Question 5 (a)
Brazil's television market: surplus changes when the world price falls by ₹120
6 marks
- Time to write
- About 12 minutes
Question
Question 5 (a) · 6 marksAssume Brazil is an importer of televisions and that there are no trade restrictions. Brazilian consumers buy 15,000 televisions per year, of which 6,000 are produced domestically and 9,000 are imported. Suppose that a technological advance among Korean television manufacturers causes the world price of televisions to drop by ₹120. After the fall in price, Brazilian consumers buy 18,000 televisions, of which 3,000 are produced domestically and 15,000 are imported. Calculate the change in consumer surplus, in producer surplus and in total surplus caused by the price reduction of ₹120.
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
- Assume Brazil is an importer of…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.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Change in consumer surplus 2½ marks 4 min
- 2 Change in producer surplus 2 marks 3 min
- 3 Change in total surplus 1½ marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
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.
The setting. Brazil imports televisions and trades freely, so its domestic price equals the world price. When the world price falls, the domestic price falls with it. In an importing country a lower price benefits domestic buyers and harms domestic sellers, while the country as a whole gains, because the buyers' gain is larger than the sellers' loss. Consumer surplus is measured by the area that lies under the demand curve but over the price line; producer surplus by the area that lies over the supply curve but under the price line. We take Brazil's demand and supply curves to be straight lines between the two points given.
| Item (televisions a year) | Before the fall | After the fall |
|---|---|---|
| Bought by consumers | 15,000 | 18,000 |
| Produced at home | 6,000 | 3,000 |
| Imported | 9,000 | 15,000 |
Change in consumer surplus. The price falls by ₹120. Consumer surplus rises by the area between the old and new prices, to the left of the demand curve, which has two parts:
- the 15,000 televisions that were already being bought now cost ₹120 less each: 120 × 15,000 = ₹18,00,000;
- the 3,000 extra televisions bought because of the lower price add a triangle: ½ × 120 × 3,000 = ₹1,80,000.
Gain in consumer surplus = 18,00,000 + 1,80,000 = ₹19,80,000, the same as 120 × (15,000 + 18,000) / 2.
Change in producer surplus. Producer surplus falls by the area between the two prices, to the left of the supply curve:
- the 3,000 televisions still made at home sell for ₹120 less each: 120 × 3,000 = ₹3,60,000;
- on the 3,000 televisions no longer made at home, sellers lose the triangle ½ × 120 × 3,000 = ₹1,80,000.
Loss in producer surplus = 3,60,000 + 1,80,000 = ₹5,40,000, the same as 120 × (6,000 + 3,000) / 2.
Change in total surplus. Total surplus changes by the consumers' gain less the producers' loss:
19,80,000 – 5,40,000 = ₹14,40,000 (a gain).
As a check, this equals the area between the two prices and between the import levels, 120 × (9,000 + 15,000) / 2 = 14,40,000: the extra gain from buying more of the country's televisions from abroad at the lower world price.
Answer. The fall of ₹120 in the world price raises Brazilian consumer surplus by ₹19,80,000, lowers producer surplus by ₹5,40,000, and raises total surplus by ₹14,40,000.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Change in consumer surplus | 2.5 |
| 2 | Change in producer surplus | 2 |
| 3 | Change in total surplus | 1.5 |
| Total | 6 |
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