Baumol model

Baumol model
See also
Maximum stock level Profit Target Cycle stock Opening stock Independent demand Normal cost Cost avoidance Liquidity management Interdepartmental planning

The Baumol model is an economics theory that explains how businesses adjust their prices to compensate for the cost of labor. The model stipulates that businesses must continuously increase prices to keep up with the rate of change in wages. This is because labor costs typically rise faster than overall productivity, leading to a decrease in competitiveness and profit margins for businesses. The main components of the model are the cost-plus pricing strategy, which increases the price of goods and services to cover the increased costs, and the productivity lag, which is the difference between the cost of labor and the overall productivity of the business. The result of these two components is that businesses must raise prices in order to remain profitable. Ultimately, the Baumol model helps to explain why the cost of services often increases faster than the cost of goods.

Applications of the Baumol model

The Baumol model, also known as the Baumol-Allais-Tobin (BAT) model, is a cash management model.In 1952, William Baumol presented the idea of managing the surplus of funds through the optimal use of stock supply quantities. He came to the conclusion that money can also be treated as a specific type of stock, one that is necessary when doing business. When we talk about cash optimization and their balances, there is a clear analogy between cash and materials. When we compare cash management and inventory management, it results from the fact that cash surpluses are kept in enterprises as securities, most often they are treasury bills. The Baumol model is based on the economic model of supply size, i.e. Model EOQ (economic order quantity).

Assumptions of Baumol model

The main assumptions of the BAT model include:

• possible to be forecast and fixed for the entire period, the demand for cash,
• constant and predictable inflow of cash,
• fixed interest rate throughout the period when investing in securities,
• rhythmic cash receipts,
• instant cash transfers.

Baumol model formula

Looking at the above assumptions, one can draw conclusions that cash is consumed in a steady manner. At the moment when they reach the minimum level, the one equal to 0, then the equivalence of cash is converted into cash in such a height as to reach the maximum level. Then the cycle repeats.

The task of the Baumol model is to show the bottom margin of security and at the moment when the current funds approach is approaching this point, then the sale of Treasury bills or other securities is completed in order to supplement the funds. In the Baumol model, the optimal cash level is calculated as follows:

$C={\sqrt {\dfrac {2*T*F}{R}}}$

Where:

C-optimal cash level

T-demand for cash over the entire period considered (year)

F-fixed costs of cash transfer

R-alternative cost of maintaining cash.

This formula comes from the fact that if the level of cash is to be optimal, then the following equality must exist: KA = KT, the alternative cost must equal the transaction costs. These, in turn, are calculated as follows:

$K_{A}={\dfrac {C*R}{2}}$

$K_{T}={\dfrac {T*F}{C}}$

The Baumol model is used to determine the appropriate level of cash, which will minimize the total transaction costs and alternative costs as a result of maintaining a given level of cash.

Restrictions on the Baumol model

Although the Baumol model is a classic model of cash management, it is difficult to apply it in everyday life. The main limitation is that the company has to use up the stock evenly in order for the model to work. In practice, this is almost impossible. Also, the difficulty is that in the enterprise it is difficult to determine the precise demand for financial resources, also the expenses incurred by the company do not spread equally over the entire period. Another limitation in the application of the model is also a time-varying transaction commission, which can often be negotiated and depends on the size of the transaction and the maturity date.Another difficulty is that the interest rate on the current account is variable over time, as is the yield on treasury bills, which additionally depends on the maturity of separate series.

When planning the optimal level of financial resources, the Baumol Model is a helpful tool, but it has many limitations that reduce its usefulness. The model is based on assumptions that are not realistic for the company, therefore it is not used in the work.

Advantages of the Baumol model

The Baumol model has several advantages. These include:

• It provides an effective way of measuring the impact of labor costs on businesses and their pricing decisions.
• It helps to explain the disparity between the cost of goods and services, as labor costs typically increase faster than the overall productivity of the business.
• It helps to explain why businesses must continuously increase prices in order to remain profitable.
• It helps to provide insight into how businesses must adjust their prices to remain competitive.

Overall, the Baumol model is a helpful tool for businesses to understand the impact of labor costs on pricing decisions and to remain competitive in the marketplace.

Limitations of the Baumol model

The Baumol model has several limitations. These include:

• It fails to account for the impact of technological advancements on productivity, as technological advances often increase productivity faster than the increase in labor costs.
• It fails to account for the impact of competition on prices, as businesses may choose to lower their prices in order to remain competitive.
• It fails to account for the influence of government policies on pricing decisions, as government policies can either increase or decrease the cost of production.
• It does not consider the impact of factors such as advertising and marketing, which can also have an effect on pricing decisions.

Overall, the Baumol model is a useful tool for understanding the relationship between labor costs and the resulting prices of goods and services, but it does have certain limitations.

Other related models

Other models that are similar to the Baumol model include:

• The Williamson Model: This model suggests that the price of a good or service is determined by the cost of production and the total amount of profit that the producer wishes to make.
• The Stigler-Becker Model: This model posits that the price of a good or service is determined by the cost of production and the bargaining power of the producer and consumer.
• The Lerner Index: This index is used to measure the degree of market power of a producer. It takes into consideration the cost of production and the difference between the price of the good or service and the cost of production.
• The Cournot Model: This model suggests that the quantity of a good or service produced is determined by the cost of production and the amount of profit that the producer wishes to make.

Overall, these models are all useful in understanding the relationship between the cost of production and the resulting prices of goods and services.

References

• Tavor, T., Gonen, L. D., Weber, M., & Spiegel, U. (2018). The Modified Baumol Equation: Theory and Evidence. Review of European Studies, 10(1), 25.
• Gonen, L. D., Weber, M., Tavor, T., & Spiegel, U. (2017). Holding Cash and Spontaneous Behavior: A Modification of the Baumol Equation. Review of European Studies, 9(1), 209.
• Dequan, Z., & Yunlong, D. (2014). Study on the Effect of Rising Service Employment on Productivity Growth in China: A Test of Baumol’s Model. Journal of Applied Sciences, 14(5), 482-488.