Setting price controls while facing variable or uncertain market conditions

Price controls under variable or uncertain market conditions do not lead to market equilibrium. Under different assumptions for the rationing mechanism during shortages and surpluses, I find, assuming small market shocks, that the optimal regulated price can be related in a simple way to the relative slopes of the marginal benefit and marginal cost functions. In addition, if the consumption price may differ from the production price, then consumers should pay less than or equal to what producers receive, implying possibly a unit subsidy to market transactions.