Storage and convenience yield

(a) Prove Prop. 7.11 and explain why it is an inequality. (b) (Hypothetical numbers.) MCX crude spot is equivalent to ₹7,800 a barrel; the one-month future (30 days) is ₹7,700 and the two-month future (61 days) is ₹7,650. With $r = 5.5\%$ and storage $u = 2\%$ a year, compute the implied convenience yield for each maturity. (c) (Hypothetical numbers.) Gold spot is ₹1,38,900 per 10 g and a 91-day MCX future trades at ₹1,40,600. With $r = 5.5\%$ and $u = 0.2\%$, compute the fair price under Prop. 7.10 and the implied $y$. Interpret a small positive $y$ for gold.