The amount of money demanded for transactions however is also likely to depend on the nominal interest rate. This arises due the lack of synchronization in time between when purchases are desired and when factor payments (such as wages) are made. In other words, while workers may get paid only once a month they generally will wish to make purchases, and hence need money, over the course of the entire month.
The most well-known example of an economic model that is based on such considerations is the Baumol-Tobin model. In this model an individual receives her income periodically, for example, only once per month, but wishes to make purchases continuously. The person could carry her entire income with her at all times and use it to make purchases. However, in this case she would be giving up the (nominal) interest rate that she can get by holding her income in the bank. The optimal strategy involves holding a portion of one's income in the bank and portion as liquid money. The money portion is continuously run down as the individual makes purchases and then she makes periodic (costly) trips to the bank to replenish the holdings of money. Under some simplifying assumptions the demand for money resulting from the Baumol-Tobin model is given by
where t is the cost of a trip to the bank, R is the nominal interest rate and P and Y are as before.
The key difference between this formulation and the one based on a simple version of Quantity Theory is that now the demand for real balances depends on both income (positively) or the desired level of transactions, and on the nominal interest rate (negatively).
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