An important feature of the mixed economic system under consideration, besides the presence of a mixed production sector, is that two different regulation mechanisms function jointly: central planning and flexible market prices. Thus, this model is characterized by the presence of dual markets. In the first market, prices are stable and the allocation of commodities is determined by rationing schemes and governmental orders. In the second market, prices are flexible and are formed by the standard mechanism of equating demand and supply. We assume that the excess of any commodity purchased in the first market may be resold by any economic agent at flexible market prices. Whereas a lot of papers are devoted to existence and efficiency of mixed market equilibria, this paper investigates extremal properties of equilibrium allocations in a mixed economy of Arrow-Debreu type. A notion of fuzzy domination in a mixed environment is given, and coincidence of the fuzzy core and equilibrium allocations in certain specifications of economy in question is shown to hold.