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}