Question 3 (i)(c)
A tax of $36 a unit on producers with Qs = 2P and Qd = 360 - P
3 marks
- Time to write
- About 6 minutes
Question
Question 3 (i)(c) · 3 marks- The equations of supply and demand are given as following:
Q^s^ = 2P, Q^D^ = 360-P
- Rather than controlling the price, the government levies a tax on producers of $36 per unit.What will be the price, quantity demanded, quantity supplied and the size of shortage or surplus?
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
What the paper leaves open
"given as following" is as printed.
Write it in this order
- 1 Supply after the tax and new equilibrium 1½ marks 3 min
- 2 Price paid, price received, quantity 1 mark 2 min
- 3 No shortage or surplus, with the reason ½ mark 1 min
Short on time? Step 1 carries 1½ of the 3 marks: guard its minutes.
Try it first. About 6 minutes for 3 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 tax shifts supply. A tax collected from sellers drives a wedge between the price buyers pay (P) and the price sellers keep (P - 36). Sellers now supply what they would have supplied at the price they keep, so the supply curve shifts up (left) by the tax: Qs = 2(P - 36) = 2P - 72.
New equilibrium. 2P - 72 = 360 - P, so 3P = 432 and P = $144 (the price buyers pay). Sellers keep 144 - 36 = $108. Quantity: Qd = 360 - 144 = 216, and Qs = 2 x 108 = 216.
| Item | Before the tax | After the tax |
|---|---|---|
| Price paid by buyers | $120 | $144 |
| Price received by sellers | $120 | $108 |
| Quantity bought and sold | 240 | 216 |
Who bears the tax. Buyers pay $24 more and sellers receive $12 less: the $36 tax is shared, two-thirds by buyers and one-third by sellers, although it is levied on sellers; whoever pays the tax to the government, its burden is shared. The government collects 36 x 216 = $7,776.
Answer. With the tax, buyers pay $144, sellers receive $108, and 216 units are demanded and supplied. Unlike a price control, a tax lets the market clear at the new price, so there is no shortage and no surplus; the effect is a smaller quantity (216 instead of 240), not an imbalance.
Where the 3 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Supply after the tax and new equilibrium | 1.5 |
| 2 | Price paid, price received, quantity | 1 |
| 3 | No shortage or surplus, with the reason | 0.5 |
| Total | 3 |
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