perfectly inelastic: |eD| = 0 at every price.
• Horizontal demand curve. Demand is perfectly elastic: |eD| = ∞.

• This is the demand curve facing a perfectly competitive firm. The firm can sell any amount at the market price P̄. If it charges even slightly more, it sells nothing.

• Rectangular hyperbola. This is any curve of the form xy = c, where the product of the two variables is always the same number.

• As a demand curve, p × q = constant, so |eD| = 1 at every point.
• Every rectangle drawn under the curve has the same area. So spending is the same at every price.
• Example: pq = 100. At ₹10, q = 10. At ₹20, q = 5. Spending is ₹100 both times.
• The average fixed cost (AFC) curve has the same shape, because AFC × output = total fixed cost, which is a constant.

7. Beyond NCERT: the arc (midpoint) formula

• The problem: NCERT divides by the starting values. So a price rise and a price fall between the same two points give different answers.
• Example 2.2 in reverse (₹7 → ₹5, quantity 12 → 15): %ΔQ = 3/12 = +25%, %ΔP = 2/7 = −28.6%.

• |eD| = 25/28.6 = 0.875, not 0.5.

• The fix is the arc (midpoint) formula. It divides by the average of the old and new values:

• eD = [ΔQ / ((Q₁ + Q₂)/2)] ÷ [ΔP / ((P₁ + P₂)/2)]

• Example 2.2: average Q = 13.5, average P = 6.

• (3/13.5) ÷ (2/6) = 0.222 ÷ 0.333 = 0.67. You get the same answer in both directions.

8. Determinants of price elasticity of demand

NCERT gives two determinants

• Nature of the good
• Necessities (things people must buy, such as food) are inelastic.

• Luxuries (things people can put off) are elastic.

• Close substitutes (other goods that can do the same job)

• Food as a whole is inelastic.
• But one variety of pulses is elastic. If its price rises, buyers simply switch to another variety.

Other determinants (beyond NCERT)

• Share of the budget
• Salt is inelastic because it is a tiny part of spending. A 20% rise hardly hurts.

• Cars are elastic because they take a large part of income.

• Time horizon

• Demand is more elastic in the long run. People have time to find substitutes, for example by switching to electric vehicles (EVs) when fuel prices stay high.

• The IMF survey figure of −0.6 to −0.9 for gasoline is a long-run estimate [4].

• Habit or addiction

• Tobacco and alcohol are inelastic.

• Cigarette elasticity is nearly always between 0 and −1 [2].

• Income level of the buyer

• Poorer buyers react more strongly to price. A price rise takes a larger share of their income.
• India, 2011-12 Consumer Expenditure Survey data (101,662 households; Selvaraj, Srivastava and Karan) [3]:
  • cigarettes: −0.832 (poorest group) vs −0.2645 (richest group)
  • bidis: −0.4328 (poorest) vs −0.0815 (richest)
  • leaf tobacco: −0.557 (poorest) and −0.4537 (middle group)

• WHO also notes that young people and the poor react most to cigarette prices [2].

• Breadth of definition

• "Food" is less elastic than "basmati rice of brand X". The narrower the category, the more substitutes it has.

• WHO gives a tobacco example: when cigarette prices rise, people buy more roll-your-own tobacco. So taxes should rise evenly across all tobacco products, or buyers just switch to the cheaper one [2].

• Number of uses

• Goods with many uses (electricity, milk) are more elastic. When the price rises, buyers can cut the less important uses.

9. Elasticity and expenditure

• Expenditure on a good = P × Q. This is the total amount buyers spend on it, which is also the seller's total revenue.
• The rule linking elasticity and expenditure:
• Elastic: price and expenditure move in opposite directions. A price cut raises spending.
• Inelastic: price and expenditure move in the same direction. A price rise raises spending.
• Unitary: expenditure does not change.

Table 2.5

Row	Price change	Quantity change	Expenditure	Type
1	+10%	−8%	Rises	Inelastic
2	+10%	−12%	Falls	Elastic
3	+10%	−10%	No change*	Unitary
4	−10%	+15%	Rises	Elastic
5	−10%	+7%	Falls	Inelastic
6	−10%	+10%	No change*	Unitary

*Approximately. For example, 1.1 × 0.9 = 0.99, so spending falls by about 1%. The rule is exact only for very small changes.

The algebra

• New spending = (p + Δp)(q + Δq). So ΔE = qΔp + pΔq + ΔpΔq.
• For small changes, ΔpΔq is tiny and can be ignored. Then ΔE ≈ Δp · q(1 + eD).
• eD < −1 (elastic): (1 + eD) is negative, so ΔE has the opposite sign to Δp.
• eD > −1 (inelastic): (1 + eD) is positive, so ΔE has the same sign as Δp.
• eD = −1 (unitary): ΔE = 0.

Policy link: taxing goods with inelastic demand

• A tax on a good with inelastic demand raises more money for the government.
• The tax raises the retail price.
• Quantity falls by a smaller percentage than the price rises.

• So total government revenue rises, while use of the good still falls. WHO calls this the "win-win" of tobacco excise [2].

• The fall in cigarette use has two parts: fewer smokers and fewer cigarettes per smoker. In many countries these two effects are about equal [2].

10. Exercise traps (Class 12)

• eD = −0.2 and price rises 5%: quantity falls 0.2 × 5 = 1%.
• eD = −0.2 and price rises 10%: quantity falls 2%. Demand is inelastic, so spending rises.

• New spending = 1.10 × 0.98 = 1.078, a rise of about 7.8%.

• A 4% price cut raises spending by 2%: price fell and spending rose, so demand is elastic.

• 0.96 × (1 + x) = 1.02, so x ≈ 6.25% rise in quantity.
• |eD| ≈ 6.25/4 ≈ 1.56.

Prelims Hooks

• eD = (ΔQ/Q) × (P/ΔP). It is unit-free and negative, but quoted in absolute value.
• Along a straight-line demand curve the slope is constant but elasticity is not. It runs from 0 on the quantity axis, to 1 at the midpoint, to ∞ on the price axis.
• Geometric measure: eD = lower segment ÷ upper segment.
• Rectangular hyperbola (pq = constant): |eD| = 1 everywhere and spending is constant. The AFC curve has the same shape.
• Horizontal demand curve = perfectly elastic = the demand curve facing a perfectly competitive firm. Vertical = perfectly inelastic.
• Trap: when demand is inelastic, a price rise increases total spending. When it is elastic, a price cut increases total spending.
• Trap: a steeper line does not mean "inelastic at every point". Only the vertical line (0) and the horizontal line (∞) have constant elasticity. On any other straight line, elasticity changes from point to point.
• IMF estimates (2014) for India: petrol −0.66, diesel −0.36, kerosene −0.54. All are inelastic [4].
• WHO: cigarette elasticity is about −0.4 in high-income countries and −0.2 to −0.8 in low- and middle-income countries [2].
• India, 2011-12 data: the poorest households are the most price-responsive for tobacco. Cigarettes: −0.832 (poorest) vs −0.2645 (richest) [3].

Mains Points

• Taxing goods with inelastic demand (tobacco, fuel) is a strong source of revenue. Because demand is inelastic, the tax raises revenue while use falls only a little [2].
• This is why tobacco carries GST at the highest rate plus extra cesses, and why petroleum products stay outside GST.

• Trade-off: a tax on a necessity with inelastic demand falls hardest on the poor. For those goods, the revenue gain comes at the cost of equity.

• Tobacco taxes help the poor more than their cost suggests. Poorer and younger smokers are the most price-responsive, so they cut back the most [2][3].

• This shrinks their health costs, which reduces the charge that such taxes are regressive (take a larger share of income from the poor than from the rich).

• Rates should be kept uniform across cigarettes, bidis and leaf tobacco. Otherwise smokers switch to the cheaper, lightly taxed product (low bidi elasticity: −0.0815 for the richest) [2][3].

• Fuel pricing reform is supported by elasticity evidence. Demand for oil does respond to price, with diesel at −0.36 [4].

• Market-linked prices (as opposed to government-fixed, subsidised prices) cut consumption and oil imports.
• Diesel priced at market level in 2011-13 would have lowered the current account deficit by about 0.5% of GDP a year [4].

• This supports ending price controls (petrol in 2010, diesel in 2014) and shifting to targeted subsidies.

• Farm prices and the "paradox of plenty". Food demand is inelastic, so a bumper harvest pushes prices down more than quantity rises.

• As a result, farmers' total income can fall.
• This is a reason for price-support tools such as MSP (the minimum support price at which the government offers to buy crops), buffer stocks and better storage.