Goal: move from quick multiple-choice recognition to full reasoning and computation.
Elasticity asks: when X changes by a percentage, how much does Y change by a percentage?
Price elasticity of demand = % change in quantity demanded / % change in price
Classification uses absolute value:
Revenue rule: if demand is elastic, raising price lowers total revenue. If inelastic, raising price raises total revenue.
Use midpoint to avoid getting different answers based on direction:
%ΔQ = (Q2-Q1)/((Q1+Q2)/2)
%ΔP = (P2-P1)/((P1+P2)/2)
E = %ΔQ / %ΔP
Common trap: standard percent change from an arbitrary base gives asymmetric answers.
Narrow market: "Coke at one gas station".
Broad market: "all soda in the U.S.".
Narrower definition means more close substitutes nearby, so demand is more elastic.
As market definition broadens, elasticity usually falls because there are fewer near substitutes for the whole category.
Along a straight-line demand curve, elasticity changes by location: top section is elastic, midpoint is unit elastic, bottom section is inelastic.
| Problem | Result | Reasoning Target |
|---|---|---|
| Q1: Qd=20-P, Qs=2P-4 | P*=8, Q*=12. Binding floor if Pfloor>8. At P=10: surplus=6. | Can you derive equilibrium and binding condition without guessing? |
| Q2 with tax t=50 | Before tax: P*=200, Q*=30. After tax: buyers pay 237.5, sellers receive 187.5, Q=26.25. | Practice wedge logic: buyer price - seller price = tax. |
| Q3 midpoint elasticity of supply | ~0.485 (inelastic) | Distinguish elasticity from slope. |
| Q4 income elasticity | negative (~ -0.17 midpoint) | Negative income elasticity => inferior good. |
| Q5 cross-price | Exy=-0.4 and orange price -3% => apple demand +1.2% | Negative cross-price means complements. |
| Q6 demand Q=50-0.5P, P:60->40 | Standard method: 1.5; midpoint: 1.0 | Know why midpoint is preferred for interval comparisons. |
1) Explain why your tea-coffee logic gives a positive cross-price elasticity without assuming tea demand is elastic.
2) For Q = 50 - 0.5P, compute point elasticity at P=60 and P=40 and explain why it changes along one line.
3) Give one case where slope is the same but elasticity differs.
If you can answer these clearly, you are above worksheet depth.