baumol's demand for money

7/23/2019 Baumol's Demand for Money

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BAUMOL’S THEORY OF DEMAND FOR MONEY/THE BAUMOL-TOBIN MODEL OF CASH

MANAGEMENT/BAUMOL’S INVENTORY THEORETIC APPROACH/THE INTEREST

ELASTICITY OF TRANSACTION DEMAND FOR MONEY/PORTFOLIO BALANCE

APPROACH/BAUMOL’S SQUARE ROOT FORMULA FOR DESCRIBING DEMAND FOR

MONEY

Keynes had designated the transaction demand for money as due to the transaction

motive but had not provided a theory for its determination. In particular, he had assumed

that this demand depended linearly on current income but did not depend on interest

rates.

Subsequent contributions by Baumol and Tobin in 1950s established the theory of

the transactions demand for money. These showed that this demand depends not only on

income but also on the interest rate on bonds. Further, there are economies of scale in

money holdings.

The transactions demand for money is derived under the assumptions of certainty

about the yields on bonds, as well as the amount and the time patterns of income and

expenditure.

Developments during the 1950s analysed the demand for transactions balances

rigorously from the standpoint of an individual who minimizes the costs of financing

transactions by holding money balances and other assets. This analysis showed that the

transactions demand for money depends negatively upon the rate of interest and that its

elasticity with respect to the real level of expenditures is less than unity. The original

analyses along these lines were presented by Baumol [1952] and Tobin [1956].

Modern theories of transactions demand for money originated in the work of

Baumol and Tobin, who adopted an inventory theoretic approach. It is based on the

existence of a time lag between payments and receipts, and the presence of short term

financial assets [say bills] other than money which yield an improved store of value since

they are earning a rate of interest. The time lags are implicit in specialization and the

division of labour; the availability of a range of alternative assets depends upon the

sophistication of the financial system. In addition there is also a cost involved in switching

in and out of bills. However, if the yield is high enough, transactions costs low enough, and

the transactions period long enough, it will be worthwhile placing some of the money

designated for spending during the period into bills.

According to this approach, the demand for money can be shown to be a function of the

rate of interest even in the absence of asset price uncertainty. The relevant behavioural

determinants are:



i. Relative interest rates between money and bills

ii. The transfer cost involved in switching between money and bills; and

iii. The length of the payments period.

The difference between the two theories developed by Tobin and Baumol is that

Baumol assumed only fixed transfer costs, whereas Tobin included a variable cost as well,related to the size of the transaction. Since the results of both approaches are practically

identical only the simplest is developed below.

According to Keynes, the transactions demand for money is function of the level of

income and the relation between transaction demand for money and income is linear and

proportional. Further the transaction demand for money is interest inelastic.

Prof. Baumol pointed out that the transaction demand for money is also interest elastic

like the speculative demand for money. Further he showed that the relation between

transaction demand and income is neither linear nor proportional. William Baumol appliedthe capital theory to the analysis of the transaction demand for money. Baumol assumes

that an individual or a firm has an optimum inventory of money for transaction purposes.

Cash balances are held by the people, as income and expenditure do not take place,

simultaneously. But it is expensive to have large amount of money in the form of cash

balances. That money could otherwise be used profitably elsewhere, for example, in bonds

and securities. In this situation, money balances held to make expenditures are considered

as a kind of inventory and the objective of an individual is to minimize the cost associated

with the inventory.

When cash held for expenditure, two types of costs are there:

1. Interest cost [Sacrifice of interest]

2. Non-Interest cost [Conversion Cost or Brokerage Cost]

The interest cost is an opportunity cost. When cash balances are held, we forego

interest income by not holding other forms of interest yielding assets. The non-interest

costs are mailing expenses, brokerage fees and so on. An individual always tries to keep

minimum transactions balances in order to earn maximum interest. So if the interest rate

on bonds is high, the lesser the transaction demand for money.

Assumptions

1. Over any given time period the individual knows his income, Y, with certainty.

2. The time path of expenditures is known and distributed evenly over the period

summing to T, with Y=T, and that they all have to be paid for with money. This

means that over any two sub-periods of equal length the value of transactions will

be identical.



3. The rate of interest, r, is fixed

and known.

4. The cost of switching from

bills/bonds to money is a fixed

amount, b[what Baumol calls

“the brokerage fee”] reflecting

both subjective and objective

costs.

5. Individual always transfers the

same quantity of money out of

bills each time, K, running this

holding down to zero before

making his next withdrawal.

i.e., K is the size of each cash

withdrawal at intervals when

bonds are sold. is the amount

of withdrawals that occur over

the year [particular period]

There are two types of cost incurred

by the market operator.

i. The brokerage charge, which is , i.e., the brokerage fee times the number of

transfers made; andii. The income foregone by holding money-since expenditure is assumed to be a

constant flow, so that actual money balances are run down evenly over the holding

period, the average money balance must be . The cost is therefore this average

holding times the rate of interest foregone, .

Since transactions are directly proportional to time, the pattern of money holding

over time can be related to the income-expenditure pattern.

[In other words, Baumol takes into account an individual’s demand for money. Suppose

‘T’ indicates the transactor’s real income. ‘K’ is the real value of the bonds that the

transactor encashes frequently, ‘b’ is the brokerage for transforming bonds into cash

and vice versa. The transactor’s real income is given at the beginning of the month and

it gets fully spent up to the end of the month. Now the transactor will try to minimize

this cost of turning bonds into money. The transactor gets income as a lump sum only

Time

I

t i t f

t r

f r r

Time



once and that also at the beginning of the month. So there is no sense in keeping the

money idle throughout the month. It is better to invest this idle money into bonds and

to encash them in equal lots of the size-value ‘K’ when required. Here two types of costs

are involved-one is transformation cost for transforming bonds into cash, and the other

is the interest income that the transactor sacrifices by holding money. The transactor’s

real income is ‘T’ and he has to frequently turn bonds of ‘K’ size value into cash. So if we

want to find out the frequency of these transformation events, we have to divide ‘T’ by

‘K’. But every time that bonds are transformed into cash, brokerage ‘b’ has to be

incurred. So in order to find out the total brokerage-cost during the period of one

month, we have to multiplyby b. So, gives us the total brokerage cost of turning

bonds into money for the whole month. When the bonds are transformed into cash,

though cash is to be spent immediately, still it will be kept idle at least for some time. So

for that period of time, interest-income has to be foregone by the transactor. Now the

average demand for money will be given by ‘K’. This is because, money of the value ‘K’ is

held throughout the equal time intervals during the month and hence the average

holding of money will be given by . Now when a transactor holds money, he sacrifices

his interest-income ‘r’. So is to be multiplied by r and hence will indicate the loss of

interest-income that the transactor bears, and hence it is cost for him.]

The total cost , C, will be the sum of the two separate costs:

()

The value of K that minimizes total costs is found by differentiating equation (1)

with respect to K, and setting it equal to zero.

()

()

For this is to be a necessary condition is that the second derivative or must

be positive. In this case,

[ ]



()

So that the second condition for minimum value is also satisfied.

The demand for transactions balances in real terms can be derived as

Which can be rewritten as

Where √

The demand for money is positively proportional to the square-root of transactions,

and negatively proportional to the square-root of the rate of interest. This theory has got

three important implications. The first is regarding the importance of the distribution of

national income among the people in relation to the demand for money. So when there is a

concentration of income in the society, the demand for money will be comparatively less.

But when this concentration of income is lessened, then the total demand for money will be

more. Thus this theory indirectly implies the importance of the distribution of national

income, pertaining to the total demand for money in the society.

The second implication is that in a situation of depression, if money supply isdoubled, income will be quadrupled because of the square-root rule. But in a full

employment situation, if the amount of money is doubled and not quadrupled, because the

brokerage fee and the money value of the transactions will increase proportionately to the

price level, creating a proportional relationship between the demand for money and the

price level. Thus it shows the enhanced capacity of money supply variations in influencing



K0

TC

Brokerage charge

s t

K Transactions size

C0

real income in the short period due to the square root rule, implying economies of scale in

the demand for money.

The third implication is about introducing interest rate also as one of the

independent variables along with income even in relation to the transaction demand for

money. Thus the asset demand for money approach of Keynes which was applied byKeynes to the speculative demand for money, has now been applied by Baumol to the

transaction demand for money also. This enhances the importance of the interest rate in

contrast to that of real national income with regard to the demand for money. This

implication may emphasize the greater significance of the velocity of money in place of

money supply, and the interest elasticity of demand for money is thus attempted to be

shown as higher. Thus there are implications in the opposite directions-the second

enhances the importance of money while the third decries it.

Figure : Minimizing Transaction costs

Superiority Of Baumol’s Analysis

Baumol’s inventory theoretic approach to the transactions demand for money is an

important improvement over the Classical and Keynesian approaches in the following

aspects.



a. Realistically, Baumol integrates capital theory [by taking assets and their costs] with

the transaction theory of demand for money.

b. Baumol shows interest elasticity of transaction demand for money. This is more

meaningful than Keynesian interest inelasticity of transaction demand for money,

because the households sometimes behave like business people.

c. Baumol has shown empirically the less than proportionate relationship between

income increase and the increase in the transaction demand for money.

d. Baumol’s analysis is the analysis of demand for real balances. Hence money illusion

is absent.

baumol's demand for money

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