Baumol-Tobin Model

By Mauricio Villamizar-Jaimes1

Abstract

The Baumol-Tobin model negatively relates money demand to the interest rate because when the
interest rate rises, the quantity of money demanded decreases due to the increased opportunity cost of
holding cash. It is named after William Baumol and James Tobin, who developed it independently.

Theoretical Foundation

Money demand differs from the demand for goods and services because money is not desired for itself;
people do not eat banknotes or coins but use money to purchase goods and services.

According to the Baumol-Tobin model, there are only two ways to accumulate wealth: money and
bonds. In mathematical terms:

Y = Md + Bd

Where:

Y = Nominal GDP (income)

Md = Money demand
Bd = Bond demand

The incentive to hold cash rather than bonds is related to the return on cash compared to the return on
bonds.

• The return on cash is zero because cash does not earn interest.

• The return on bonds is related to:

a. Interest payments, which are constant.

b. Capital gain or loss, because bonds appreciate or depreciate depending on the investor's
interest rate.

The investor's interest rate is the rate an investor would earn if they invested in other assets with similar
risk. It is also known as the opportunity interest rate (OIR).

When new issues increase the investor’s interest rate, the price of previously issued bonds falls, as
they must compensate with capital for the interest the investor will no longer receive. If the bond is sold
before maturity, the investor will lose money. However, if the bond is held to maturity, the nominal value
will be received. Bonds are accounted for at market price, so when the investor's interest rate increases,
bondholders may experience negative returns.

People only hold cash if its expected return is higher than that of bonds. The return on money is zero,
whereas the return on bonds can sometimes be negative. In such cases, the return on cash is higher
than the return on bonds, as zero is greater than a negative return. Therefore, people prefer to hold
cash instead of bonds.

The opportunity cost of holding cash is the return forgone by not holding bonds. Most of the time, money
yields less than bonds. However, cash is a more liquid and less risky asset. Additionally, every time a
person wants to buy or sell bonds, they must pay fees to a broker.

This analysis applies not only to bonds but also to interest-bearing bank accounts.

1 Economist and Master of Business Administration. Email: mvillamizarj@gmail.com

• The return on money in bank accounts (bank money) is related to:

a. Interest payments on balances.

b. Monthly maintenance fees, transaction fees, and mandatory insurance.

Bank deposits offer very low interest rates. However, people prefer to keep their money in financial
institutions for the services they provide, such as electronic bill payments and online transactions.

The velocity of money is the number of times money circulates in the economy in a year. If the money
supply is small relative to nominal GDP, money circulates quickly. The velocity of money is determined
by the institutions and technology of the economy. The more bank money is used, the less cash is used.
Therefore, less money is needed in the economy, and the velocity of money increases.

According to this model, the velocity of money is not constant but fluctuates with changes in the interest
rate. If the interest rate rises, people hold less cash, and the velocity of money increases.

Assumptions

The Baumol-Tobin model assumes that people can hold their wealth either entirely in money or in
money and bonds simultaneously because if people held all their wealth in bonds, they would need to
sell a bond every time they wanted to make a transaction.

• People can hold their entire salary in cash and spend it throughout the month. The cost of holding
only cash is the opportunity cost, i.e., the interest lost by not holding bonds. The benefits of holding
only cash are the transaction costs avoided.

• People can hold half of their salary in cash and invest the other half in bonds, then sell the bonds
mid-month and spend the money. The costs of holding both cash and bonds simultaneously are
transaction costs incurred for broker fees and time spent (which is money). The benefits are the
interest received from bonds.

Formalization

According to the Baumol-Tobin model, money demand is calculated as follows:

Yc 0,5
Md = ( 2i )
Where:

Md = Money demand
Y = Income
c = Transaction cost
i = Interest rate

And the velocity of money is calculated as:

2Yi 0,5
V= ( C )
Where:

V = Velocity of money
Y = Income
i = Interest rate
c = Transaction cost
Demonstration

• Suppose a person has an income (Y) of 2,000 per month. The cost of withdrawing money from their
bank account (c) is 5 per withdrawal. If the bank account interest rate (i) is 2% per month. What is
the value of money demand (Md)? And what is the velocity of money (V)?

Yc 0,5
Md = ( 2i )
2.000 x 5 0,5
Md =( )
2 x 2%
10.000 0,5
Md =( )
4%
Md = (250.000)0,5
Md = 500

2Yi 0,5
V= ( c )
2 x 2.000 x 2% 0,5
V =( )
5
80 0,5
V =( )
5

V = (16) 0,5
V=4

Under these conditions, the person would make 4 withdrawals of 500 per month.

• With the initial data, suppose now that the bank account interest rate (i) increases to 8% per month.
What is the value of money demand (Md)? And what is the velocity of money (V)?

Yc 0,5
Md = ( 2i )
2.000 x5 0,5
Md = (
2 x 8% )
10.000 0,5
Md = (
16% )
Md = (62.500)0,5
Md2 = 250

2Yi 0,5
V= ( c )
2 x 2.000 x 8% 0,5
V= ( 5 )
320 0,5
V= ( 5 )
V = (64) 0,5
V2 = 8

Under these conditions, the person would make 8 withdrawals of 250 per month.

• With the initial data, suppose now that the cost of withdrawing money from the bank account (c)
increases to 20 per withdrawal. What is the value of money demand (Md)? And what is the velocity
of money (V)?

Yc 0,5
Md = ( 2i )
 2.000 x 20 0,5
Md = ( 2 x 2% )
40.000 0,5
Md = ( 4% )
Md = (1.000.000) 0,5
Md3 = 1.000

2Yi 0,5
V= ( c )
2 x 2.000 x 2% 0,5
V =( )
20
80 0,5
V =( )
20
V = (4) 0,5
V3 = 2

Under these conditions, the person would make 2 withdrawals of 1,000 per month.

Conclusions

People are concerned not only with the return on assets but also with risk and liquidity. Since most
people are risk-averse, they are willing to hold a lower-yielding asset if it is less risky. The return on
cash is zero, whereas the return on bonds can sometimes be negative. Therefore, people hold both
bonds and cash as a store of wealth simultaneously.

According to this model, money demand is negatively related to the interest rate. If the interest rate
rises, the benefits of holding bonds outweigh the transaction costs, thus increasing bond demand and
decreasing cash demand. Conversely, if the interest rate falls, the benefits of holding bonds are less
than the transaction costs, leading to a decrease in bond demand and an increase in cash demand.

Cite as

VILLAMIZAR, M. (2024) Macroeconomics (2nd ed.). Ediciones de la U.

This is the end of the study guide. If you find any errors or have any questions or comments
about this study guide, feel free to email me at mvillamizarj@gmail.com. Thanks a lot for
reading.