A two-period storage equilibrium

Inverse demand in each period is $P(q) = 200 - q$. The interest rate is zero and storage costs $k = 2$ per unit carried from period 1 to period 2. Period-2 harvest is 60 or 140 with equal probability. Storers are competitive and risk neutral. (a) With period-1 harvest $h_1 = 100$, find equilibrium inventory $I$, $S_1$, $\mathbb{E}[S_2]$ and the one-period futures price $F_1 = \mathbb{E}[S_2]$. Is the market at full carry? (b) Repeat with $h_1 = 120$. (c) Interpret (a) and (b) with Propositions 10.3 and 10.4.