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Economics 3% exam weight

Elasticity

Part of the ICAN (Nigeria) study roadmap. Economics topic econom-003 of Economics.

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Elasticity

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your ICAN Economics paper.

Elasticity measures how sensitively quantity responds to a change in a determinant — price, income, or the price of another good. For ICAN, four measures matter: PED, YED, XED, and PES, each expressed as a ratio of percentage changes.

MeasureFormulaWhat it tells you
PED%ΔQd ÷ %ΔPPrice sensitivity of buyers
YED%ΔQd ÷ %ΔYWhether a good is normal or inferior
XED%ΔQa ÷ %ΔPbWhether goods are substitutes or complements
PES%ΔQs ÷ %ΔPHow quickly sellers react to price changes
  • Values: |E| > 1 elastic, |E| = 1 unit elastic, |E| < 1 inelastic.
  • A price cut raises total revenue when demand is elastic and lowers it when demand is inelastic — the Total Revenue Test.
  • In Nigeria, staple foods (garri, rice) and fuel are typical inelastic examples examiners use.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students working through the Economics paper over weeks.

Definitions and formula set

Price Elasticity of Demand (PED) is the responsiveness of quantity demanded to a change in own price, holding other determinants constant. ICAN questions usually present the percentage-change form: PED = [(Q1 − Q0)/Q0] ÷ [(P1 − P0)/P0], where Q is units demanded and P is in Naira per unit (₦/unit). The arc (mid-point) version divides each change by the average of the two values, removing bias from the choice of base period.

Income Elasticity of Demand (YED) replaces the denominator with % change in disposable income Y (₦). Cross Elasticity of Demand (XED) uses the % change in the price of another good and identifies substitutes (XED > 0) and complements (XED < 0). Price Elasticity of Supply (PES) mirrors PED on the supply side and is governed by production-side factors rather than consumer preference.

Classification and the Total Revenue Test

Elasticity is read by magnitude, ignoring the negative sign that PED carries because price and quantity move in opposite directions. The Total Revenue Test connects PED to revenue outcomes: if demand is elastic, a fall in ₦ price lifts quantity by a larger percentage, so P × Q revenue rises; if inelastic, the price fall cuts revenue; at unit elasticity revenue is maximised.

Determinants and typical ICAN patterns

ConceptKey point
PED determinantsSubstitutes, proportion of income, necessity vs luxury, time horizon, market definition
PES determinantsSpare capacity, stockholding, factor substitution, production cost, number of sellers
Goods via YEDYED > 0 normal, YED > 1 luxury, 0 < YED < 1 necessity, YED < 0 inferior
XED signsPositive = substitutes, Negative = complements, ~0 = unrelated
  • Movement along a demand curve is a change in quantity demanded — elasticity applies here.
  • A shift of the curve is a change in demand — do not compute elasticity across shifts.
  • Drop the minus sign only after computing; never confuse elasticity with slope.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for candidates building examiner-level command before Professional level.

Mechanism: why elasticity falls along a linear demand curve

A straight-line demand curve has a constant slope (ΔP/ΔQ) but varying elasticity. As price falls and quantity rises, the ratio (P/Q) shrinks, so PED = (dQ/dP) × (P/Q) declines. The upper half of the curve is elastic (|PED| > 1), the midpoint is unit elastic, and the lower half is inelastic (|PED| < 1). This is why revenue peaks at the midpoint of a linear demand curve — a detail ICAN examiners reward in revenue-maximisation questions.

Worked micro-example

Suppose a Lagos retailer raises the price of a bag of rice from ₦50,000 to ₦55,000 and monthly sales fall from 1,200 bags to 1,080 bags.

  • Using the simple formula: %ΔQ = (1,080 − 1,200)/1,200 = −10.00%; %ΔP = (55,000 − 50,000)/50,000 = +10.00%.
  • PED = −10 ÷ 10 = −1.0, i.e. unit elastic. A 10% price rise would leave revenue at ₦1,200 × 50,000 = ₦60,000,000 unchanged at ₦55,000 × 1,080 = ₦59,400,000 (≈ unchanged, confirming unit elasticity).
  • Perfectly inelastic (PED = 0) is a vertical curve — quantity is fixed regardless of price; perfectly elastic (PED = ∞) is horizontal — any price rise wipes out demand.
  • Tax incidence: the more inelastic side of the market bears more of an excise burden, a standard ICAN application for petroleum products.
  • Marshall–Lerner condition: a depreciation of the naira improves the trade balance only when the sum of import and export demand elasticities exceeds 1 — a useful bridge into international trade topics.
  • Common slips: treating inelastic as “no change” (it changes, just by a smaller %); applying PED across curve shifts; confusing XED signs for complements.

Practice prompts

  1. Given the data above, recompute arc elasticity using the mid-point formula and confirm the result.
  2. A firm faces |PED| = 1.4 for product X and |PED| = 0.6 for product Y. Which good should the government tax more heavily, and why?

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