ECB1101 · Introductory Microeconomics
Elasticity
Elasticity turns a curve's slope into a unit-free number measuring how much quantity responds to a change in price, income or another good's price. This is the most calculation-heavy week of ECB1101, and it computes elasticity by the midpoint (arc) method: each percentage change is the change divided by the average of the two values, so the same number comes out whichever direction you move along the curve. You classify price elasticity of demand on its absolute value — |E| > 1 elastic, < 1 inelastic, = 1 unit-elastic — and link it to revenue through the total-revenue rule. Income and cross-price elasticities are read by their sign: positive income elasticity = normal good, negative = inferior good; positive cross-price = substitutes, negative = complements. Price elasticity of supply follows the same midpoint logic.
What this chapter covers
- 014.1 Price elasticity of demand — the midpoint (arc) method
- 02The three regions: elastic, inelastic, unit-elastic
- 034.2 Determinants of PED
- 044.3 The total-revenue rule
- 05Worked midpoint calculation (the Quiz 1 staple)
- 064.4 Income elasticity (sign = normal vs inferior)
- 074.5 Cross-price elasticity (sign = substitutes vs complements)
- 084.6 Price elasticity of supply
Worked example: price elasticity of demand by the midpoint method
- +1%ΔQ = (32 − 40) ÷ [(40 + 32)/2] = −8 ÷ 36 = −0.2222.
- +1%ΔP = (10 − 8) ÷ [(8 + 10)/2] = 2 ÷ 9 = +0.2222.
- +1PED = −0.2222 ÷ 0.2222 = −1.0.
- +1(b) Classify: |PED| = 1, so demand is unit-elastic at this point.
- +1(c) Total-revenue rule: at |PED| = 1, total revenue is at its maximum and is unchanged by this price move.
Key terms
- Price elasticity of demand (PED)
- The percentage change in quantity demanded divided by the percentage change in price, computed by the midpoint method (each change over the average of the two values). Because demand slopes down PED is negative, so the course classifies on the absolute value |PED|.
- Midpoint (arc) method
- An elasticity formula that divides each change by the average of the start and end values rather than the starting value. Its virtue is direction-independence: the elasticity from $8 to $10 equals the elasticity from $10 to $8, because both use the same midpoint as the base.
- Total-revenue rule
- Because TR = P × Q, a price rise lifts P but cuts Q. If demand is inelastic, raising price raises TR; if elastic, raising price lowers TR; TR peaks at the unit-elastic point. To raise revenue, push price toward the inelastic region.
- Income elasticity
- The percentage change in quantity demanded divided by the percentage change in income, by the same midpoint method. Positive means a normal good (demand rises with income); negative means an inferior good (demand falls as income rises).
- Cross-price elasticity
- How the quantity of good A responds to the price of good B. A positive sign means substitutes (a rise in B's price shifts A's demand right), a negative sign means complements, and roughly zero means the goods are unrelated.
Elasticity FAQ
Why does ECB1101 use the midpoint method instead of a simple percentage change?
Because the midpoint (arc) method is direction-independent: dividing each change by the average of the start and end values means you get the same elasticity whether price rises $8 to $10 or falls $10 to $8. A plain percentage-change formula would give two different answers depending on which price you start from. The workshop solutions and quizzes use the midpoint method, so match it exactly: each change over the average, top and bottom.
Is elasticity the same as the slope of the demand curve?
No — this is the most common trap, and the workshop's own true/false item ('linear demand has constant elasticity') is FALSE. A straight-line demand curve has a constant slope but a changing elasticity: it is elastic near the top (high price, low quantity) and inelastic near the bottom. Constant slope, not constant elasticity. So 'the steeper curve is more inelastic' is only valid when you compare two curves at the same point.
Which way should I move price to raise revenue?
Push price toward the inelastic region. If demand is inelastic (|PED| < 1), raise the price — you lose little quantity. If demand is elastic (|PED| > 1), cut the price — you gain a lot of quantity. Total revenue peaks where |PED| = 1, so the revenue-maximising price is the unit-elastic point, where any move either way lowers TR. The drug-interdiction application is the classic case: demand is inelastic, so cutting supply raises price more than proportionally and total spending on the drug rises.
How do I handle income and cross-price questions — do I need a precise number?
Usually the marks are in the sign, not a precise figure. Income elasticity: positive means a normal good, negative means an inferior good. Cross-price elasticity: positive means substitutes, negative means complements, about zero means unrelated. These signs are just the Week 3 demand shifters made numeric. Note that 'income elasticity is always positive' is FALSE — a negative income elasticity is the giveaway for an inferior good.
Exam move
Run a fixed checklist: first identify which elasticity is asked — own-price, supply, income or cross-price. For every one, use the midpoint method (change ÷ average, top and bottom) and show every division, because partial steps still earn marks. For PED, take the absolute value and classify against 1, then apply the total-revenue rule (TR peaks at |PED| = 1). For income and cross-price, the marks live in the sign: + or −, then name the good or the relationship. Watch the two recurring traps: don't read elasticity off the slope (constant slope, changing elasticity), and remember an elasticity is a percentage-on-percentage ratio, not a multiplier — 'PES = 2' means a 1% price rise raises quantity supplied by 2%, not that quantity doubles.
