During the decades following the presentation of the original Baumol equation (1952) the role of holding cash was significantly changed. The original Baumol equation considered the two elements of (i) the value of transactions, positively affecting cash holding; and (ii) the interest rate, negatively affecting cash holding. A third element that was not considered is the economic behavioral aspect of the availability of money that may lead to spontaneous purchasing. This element reduces the inclination of customers towards holding cash.

The present paper develops various kinds of loss functions due to spontaneous purchasing behavior and presents several different modified Baumol equations that are more reliable and realistic than the original Baumol equation.

An important implication of our paper relates to the ineffectiveness of monetary policy. When the interest rate is very low, in the original Baumol model we approach the liquidity trap range in which monetary policy is ineffective. However, according to our new model the monetary policy still remains effective, even at low or zero interest rates. This is the case even in an environment in which the monetary policy seems to be totally inefficient, as we recently find in several industrial countries throughout the world. In some sense, this reminds us of the idea of an automatic stabilizer that supports fiscal policies. The new modified Baumol equation in the current paper reveals an automatic stabilizer which accelerates the effectiveness of monetary policy, and avoids the phenomenon of the liquidity trap, even in cases of zero interest rates.