This paper considers a model of an exchange economy with money. The shrinking process of the core of an economy is shown, and further the mechanism of the occurrence of a competitive equilibrium is verified. The core, herein, is the organizationally stable imputation in the sense that it consists of the imputation which is not blocked by a coalition of the economy. The paper proceeds in the following manner. First, a game-theoretic model of an exchange economy with money, is constructed and the upper and lower bounds of the core of an Edgeworth market in the explicit form is shown. Then the shrinking process of the core is analized, and the occurrence of a competitive equilibrium as a limit theorem on the core is established. Finally, several special markets, and some examples of the calculution experiments on the shrinking process of the core, are investigated.