Abstract
<p>Baumol developed an equation for the transaction demand for money. It is affected positively by cost per withdrawal and transaction value, and negatively by the interest loss from holding cash.</p><p>Our objective is to modify the Baumol equation by including another factor. The demand for money is also affected by the customer concern that holding a more available liquid asset encourages more spontaneous purchases with resulting losses in their real value. We develop a new theoretical model by adding to the original Baumol cash demand equation another demand for a deposit which has positive yield and is less liquid. Holding this deposit restrains some of the spontaneous purchases. This modified Baumol equation leads to the following new results: Customers withdraw cash more often; maintain, on average, a smaller cash balance and larger amount of less liquid assets; and reduce their spontaneous and “nonrational” purchases.</p>
Highlights
Baumol developed an equation for the transaction demand for money
Each time that a consumer performs a transaction of Y dollars in nominal value, he is required to retain a certain amount of liquid assets
From (4) and (6) we find for each transaction the optimal amount that the consumer leaves in his checking account that yields
Summary
Baumol (1952) established a model of the demand for cash based on the micro-economic idea of optimal enterprise inventory. Following up on Baumol’s approach, Miller and Orr (1966) found that the typical pattern of cash management by firms is somewhat complex, with a cash balance that irregularly fluctuates in both directions As such, they developed an analytical model, which added this varying cash balance in business operations to the aspect of transfer cost in the established Baumol model. They found that firms would have to transfer money from one asset account to another by buying or selling securities The results, they argued, showed a model superior to the Miller-Orr model. Another alternative method to the Miller-Orr model came from da Costa Moraes and Nagano (2012) They Applied Genetic Algorithms (AGA) and Particular Swarm Optimization (PSO) to cash balance management in conjunction with the aforementioned model. Amromin and Chakravorti (2009), showed that despite the introduction, acceptance and usage of cash alternatives, cash remains significant for businesses and households
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