Page 129 - DECO402_Macro Economics

Macroeconomic Theory

Notes into bonds or from bonds into cash in the non-interest cost Brokerage, postage, bookkeeping expenses
are also included.
So, whenever any firm keeps the money for transaction, it has to bear interest-costs and brokerage (non-
interest-costs). Let us assume that the interest rate is r is constant throughout the year and brokerage
b is also constant. Assume that firm’s income is Y in the beginning of the year which is equal to actual
value of transactions done by it and is the size of amount withdrawn each time on K intervals which
is withdrawn on the time bond selling. So, amount is withdrawn Y/K times throughout the year.
During the year b(Y/K) cost will appear on brokerage. Because average cash withdrawals are K/2,
so the interest-cost of keeping the remaining cash is rK/2. So the total cost of transaction i.e., C can
be written in the functional form as following:
K Y
C = r + b
2 K ...........(1)
The optimal value of K would be so from which the total cost of inventory became zero. Derived on
differentiating C with respect to K, dC/dK and keeping it equal to zero and then solving it for C we
get,
dC = r + by = 0
dK 2 K 2
r = by
2 K 2
Or,
Or on multiplying both the sided with 2K /r, we get:
2
2
K = 2bY
r
2bY
K =
Or r ...........(2)

Self Assessment

Fill in the blanks:
1. ……………………… has given important contribution in transaction demand of money
presented by Keynes.
2. Remaining cash is kept so that …………………………………….. don’t happen together.
It is clear from equation (2) that if brokerage will increase, then the number of withdrawals will be
lesser. In other words, optimal cash remaining will be increased, because firm will less invest in bonds.
On the other side, if the interest rates on bonds will be increased, then it would be more beneficial for
the firms to invest in bonds and optimal cash remaining will comparatively lesser and vice versa.
Boumol’s analysis also targets one more important fact for the behave of demand of transaction
remaining. When any firm or person purchases the bonds in big amount, then he has less transaction
remaining and vice versa. But the non-interest costs are found in the form of brokerage, posteen etc.
in each purchase which buyer has to pay. So it has to balance the deficiency of expanse incurred on
the purchase of bonds in a larger number in comparison to the income received on the purchase of
bonds in smaller number. This decision depends on the interest rate on bonds.
However, the interest rate will be larger, firm could expense as more in purchase the bonds. One more
important cause of determining this decision is that amount of money which is kept for transaction
because the brokerage of purchase or sell of bonds is comparatively constant and doesn’t change more

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