The demand function is $p = 50 - x^{2}$ , and the market sells 5 units. What is the consumer surplus?

₹

\frac{250}{3}

Correct answerYour answer₹125Correct answerYour answer₹

\frac{500}{3}

Correct answerYour answer₹

\frac{625}{3}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

At $x_0 = 5$ the price is $p_0 = 50 - 25 = 25$ , so consumers pay $25 \times 5 = 125$ .
$CS = \int_{0}^{5} (50 - x^{2})\,dx - 125 = \left(250 - \frac{125}{3}\right) - 125 = \frac{250}{3}$ rupees, about ₹83.33.

Worth noting

₹125 treats the demand curve as a straight line from $(0, 50)$ to $(5, 25)$ , a triangle; the curve bulges above it.

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

The demand function is p=50−x2p = 50 - x^{2}p=50−x2, and the market sells 5 units. What is the consumer surplus?