ECON10004 · Introductory Microeconomics
Elasticity
Elasticity turns the slope of a demand or supply curve into a unit-free number measuring how much quantity responds to a change in price, income, or another good's price. A demand curve already tells you quantity falls when price rises; elasticity tells you by how much, and lets you compare goods and link price moves to revenue. In ECON10004 this is a calculation staple: the course uses the point formula ε = (dQ/dP)(P/Q), reported as an absolute value, and tests it with clean numeric-entry questions. It sits in Chapter 3, building directly on the supply-and-demand model and its shifters from Chapter 2, and feeds the surplus, tax-incidence, and revenue reasoning that follow. You must compute price elasticity of demand, classify it as elastic, inelastic, or unit-elastic, apply the total-revenue rule, and read income and cross-price elasticities by their sign.
What this chapter covers
- 013.1 Price elasticity of demand (PED) and the point formula
- 02The three regions: elastic, inelastic, unit-elastic
- 033.2 Determinants of PED
- 043.3 The total-revenue rule
- 053.4 Price elasticity of supply
- 063.5 Income elasticity
- 073.6 Cross-price elasticity
Worked example: point elasticity of demand (AFL Grand Final tickets)
- +1Read off the slope: for the linear demand Q = 200,000 − 10,000P, the coefficient on P is the slope, so dQ/dP = −10,000 at every price.
- +1(a) Quantity at P = $10: Q = 200,000 − 10,000×10 = 100,000.
- +1(a) Apply the point formula: ε = (dQ/dP)(P/Q) = (−10,000)×(10 / 100,000) = −1, so demand is unit-elastic at $10.
- +1(b) Quantity at P = $15: Q = 200,000 − 10,000×15 = 50,000; then ε = (−10,000)×(15 / 50,000) = −3, so demand is elastic at $15.
- +1(c) Revenue-maximising price: total revenue peaks where |ε| = 1, which is P = $10; any move up or down from there lowers TR.
- +1(c) Advise on raising price above $15: demand is elastic (|ε| = 3 > 1), so a higher price cuts quantity more than proportionally and reduces total revenue.
Key terms
- Price elasticity of demand (PED)
- The percentage change in quantity demanded divided by the percentage change in price — the responsiveness of quantity to price. Computed by the point formula ε = (dQ/dP)(P/Q) and reported as an absolute value, since demand slopes down and ε is negative.
- Unit-elastic
- Demand for which |ε| = 1, so quantity changes in exactly the same proportion as price. At this point total revenue is at its maximum: any price move, up or down, lowers TR. It separates the elastic region above it from the inelastic region below.
- 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, cutting price raises TR; TR peaks at the unit-elastic point. To raise revenue, push price toward the inelastic region.
- Income elasticity
- εI = %ΔQ / %ΔIncome, the responsiveness of demand to income. A positive value means a normal good (demand rises with income); a negative value means an inferior good (demand falls as income rises).
- Cross-price elasticity
- εAB = %ΔQA / %ΔPB, how the quantity of good A responds to the price of good B. A positive sign means substitutes (tea & coffee), a negative sign means complements (petrol & cars), and roughly zero means the goods are unrelated.
Elasticity FAQ
Is elasticity the same as the slope of the demand curve?
No — this is the most common trap. A straight-line demand curve has a constant slope (dQ/dP is fixed) but a changing elasticity, because ε also depends on P/Q, which changes as you slide along the curve. Elasticity is large (elastic) near the top where P/Q is large and small (inelastic) near the bottom. So 'the steeper curve is more inelastic' is only valid when you compare two curves at the same point; never read elasticity off the slope alone.
Why does the same demand curve give ε = −1 at one price and ε = −3 at another?
Because only the P/Q ratio changes, not the slope. In the AFL ticket example dQ/dP = −10,000 at every price, yet ε moves from −1 at P = $10 to −3 at P = $15 because P/Q rises as you move up the curve. This is why 'raising price above $10 raises revenue' is wrong (you are already at the TR peak), while 'raising price above $15 lowers revenue' is correct (you are in the elastic region).
Which way should I move price to raise revenue?
Push price toward the inelastic region. If demand is inelastic (|ε| < 1), raise the price — you lose little quantity. If demand is elastic (|ε| > 1), cut the price — you gain a lot of quantity. Total revenue peaks where |ε| = 1, so the revenue-maximising price is the unit-elastic point, where any move either way lowers TR.
How do I handle income and cross-price questions — do I need the point formula?
Usually no. For income and cross-price elasticities the marks are in the sign, not a precise number. 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. State the sign, then name the good or the relationship. Reserve the point formula ε = (dQ/dP)(P/Q) for own-price (and supply) elasticity.
Exam move
Run a fixed checklist. First identify which elasticity is asked — own-price, supply, income, or cross-price. For PED, read dQ/dP straight off the demand equation (the coefficient on P), multiply by P/Q at the stated point, take the absolute value, and classify against 1; marks are lost when students confuse the constant slope with the changing elasticity or forget that P/Q differs at every point. For revenue questions, apply the total-revenue rule and remember TR peaks at |ε| = 1. For income and cross-price, the marks live in the sign: + or −, then name the good or relationship. Numeric-entry items want a clean answer such as −1 or −3, so keep the arithmetic tidy.
