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If the quantity demanded by Xi is given by X1=M/2p and given that p = 10, what is the consumer surplus when p falls to 5?

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Answer to a math question If the quantity demanded by Xi is given by X1=M/2p and given that p = 10, what is the consumer surplus when p falls to 5?

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Seamus
4.9
98 Answers
X_1 = \frac{M}{2p}
Given \(p = 10\):

X_1 = \frac{M}{20}

When \(p\) falls to 5:

X_1' = \frac{M}{10}

Change in quantity demanded:

\Delta X_1 = \frac{M}{10} - \frac{M}{20} = \frac{M}{20}

Change in price:

\Delta P = 10 - 5 = 5

Consumer surplus:

CS = \frac{1}{2} \times \frac{M}{20} \times 5 = \frac{5M}{40} = \frac{M}{8}

Answer:

CS = \frac{M}{8}

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