The earphone price rises to ₹41.

Question 54

HardOriginal question

The demand function for a brand of earphones is $p = 50 - x^{2}$ , where $p$ is the price in rupees and $x$ the quantity demanded. The market price is ₹14.

The earphone price rises to ₹41. What is the consumers' surplus now?

₹18Correct answerYour answer₹27Correct answerYour answer₹36Correct answerYour answer₹144Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$50 - x^{2} = 41$ gives $x = 3$ .
$CS = \int_0^{3}(50 - x^{2})\,dx - 41 \times 3 = (150 - 9) - 123 = 18$ .

Worth noting

₹27 forgets that $\frac{x^{3}}{3}$ at $x = 3$ is 9, using $x^{2}$ instead.

Concept: How a price rise cuts the surplus
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsConsumer surplus

Practise this chapter →

Ten questions from Consumer & Producer Surplus, at your own pace.

Practise this chapter →

Ten questions from Consumer & Producer Surplus, at your own pace.

The earphone price rises to ₹41.

Question 54

Explanation