Question 6 (b)
A tax of Rs. 10 a unit on consumers with Q = 360 − P and Q = 2P: the price paid and the price received
10 marks
- Time to write
- About 20 minutes
Question
Question 6 (b) · 10 marksFind the price paid by the consumers and the price received by producers when a tax of Rs. 10 per unit is levied on the consumers.
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
Read from the question
- FindFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The demand and supply curves are those printed with Q6 (a) (907-Q6a), which this slot does not repeat; the tax of 10 is kept as printed because the figure is also the mark of this part.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Set-up, the tax as a wedge and the shifted demand curve 2 marks 4 min
- 2 New equilibrium, solved 2 marks 4 min
- 3 Price paid by consumers 2 marks 4 min
- 4 Price received by producers 2 marks 3 min
- 5 Split of the burden checked against the elasticities, revenue and loss 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 20 minutes for 10 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.
The curves and the tax. The curves are those of Q6 (a): demand Q = 360 − P and supply Q = 2P, which without a tax give equilibrium at P = 120 and Q = 240. A tax of Rs. 10 a unit is now collected from consumers. Let Pc be the price consumers pay (including the tax) and Ps the price producers receive. The tax drives a wedge between the two:
Pc = Ps + 10.
How the tax on consumers shifts demand. Buyers decide how much to buy by the full price they pay, Pc. At any price producers receive, buyers now pay Rs. 10 more, so they buy less: a tax collected from buyers shifts the demand curve to the left (down by the tax), while the supply curve stays where it was. In terms of the producers' price, demand becomes
Q = 360 − (Ps + 10) = 350 − Ps.
New equilibrium. The market clears where this demand equals supply at the producers' price:
350 − Ps = 2Ps 3Ps = 350 Ps = 350 ÷ 3 = 116.67 (to two decimals)
Quantity: Q = 2 × 350 ÷ 3 = 700 ÷ 3 = 233.33 units; from demand, Q = 360 − 126.67 = 233.33 as well.
Price paid by consumers and price received by producers.
- Price paid by consumers: Pc = 116.67 + 10 = 380 ÷ 3 = Rs. 126.67.
- Price received by producers: Ps = 350 ÷ 3 = Rs. 116.67.
| Item | Before the tax | After the tax | Change |
|---|---|---|---|
| Price paid by consumers (Rs.) | 120 | 126.67 | +6.67 |
| Price received by producers (Rs.) | 120 | 116.67 | −3.33 |
| Quantity bought and sold | 240 | 233.33 | −6.67 |
Who bears the tax. Although the tax is levied on consumers, its burden is shared, because the price producers receive also falls:
| Share of the Rs. 10 tax | Rs. a unit |
|---|---|
| Borne by consumers (126.67 − 120) | 6.67 |
| Borne by producers (120 − 116.67) | 3.33 |
| Tax per unit | 10 |
Consumers bear two-thirds and producers one-third. This is what the elasticities predict: the burden on sellers ÷ the burden on buyers equals the elasticity of demand ÷ the elasticity of supply. At the original equilibrium these are 0.5 and 1 (Q6 (a)), and 3.33 ÷ 6.67 = 0.5 ÷ 1 = 1/2. Demand is the less elastic side, so buyers bear more of the tax.
The government collects 10 × 233.33 = Rs. 2,333.33. The tax also stops 240 − 233.33 = 6.67 units from being traded; with straight-line curves the deadweight loss on them is the triangle 1/2 × 10 × 6.67 = Rs. 33.33.
Answer. With the Rs. 10 tax on consumers, consumers pay Rs. 126.67 (380/3) a unit and producers receive Rs. 116.67 (350/3) a unit; 233.33 units are traded. Consumers bear Rs. 6.67 and producers Rs. 3.33 of each Rs. 10 of tax.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Set-up, the tax as a wedge and the shifted demand curve | 2 |
| 2 | New equilibrium, solved | 2 |
| 3 | Price paid by consumers | 2 |
| 4 | Price received by producers | 2 |
| 5 | Split of the burden checked against the elasticities, revenue and loss | 2 |
| Total | 10 |
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