Question 4 (a)

Tables: equilibrium, a tax of 48 levied on buyers, and the deadweight loss

6 marks

Time to write: About 12 minutes
Topic: Tax incidence, deadweight loss and subsidies

Question

Question 4 (a) · 6 marks

Consider a market for tables that is described by these supply and demand functions: Q~S~ = 3P; Q~D~ = 240 – P. Calculate the equilibrium price and the equilibrium quantity of tables. Assume that a tax of 48 is levied on buyers. Work out the new equilibrium. What happens to the price that sellers receive, the price that buyers pay and the quantity sold? Calculate the dead weight loss.

Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.

Before you write

Read off the question and its marks

12 minfor 6 marks

Read from the question

Calculate…What…?3 questions in all: answer every one.
Assume that a tax of 48…The paper fixes this: use it as given, and say so in your answer.
CalculateFormula first, then the working, then the answer with its unit (₹, %, units).

What the paper leaves open

The paper prints the marks once, (6+6+6), at the end of part (c): 6 marks for each of (a), (b), (c). This part carries 6 marks. The paper does not say "per unit"; our reading is a tax charged on each unit bought, collected from buyers.

Write it in this order

Read the data; note exactly what is asked 1 min
1 Equilibrium price and quantity 1 mark 2 min
2 New equilibrium with the tax on buyers 2 marks 3 min
3 Price paid by buyers, price received by sellers and quantity sold 1½ marks 3 min
4 Deadweight loss 1½ marks 2 min
Check: arithmetic, units (₹, %), final answer underlined 1 min

1234

Try it first. About 12 minutes for 6 marks. Write it out, then open the solution.

Solution

Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.

Equilibrium before the tax. Quantity supplied equals quantity demanded:

3P = 240 – P, so 4P = 240, P = 60 and Q = 3 × 60 = 180 tables.

The tax of 48 on buyers. We read the tax as 48 on each table bought, collected from buyers (see the paper note). A tax collected from buyers shifts the demand curve to the left, and the market settles where buyers pay more and sellers receive less. The price buyers pay (Pb) is then the price sellers receive (Ps) plus the tax:

Pb = Ps + 48.

Buyers' demand depends on what they pay: QD = 240 – Pb = 240 – (Ps + 48) = 192 – Ps. Sellers' supply depends on what they receive: QS = 3Ps.

New equilibrium. 3Ps = 192 – Ps, so 4Ps = 192 and:

price received by sellers Ps = 48;
price paid by buyers Pb = 48 + 48 = 96;
quantity sold Q = 3 × 48 = 144 tables (check: 240 – 96 = 144).

Prices and quantity compared.

Item	Before the tax	After the tax	Change
Price paid by buyers	60	96	rises by 36
Price received by sellers	60	48	falls by 12
Quantity sold	180	144	falls by 36
Tax revenue: 48 × 144	0	6,912

The tax is collected from buyers, yet the burden is shared: buyers bear 36 of the 48 and sellers 12, since the incidence of a tax falls on both sides whichever side pays it. Buyers bear the larger share because demand is less elastic than supply at the old equilibrium: demand elasticity = 1 × 60 / 180 = 1/3 and supply elasticity = 3 × 60 / 180 = 1. The buyers' share is to the sellers' share as the supply elasticity is to the demand elasticity, 1 ÷ (1/3) = 3, and indeed 36 ÷ 12 = 3.

Deadweight loss. The tax stops 180 – 144 = 36 tables from being sold. For each of them a buyer valued the table above its cost to a seller, and that gain is now lost to both sides without becoming tax revenue; this lost surplus is the deadweight loss. With straight-line curves it is the triangle with base equal to the fall in quantity and height equal to the tax:

Deadweight loss = ½ × 48 × (180 – 144) = ½ × 48 × 36 = 864.

Answer. Before the tax, P = 60 and Q = 180. With a tax of 48 levied on buyers, buyers pay 96, sellers receive 48, and 144 tables are sold. The price buyers pay rises by 36, the price sellers receive falls by 12, the quantity falls by 36, and the government collects 6,912. The deadweight loss is 864.

Where the 6 marks sit

#	Component	Marks
1	Equilibrium price and quantity	1
2	New equilibrium with the tax on buyers	2
3	Price paid by buyers, price received by sellers and quantity sold	1.5
4	Deadweight loss	1.5
	Total	6

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