Rationed price controls and “prices versus quantities”

We interpret Weitzman's prices‐versus‐quantities model as applying to a private‐good market, and we formulate a “rationed price control,” with quantity determined endogenously as the minimum of supply and demand. With efficient rationing and no externalities, the optimal rationed price control exceeds the price at the expected demand–supply intersection if (the numerical value of) the demand slope curve exceeds the supply slope, and is less than this level for the reverse ordering of slopes. If uncertain demand is steeper than deterministic supply, or if uncertain supply is steeper than deterministic demand, expected welfare is greater with the optimal rationed price control than with the optimal quantity control. We obtain, for any specified price level, a partial ranking of the rationed price control and alternative simple price controls. Extending the model to incorporate externalities, we show that, for demand steeper than supply, with a negative externality on either benefit or cost, the optimal rationed price control exceeds the price at the expected intersection of marginal social benefit and marginal social cost; a converse result also obtains. For an example with inefficient rationing, we show that the optimal pure price control always exceeds the price at the expected intersection of demand and supply.