A number of recent works have addressed the problem of describing the allocation of resources in an economy where prices are fixed at a value that does not achieve equilibrium of supply and demand in the classical sense. In the context of a model developed by Dreze, the purpose of this paper is to describe more precisely the different states of the markets (excess supply or excess demand) that may occur near a competitive equilibrium. A general analytical picture is obtained, which associates with each state of the markets the region of the price domain where it prevails. This allows us to point out an important difficulty which arises in the local comparative statics of this class of model: local unicity is not warrantied, that is, there may exist price systems very close to some competitive price, for which all the fixed price allocations are far from the competitive allocation. Examples are shown in the macroeconomic model (two aggregate agents: households and firms, and three goods: money, output, and labor); necessary and sufficient conditions for local unicity are given in this context. They require that all commodities be Hicks-substitute for the consumer, which is another way of saying that both the marginal propensities for consumption and leisure are positive and smaller than one. On the other hand, assuming local unicity, one can look for the implications of the foregoing results for the long-run determination of prices. It is easy to show that, if the economy always reaches a fixed price allocation, an increase of the price of one commodity near the competitive equilibrium is always to the advantage of the sellers and to the disadvantage of the buyers. This suggests that the determination of prices should take the form of a struggle between buyers and sellers in each market.