Fig. 1.
Profit and risk sharing between the risk averse producer and the intermediary. Co-op generates revenue |$R\left( q \right)$| from selling processed products into a downstream market with amount q and uncertain price |$p\left( q \right)$|, which has mean |$\bar P\left( q \right)\,\,$|and variance|$\,{\sigma _p}{\left( q \right)^2}$|. The co-op’s profit is derived after paying the input payment to the farmer. Co-op’s sharing rule distributes the profit along with the associated risk between the farmer and intermediary via patronage refund and dividend, respectively. The patronage refund ratio is denoted by |$\beta $|.