8 min readConcept sheet5-mark calculation; 10 marks with a per-unit tax

Demand, supply and market equilibrium

Demand slopes downward and supply slopes upward. Market equilibrium is the price where quantity demanded equals quantity supplied: solve the two equations together.

Linear demandp = a − bq (b > 0)

Linear supplyp = c + dq (d > 0)

EquilibriumDemand price equals supply price

Per-unit tax tSupply becomes p = c + dq + t

Market model

Demand (price form)p = a − bq: price falls as quantity rises

Supply (price form)p = c + dq: price rises with quantity

Equilibriuma − bq = c + dq, so q* = (a − c) ÷ (b + d)

Equilibrium pricePut q* back into either equation

Per-unit tax t on sellersSupply shifts up: p = c + t + dq

Price above equilibriumSurplus (supply > demand)

Price below equilibriumShortage (demand > supply)

Finding equilibrium (price form)

Problem

Vegetable demand is p = 200 − 3q and supply is p = 40 + 5q, where p is Rs. per kg and q is thousands of kg. Find the equilibrium.

Working

At equilibrium the two prices are equal: 200 − 3q = 40 + 5q.
200 − 40 = 5q + 3q, so 160 = 8q and q = 20.
p = 200 − 3(20) = 140. Check with supply: 40 + 5(20) = 140. ✓

Answer

q = 20 (20,000 kg) at Rs. 140 per kg.

Finding equilibrium (quantity form)

Problem

Demand is Qd = 1,000 − 4p and supply is Qs = 6p − 200. Find the equilibrium price and quantity.

Working

Set Qd = Qs: 1,000 − 4p = 6p − 200.
1,200 = 10p, so p = 120.
Q = 1,000 − 4(120) = 520. Check: 6(120) − 200 = 520. ✓

Answer

p = Rs. 120 and Q = 520 units.

Effect of a per-unit tax

Problem

In the vegetable market above (demand p = 200 − 3q, supply p = 40 + 5q), the government places a tax of Rs. 16 per kg on sellers. Find the new equilibrium, who bears the tax, and the tax collected.

Working

New supply: p = 40 + 16 + 5q = 56 + 5q.
200 − 3q = 56 + 5q, so 144 = 8q and q = 18.
Buyers' price p = 200 − 3(18) = 146. Sellers keep 146 − 16 = 130.
Buyers pay 146 − 140 = Rs. 6 more; sellers get 140 − 130 = Rs. 10 less.
Tax collected = 16 × 18,000 kg = 288,000.

Answer

q = 18 (18,000 kg), buyers pay Rs. 146, sellers keep Rs. 130; tax revenue Rs. 288,000.

Building a demand line from data

Problem

A Matara shop sells 500 units a week at Rs. 100 and 420 units at Rs. 120. Find the linear demand function p in terms of q.

Working

Points (q, p): (500, 100) and (420, 120).
Slope = (120 − 100) ÷ (420 − 500) = 20 ÷ (−80) = −0.25.
p − 100 = −0.25(q − 500), so p = −0.25q + 125 + 100 = 225 − 0.25q.
Check q = 420: 225 − 105 = 120. ✓

Answer

p = 225 − 0.25q

In Sri Lankan business

Vegetable prices at the Dambulla Dedicated Economic Centre move daily as farmers' supply meets traders' demand. The meeting point is the equilibrium price, which is why prices jump after floods cut supply.

Exam angle

Short answer: “What happens if the market price is set above equilibrium?” Quantity supplied exceeds quantity demanded: a surplus.

Structured question: “Demand Qd = 1,000 − 4p, supply Qs = 6p − 200. Find the equilibrium.” 1,000 − 4p = 6p − 200, so p = 120 and Q = 520.

Essay: “Demand p = 200 − 3q, supply p = 40 + 5q. Find the equilibrium, then the effect of a Rs. 16 per-unit tax on sellers.” Before: q = 20, p = 140. After: q = 18, buyers pay 146, sellers keep 130.

Remember it

Equilibrium = set demand equal to supply, solve for one variable, then substitute back for the other. A tax on sellers lifts the supply line up by the tax.