DSE Economics — Price Controls and Per-Unit Tax: Lesson Prep Guide (Tutor Edition)

2026-11-03

Tutor lesson-prep guides · Secondary Economics

Students see a price ceiling and answer only that the price falls; they cannot say how big the shortage is or who gains. One pair of equations drives all three interventions here, so the numbers are calculated, not memorised.

Objectives — Students will be able to: (1) solve Qd = 120 minus 2P and Qs = 3P minus 30 for the equilibrium price of 30 and quantity of 60; (2) calculate the 50-unit shortage under a 20 ceiling and the 50-unit surplus under a 40 floor, and name who gains in each case; (3) calculate the post-tax equilibrium of 33 and 54, tax revenue of 270, a buyer share of 60 per cent and deadweight loss of 15.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Law of demand and supply	When price rises, what happens to quantity demanded and supplied?	Demand falls, supply rises
Meaning of equilibrium	With excess demand, how does price adjust?	It rises until excess demand disappears
Elasticity	What does elasticity greater than one mean?	A one per cent price rise cuts quantity by more than one per cent
Consumer surplus	Which area is consumer surplus on a diagram?	The triangle below demand and above price

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0–8 min	Equation warm-up	Write both equations and ask students to solve them together	Find equilibrium price and quantity
8–20 min	Price ceiling	Draw a 20 ceiling and ask who cannot buy	Compute a 50-unit shortage and predict queues or rationing
20–32 min	Price floor	Draw a 40 floor and ask who cannot sell	Compute a 50-unit surplus and predict purchases or quotas
32–44 min	Per-unit tax	Levy 5 on sellers and rewrite the supply equation	Find the new price 33, quantity 54 and revenue 270
44–52 min	Question drill	One calculation, one diagram, one incidence, one policy judgement	Work independently for eight minutes
52–60 min	Exit check	Mark three written items on the spot	Complete independently

03 Teaching script (read it out)

Scene 1: A ceiling is not simply a bargain

Substitute the 20 ceiling into both equations: quantity demanded is 80 and quantity supplied is 30, so the shortage is 50 units. The price is held down, demand rises, supply falls, and the gap is the shortage. Students must see that the units actually bought go to those who queue earliest or have connections, not to those who need them most.

Ask students: why do queues or black markets appear under a ceiling?

Scene 2: A floor protects sellers and costs a surplus

At a 40 floor, quantity demanded is 40 and quantity supplied is 90, so the surplus is 50 units. Compare the two: a ceiling creates a shortage, a floor creates a surplus, and both push the traded quantity below the equilibrium 60, so both create deadweight loss, only on different sides.

Ask students: what must the government do for a floor to actually bind?

Scene 3: Incidence follows slopes, not the letter of the law

With a 5 tax on sellers, supply becomes Qs = 3(P minus 5) minus 30, giving a price of 33 and quantity of 54. Buyers pay 3 more; sellers keep 28 and lose 2. The buyer share is 60 per cent. Revenue is 5 times 54, which is 270; deadweight loss is half of 5 times the 60 minus 54 fall, which is 15.

Ask students: the law taxes the seller, so why do buyers carry sixty per cent?

04 Question types and worked steps

Type	Example	Steps	Answer
Calculation	Find equilibrium price and quantity	Set Qd equal to Qs, solve for P, substitute back	P equals 30 and Q equals 60
Diagram	Mark the shortage created by a ceiling	Draw the ceiling, read quantities demanded and supplied on it, measure the horizontal gap	The gap is 50 units
Incidence	Split a per-unit tax between buyers and sellers	Rewrite supply, find the new equilibrium, compare prices and seller receipts	Buyers 3 (60 per cent), sellers 2 (40 per cent)
Policy judgement	Should a government use a ceiling to help low-income households?	Name gainers, name losers, propose an alternative and compare	Gainers are those who still buy; losers are those priced out and producers; a direct subsidy may be better

Sanity check (teach this): Sanity check: substitute the new quantity 54 back into both equations; tax revenue uses the new traded quantity, never the old equilibrium; deadweight loss must be smaller than revenue, so any larger figure means a mistake.

05 Independent practice (3 questions)

Question	Answer	What to watch
Find the equilibrium price and quantity	P equals 30 and Q equals 60	Check the student sets Qd equal to Qs before solving
With a ceiling at 20, how large is the shortage?	50 units	Check that demand and supply are each evaluated at the ceiling
With a tax of 5, what are revenue and deadweight loss?	Revenue 270, deadweight loss 15	Check that revenue uses the new quantity

06 Common mistakes and what to say

Mistake	Student writes	Say this
Assuming a ceiling raises quantity traded	The price falls, so more people can buy	Demand rises but supply falls; the short side of the market sets the quantity.
Using the old quantity for revenue	Revenue equals 5 times 60	After the tax only 54 units trade, so revenue must use that quantity.
Equating the taxpayer with the bearer	The seller pays the tax, so the seller bears it all	Prices adjust: buyers move from 30 to 33 and already carry 3 of the 5.
Swapping shortage and surplus	A floor creates a shortage	A floor sits above equilibrium, so supply exceeds demand: that is a surplus.

07 Homework (paper, section and question numbers)

Secondary Economics chapter index — Read the index and copy the equations once by hand
Market equilibrium (S4 chapter) — Redo practice question 1 there to confirm the same equilibrium method
Consumer and producer surplus (S4 chapter) — Draw the two surplus areas and the deadweight loss using this chapter numbers

08 Exit check (last 5 minutes)

Question	Answer	Decision
State the equilibrium price and quantity	30 and 60	If one is missing: reteach solving simultaneous equations
What do a 20 ceiling and a 40 floor create?	A 50-unit shortage and a 50-unit surplus	If swapped: reteach the diagram section
Buyer share of a 5 per-unit tax	60 per cent	If the answer is 100 per cent: reteach incidence

09 Tutor FAQ

Which year level is this for?

S4; S5 revision of efficiency can extend the same equations.

Is 60 minutes enough?

Enough for three acts and one drill; spend five minutes repairing algebra first if needed and move the drill to homework.

Is there practice attached?

The homework section links to the site chapter pages, where answers appear under independent practice.

Find a tutor — free Tutor Registration →

A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.