Question 3 (i)(a)
A price ceiling of $108 with Qs = 2P and Qd = 360 - P
3 marks
- Time to write
- About 6 minutes
Question
Question 3 (i)(a) · 3 marks- The equations of supply and demand are given as following:
Q^s^ = 2P, Q^D^ = 360-P
- If the government imposes a price ceiling of $108, what are 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
As printed, the price ceiling is the first of three parts on one pair of equations; the equations are repeated in each part. "given as following" is as printed.
Write it in this order
- 1 Equilibrium price and quantity 1 mark 2 min
- 2 Ceiling binding: price, Qd and Qs 1½ marks 3 min
- 3 Size of the shortage ½ mark 1 min
Short on time? Step 2 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.
Free-market equilibrium. Equilibrium is where quantity demanded equals quantity supplied: 2P = 360 - P, so 3P = 360, P = $120 and Q = 2 x 120 = 240 units.
Is the ceiling binding? A price ceiling is a legal maximum price. It matters only if it is set below the equilibrium price; then demand exceeds supply and there is a shortage. Here $108 < $120, so the ceiling binds and the price is held at $108.
| Item | Value |
|---|---|
| Price | $108 |
| Quantity demanded: 360 - 108 | 252 units |
| Quantity supplied: 2 x 108 | 216 units |
| Shortage: 252 - 216 | 36 units |
Answer. The price is $108; quantity demanded is 252 and quantity supplied is 216, so there is a shortage of 36 units. Only 216 units are actually bought and sold, because buyers cannot buy what sellers do not supply; the excess demand must be rationed by queues, ration cards or a black market.
Where the 3 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Equilibrium price and quantity | 1 |
| 2 | Ceiling binding: price, Qd and Qs | 1.5 |
| 3 | Size of the shortage | 0.5 |
| Total | 3 |
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