Quantity guided price setting

We consider an economy with two sectors. The first sector consists of competitively behaving consumers and producers; the second, non-competitive, sector, the P-sector, consists of firms (P- firms) producing commodities (P-goods) that are not produced in the competitive sector. The P- firms receive their gross output levels and the market prices of their inputs as decision parameters. They minimize costs and set prices for their outputs according to a specific pricing rule. There is also a planning agency that ensures that a certain net production (gross production minus the intra-consumption in the P-sector) of the P-goods is achieved. We give assumptions assuring the existence of equilibrium which requires market clearing, meeting the production aspirations of the planning agency, and setting prices for the P-goods which are compatible with market prices in the sense that the market prices cannot be higher than the prices to be charged by the P-firms, and if the target for a P-good is exceeded, the price charged by the P-firm equals the market price. (authors' abstract)