Negative prices and storage

(a) Using the cash-and-carry argument between two futures maturities $T_1 < T_2$ with storage cost $U$ per barrel (paid at $T_1$) for the interval, show $F_{T_2} \le (F_{T_1} + U)e^{r(T_2 - T_1)}$, so $F_{T_1} \ge F_{T_2}e^{-r(T_2 - T_1)} - U$. (b) Suppose (hypothetically) that on 20 Apr 2020 the June WTI contract traded at $20 and the May contract settled at −$37.63. With $r = 1\%$ and one month between the maturities, what is the smallest storage cost per barrel per month consistent with no arbitrage? Interpret. (c) Why could the price of a cash-settled MCX contract become negative even though no barrel was ever delivered in India?