Question 7 (c)
A ₹32 tax on sellers of soap: new equilibrium, prices and deadweight loss
8 marks
- Time to write
- About 16 minutes
Question
Question 7 (c) · 8 marksThe market for soap is given by the following supply and demand functions: Qs = 3P and Qd = 160 – P where P is the price of soap. Compute the equilibrium price and quantity of soaps. Suppose a tax of ₹32 is levied on sellers. Now solve for the new equilibrium. What will happen to the price received by the seller, the price paid by the buyers and the quantity sold? Calculate the deadweight loss caused by this tax.
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
- Compute…What…?Calculate…3 questions in all: answer every one.
- ComputeFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Equilibrium price and quantity before the tax 1½ marks 3 min
- 2 Supply shifted by the tax and the new equilibrium solved 2 marks 4 min
- 3 Price paid by buyers, price received by sellers, quantity sold 2 marks 3 min
- 4 Deadweight loss computed and explained 2½ marks 4 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 16 minutes for 8 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. The market clears where quantity demanded equals quantity supplied:
3P = 160 − P, so 4P = 160, P = ₹40 and Q = 3 × 40 = 120 soaps.
The tax on sellers. A tax of ₹32 a unit is collected from sellers, so a seller keeps only the price buyers pay less ₹32. If Pb is the price buyers pay, sellers receive Ps = Pb − 32 and supply Qs = 3(Pb − 32). The tax drives a wedge of ₹32 between the two prices.
New equilibrium. 3(Pb − 32) = 160 − Pb, so 3Pb − 96 = 160 − Pb, 4Pb = 256 and:
| Before the tax | After the tax | Change | |
|---|---|---|---|
| Price paid by buyers (₹) | 40 | 64 | +24 |
| Price received by sellers (₹) | 40 | 32 | −8 |
| Quantity sold | 120 | 96 | −24 |
Check: demand 160 − 64 = 96 and supply 3 × 32 = 96.
What happens to prices and quantity. Buyers pay ₹24 more and sellers receive ₹8 less; together, 24 + 8 = 32, the whole tax. Although the tax is collected from sellers, its burden is shared by both sides. Buyers bear three-quarters of it here because supply responds more to price than demand does (supply changes by 3 units per rupee, demand by 1), and the side that responds less bears more of a tax. The quantity sold falls from 120 to 96.
Deadweight loss. The tax raises 32 × 96 = ₹3,072 for the government, but the 24 soaps that are no longer traded were each worth more to some buyer than they would have cost a seller to make; that gain is now lost to everyone. With straight-line curves the loss is the triangle between them over the lost units:
Deadweight loss = ½ × tax × fall in quantity = ½ × 32 × (120 − 96) = ½ × 32 × 24 = ₹384.
Answer. Before the tax the price is ₹40 and 120 soaps are sold. With the ₹32 tax on sellers, buyers pay ₹64, sellers receive ₹32, and 96 soaps are sold: the buyer price rises by ₹24, the seller price falls by ₹8 and the quantity falls by 24. The tax raises ₹3,072 and causes a deadweight loss of ₹384.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Equilibrium price and quantity before the tax | 1.5 |
| 2 | Supply shifted by the tax and the new equilibrium solved | 2 |
| 3 | Price paid by buyers, price received by sellers, quantity sold | 2 |
| 4 | Deadweight loss computed and explained | 2.5 |
| Total | 8 |
Report a problemopens an email to admin@getkunji.com with the question ID2070-Q7calready filled in.