Money Demand, the Equilibrium Interest Rate, and Monetary Policy
(Part E)
by
Charles Lamson
Having discussed the supply of money in the last several posts, we now turn to the demand for money. One goal of the next several posts and the previous posts is to provide a theory of how the interest rate is determined in the macroeconomy. Once we have seen how the interest rate is determined, we can turn to how the Federal Reserve (Fed) affects the interest rate through monetary policy.
It is important that you understand exactly what the interest rate is. Interest is the fee borrowers pay to lenders for the use of their funds. Firms and the government borrow funds by issuing bonds, and they pay interest to the firms and households (the lenders) that purchase those bonds. Households and firms that have borrowed from a bank must pay interest on those loans to the bank. The interest rate is the annual interest payment on a loan expressed as a percentage of the loan. A $1,000 bond (representing a $1,000 loan from a household to a firm) that pays $100 in interest per year has an interest rate of 10 percent. The interest rate is expressed as an annual rate. It is the amount of interest received per year divided by the amount of the loan. While there are many different interest rates, we will assume that there is only one. This simplifies our analysis yet provides a valuable tool for us to understand how the parts of the macroeconomy relate to one another. The Demand for Money What factors and what forces determine the demand for money are central issues in macroeconomics. As we shall see, the interest rate and the level of national income (Y) influence how much money households and firms wish to hold.  Before we proceed we must stress one point people find troublesome. When we speak of the demand for money, we are not asking these questions: "How much cash do you wish you could have?" "How much income would you like to earn?" "How much wealth would you like?" (The answer to these questions is presumably "as much as possible.") Instead, we are concerned with how much of your financial assets you want to hold in the form of money, which does not earn interest, versus how much you want to hold in interest-bearing securities, such as bonds. We take it as given the total amount of financial assets; our concern here is with how these assets are divided between money and interest-bearing securities. The Transaction Motive How much money to hold involves a trade-off between the liquidity of money and the interest income offered by other kinds of assets. The main reason for holding money instead of interest-bearing assets is that money is useful for buying things. Economists call this the transaction motive. This rationale for holding money is at the heart of the discussion that follows. Assumptions To keep our analysis of the demand for money clear, we need a few simplifying assumptions. First, we assume there are only two kinds of assets available to households: bonds and money. By "bonds" we mean interest bearing-securities of all kinds. By "money" we mean currency in circulation and in deposits, neither of which is assumed to pay interest. Second, we assume that income for the typical household is "bunched up." It arrives once a month, at the beginning of the month. Spending, by contrast is spread out over time; we assume that spending occurs at a completely uniform rate throughout the month---that is, that the same amount is spent each day (Figure 1). The mismatch between the timing of money inflow and the timing of money outflow is sometimes called the nonsynchronization of income and spending. FIGURE 1   Finally, we assume that spending for the month is exactly equal to income for the month. Because we are focusing on the transactions demand for money and not on its use as a store of value, this assumption is perfectly reasonable. Money Management and the Optimal Balance Given these assumptions, how would a rational person (household) decide how much of monthly income to hold as money and how much to hold as interest-bearing bonds? Suppose Jim decides to deposit his entire paycheck in his checking account. Let us say Jim earns $1,200 per month. The pattern of Jim's bank account balance is illustrated in Figure 2. At the beginning of the month Jim's balance is $1,200. As the month rolls by, Jim draws down his balance, writing checks or withdrawing cash to pay for the things he buys. At the end of the month, Jim's bank account balance is down to 0. Just in time, he receives his next month's pay check, deposits it, and the process begins again.  One useful statistic we will need to calculate is the average balance in Jim's account. Jim spends his money at a constant $40 per day ($40 per day * 30 days per month equals $1,200). His average balance is just his starting balance ($1,200) plus his ending balance (0) divided by 2, or ($1,200 + 0) divided by 2 equals $600. For the first half of the month Jim has more than his average of $600 on deposit, and for the second half of the month he has less than his average. Is anything wrong with Jim's strategy? Yes. If he follows the plan described, Jim is giving up interest on his funds, interest he could be earning if he held some of his funds in interest-bearing bonds instead of in his checking account. How could he manage his funds to give himself more interest?  Instead of depositing his entire paycheck in his checking account at the beginning of the month, Jim could put half his paycheck into his checking account and buy a bond with the other half. By doing this, he would run out of money in his checking account halfway through the month. At a spending rate of $40 per day, his initial deposit of $600 would last only 15 days. Jim would have to sell his bond halfway through the month and deposit the $600 from the sale of the bond in his checking account to pay his bills during the second half of the month. Jim's money holdings (checking account balances) if he follows this strategy are shown in Figure 3. When he follows the buy-a-$600-bond strategy, Jim reduces the average amount of money in his checking account. Comparing the dashed lines (bold strategy) with the solid green lines (buy-$600-bond strategy), his average bank balance is exactly half of what it was with the first strategy.  The buy-a-$600-bond strategy seems sensible. The object of this strategy was to keep some funds in bonds, where they could earn interest, instead of as "idol" money. Why should he stop there? Another possibility would be for Jim to put only $400 into his checking account on the first of the month and buy two $400 bonds. The $400 in his account will last only 10 days if he spends $40 per day, so after 10 days he must sell one of the bonds and deposit the $400 from the sale in his checking account. This will last through the twentieth of the month, at which point he must sell the second bond and deposit the other $400. This strategy lowers Jim's average money holding (checking account balance) even further, reducing his money holdings to an average of only $200 per month, with correspondingly higher average holdings of interest-earning bonds. You can imagine Jim going even further. Why not hold all wealth in the form of bonds (where it earns interest) and make transfers from bonds to money every time he makes a purchase? If selling bonds, transferring funds to checking accounts, and making trips to the bank are without cost, Jim would never hold money for more than an instant. Each time he needed to pay cash for something or write a check, he would go to the bank (online or in person) or call the bank, transfer the exact amount of the transaction to his checking account, and either withdraw the cash or write the check to complete the transaction. If he did this constantly, he would squeeze the most interest possible out of his funds because he would never hold assets that did not earn interest.  In practice, money management of this kind is costly. There are brokerage fees and other costs to buy or sell bonds. At the same time, it is costly to hold assets in non-interest-bearing form, because they lose potential interest revenue. We have a trade-off problem of the type that pervades economics. Switching more often from bonds to money raises the interest revenue Jim earns (because the more times he switches, the less, on average, he has to hold in his checking account and the more he can keep in bonds), but this increases the money management costs. Less switching means more interest revenue lost (because average money and holdings are higher) but lower money management costs (fewer purchases and sales of bonds). The Optimal Balance There is a level of average money balances that earns Jim the most profit, taking into account both the interest earned on bonds and the costs paid for switching from bonds to money. This level is his optimal balance.  How does the interest rate affect the number of switches that Jim makes and thus the average money balance he chooses to hold? It is easy to see why an increase in the interest rate lowers the optimal money balance. If the interest rate were only 2 percent, it would not be worthwhile to give up much liquidity by holding bonds instead of cash or checking balances. However, if the interest rate were 30 percent, the opportunity cost of holding money instead of bonds would be quite high, and we would expect people to keep most of their funds in bonds and to spend considerable time managing their money balances. The interest rate represents the opportunity cost of holding money (and therefore not holding bonds, which pay interest). The higher the interest rate is, the higher the opportunity cost of holding money, and the less money people will want to hold. This leads us to conclude:      *CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 499-503) end |
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