Supply multipliers in a centrally planned economy with a private sector

A simple model of a centrally planned economy is developed with a state sector and private sector, and with a supply constraint affecting state sector output. In such a model, a supply multiplier can be derived under the same conditions which would make an increase in state sector prices an effective means of reducing shortage. Moreover, a one-sector constrained equilibrium model of the state sector does not yield misleading results by ignoring the private sector; and the private sector price level is a reliable indicator of shortage in the economy.