The demand function is p = D(x), and the market clears at quantity x₀ and price p₀. Which expression is the consumer surplus?

Question 44

MediumOriginal question

The demand function is $p = D(x)$ , and the market clears at quantity $x_0$ and price $p_0$ . Which expression is the consumer surplus?

p_0x_0 - \int_{0}^{x_0} D(x)\,dx

Correct answerYour answer

\int_{0}^{x_0} D(x)\,dx

Correct answerYour answer

\int_{0}^{p_0} D(x)\,dx - p_0x_0

Correct answerYour answer

\int_{0}^{x_0} D(x)\,dx - p_0x_0

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\int_{0}^{x_0} D(x)\,dx$ is what consumers would be willing to pay for $x_0$ units; $p_0x_0$ is what they pay.
The surplus is the difference: the area between the demand curve and the price line.

Worth noting

$p_0x_0 - \int_{0}^{x_0} D(x)\,dx$ is the same area with the sign reversed: it is negative.

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