We consider an economy in which the price mechanism in competitive market partially malfunctions ; namely some prices do not move in response to discrepancy between supply and demand. We formalize this case as a model where some prices are flexible as usual whereas others are fixed. On the assumption that every agent is a price taker, we show that even in this situation general equilibria do exist, but at the cost of two important properties ; namely, decisive relative prices and determinacy of equilibrium. On one hand, ineffectiveness of relative prices naturally induces use of money. We show, on the other hand, that money is of great use to solve the problem of indeterminacy of equilibrium. Specifically, money proves generically to yield the local determinacy of equilibrium under some condition, which also implies that money substantially affects a real economy.