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INVENTORY DEMAND FOR
Prof. Prabha Panth,
Demand for Money
Keynes assumed Transaction and
Precautionary DM = f(Y), so changes in interest
rate has no impact on them
But Baumol showed that rate of interest also
affects Transaction motive for holding money.
-- Holding cash in hand gives high liquidity.
– But there is loss of interest as the money is
not deposited in a bank.
Therefore rate of interest also affects
Transaction Demand for Money.
The Baumol Model
Baumol model describes money
demand in terms of a trade off between
liquidity and rate of return.
Assume that consumer can keep his
income in the form of either cash in
hand or in savings account deposits.
Cash pays no nominal interest.
The savings account pays interest rate
i, this is the opportunity cost of holding
The consumer has to decide between
keeping cash (liquidity) but no interest,
and putting it in a saving deposit – earns
interest but less liquid.
If he keeps in savings deposit, he has to
spend time and money to go to the bank to
This is the opportunity cost of keeping money
in the bank.
The consumer has to decide on the optimum
allocation of his funds – between cash and
Cost of Money Management M:
M = cost of withdrawal (NF) + cost of interest
foregone due to holding cash (iM)
PY = total nominal spending, done gradually over
i = nominal interest rate on savings account
N = number of trips consumer makes to the bank
to withdraw money from savings account
F = cost of a trip to the bank (e.g., if a trip takes 15
minutes and consumer’s wage is Rs.120/hour,
then F = Rs.30)
Average money holdings is a function of N or
number of trips to the bank.
This has to be minimised.
If N=1, then the consumer keeps all his
income in the form of cash.
He spends it gradually throughout a given
time period, say a year or a month,
His expenditure is constant over the time
The money or cash in hand falls at a
constant rate, till it becomes zero at the end
of the time period.
Cost of holding money
Baumol model: The demand for money
income in the
form of cash.
Then he only
goes once to
the bank to
In one year,
holdings = Y/2
N = 1
= Y/ 2
By keeping all
Y as cash, he
keeps half his Y
Then he has to
make 2 trips to
So on average
he has Y/4
cash in hand.
N = 2
= Y/ 4
If N = 3, then 3 trips to the bank and average
cash holdings = Y/6 8
The cost of holding money
In general, average money holdings =
Foregone interest = i (Y/2N )
Cost of N trips to bank = FN
total cost =
i F N
Given Y, i, and F, consumer chooses N to
minimize total cost
Cost of trips
Finding the cost-minimizing N
For any value of N, the height of the red line equals the height
of the blue line plus the height of the green line at that N.
Equilibrium is at X, with N* optimum number of trips.
total cost =
i F N
Take the derivative of total cost with
respect to N, set it equal to zero:
Solve for the cost-minimizing N*
* i Y
The Money Demand Function
The Baumol-Tobin money
( ) = ( )
/ , ,d Y F
M P L i Y F
Money demand depends positively
on Y or income and F or foregone
interest, and negatively on i.
Summary of Baumol’s model
– A transactions theory of money demand,
stresses “medium of exchange” function
– Real money demand (Md/P) depends
positively on spending (Y), negatively on the
nominal interest rate (i),
– Positively on the cost of converting
non-monetary assets to money (F)
– It forms the Micro foundation for the LM