Theory assumption

Let’s generalize what we have discussed. Assume that the
individual makes N trips to the bank over the period. On each trip
he will withdraw Y/N dollars and he then spends the money
gradually over the period. Money holdings therefore vary from Y/N
to zero and this averages to Y/(2N).

The question that we need to answer is what is the optimal choice
of N bearing in mind that the greater N is, the less money he holds
on average and therefore the less interest he forgoes. But at the
same time the greater N is, the more trips he has to make to the
bank, which increases his inconvenience.

Let’s assume that
the cost of going to the bank is a fixed amount of $F;
and
r, represent the interest foregone or the opportunity cost
of holding money.


For any N, the average amount of money held is Y/(2N). Therefore
the forgone interest is rY/(2N). The cost of making trips to the bank
is FN. Therefore, the total cost the individual bears is :
Total cost (C) = rY/(2N) + FN

The greater is N, the smaller is the cost of interest forgone but the
greater is the cost of the trips.


The individual holds more money:
if the fixed cost of going to the bank increases;
if expenditure (Y) is higher; and
when r is lower.

So contrary to the classical economist and Keynes, in Baumol’s
model, transaction demand for money is inversely related to interest
rate.