How do I find the equilibrium price?

Set quantity demanded equal to quantity supplied, solve for the price, then substitute back to get the quantity.

Does a price change shift the demand curve?

No: a price change is a movement along the same curve; only non-price factors shift the whole curve.

S4 Economics, Paper 3: supply elasticity, price controls and tax incidence

2026-11-01

Supply elasticity shows how producers respond; a price ceiling creates a shortage and a floor a surplus; the less elastic side bears more tax.

Focus　Find equilibrium first, then compare quantities at the ceiling or floor; for tax use the elasticity-sharing rule.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S4 Economics: Demand, Supply and Elasticity
Level	S4

02　Questions (10 items)

FoundationWhat does the price elasticity of supply measure?
FoundationA good’s price rises from $10 to $12 and quantity supplied rises from 50 to 60. What is the price elasticity of supply?
FoundationIf supply of a good is perfectly inelastic and demand increases, what happens to the equilibrium price and quantity?
FoundationWhy is demand usually more elastic for goods with many substitutes?
IntermediateThe government imposes a per-unit tax on producers. How does the supply curve move, and who bears most of the tax?
IntermediateIn a market Qd = 100 – 2P and Qs = 20 + 3P. The government sets a price floor of $20. Find the equilibrium price and the surplus under the floor.
IntermediateIn a market Qd = 200 – 5P and Qs = 5P. The government sets a price ceiling of $16. Find the equilibrium price and the shortage.
ChallengeDemand elasticity is 0.5 and supply elasticity is 2. A per-unit tax of $10 is imposed. Using the elasticity-sharing rule, how much tax per unit do consumers bear?
ChallengeThe price of tea rises 10% and the quantity of coffee demanded rises 15%. Find the cross price elasticity and state whether the goods are substitutes or complements.
Error redoA student says: “An increase in supply must raise producers’ total revenue.” What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	It measures the percentage change in quantity supplied divided by the percentage change in price, showing how strongly producers react to a price change.	Price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price.
2	1.0	Price rises 20% and quantity supplied rises 20%, so 20 / 20 = 1.0, unit elastic.
3	The equilibrium price rises and the equilibrium quantity stays unchanged.	With a vertical supply curve a rightward shift of demand only pushes the price up; quantity stays at the fixed supply.
4	Because when the price rises consumers can easily switch to substitutes, so quantity demanded falls by more.	The more substitutes a good has, the easier consumers switch away when its price rises, so demand is more elastic.
5	The supply curve shifts left (upwards), and the side with the smaller elasticity bears most of the tax.	The tax raises production cost and shifts supply left (up); the burden falls more heavily on the side with the smaller elasticity.
6	Equilibrium price $16. Under the floor quantity demanded is 60 and quantity supplied is 80, so the surplus is 20 units.	100 – 2P = 20 + 3P gives P = 16 and Q = 68. A floor of $20 is above equilibrium, so Qd = 60 and Qs = 80.
7	Equilibrium price $20. Under the ceiling quantity demanded is 120 and quantity supplied is 80, a shortage of 40 units.	200 – 5P = 5P gives P = 20 and Q = 100. At a ceiling of $16, Qd = 120 and Qs = 80.
8	$8 (80% borne by consumers, $2 by producers).	The consumer share is supply elasticity divided by the sum of elasticities: 2 / 2.5 = 0.8, so 10 x 0.8 = $8.
9	Cross elasticity 1.5; it is positive, so the goods are substitutes.	Cross elasticity is 15 / 10 = 1.5. A positive value means a rise in one price raises demand for the other, so they are substitutes.
10	Wrong: extra supply pushes the price down, and if demand is inelastic the price falls proportionally more than quantity rises, so total revenue drops.	The revenue effect depends on demand elasticity; only with elastic demand can an increase in supply raise producers’ revenue.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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