2. The Determination of the Interest Rate I

Assume all money is currency, so there are no checking accounts or banks. Consider the supply of money to be fully in the control of the central bank and take nominal income as given. Then, equilibrium in the money market occurs when the supply of money (M) equals the demand for money (M^d) given in equation (4.1). Figure 4.1 illustrates the solution.

An increase in the money supply shifts the vertical line to the right, resulting in a new equilibrium with a lower interest rate. In order to induce the private sector to hold more money, bonds must become less attractive (the interest rate must fall). An increase in nominal income (for a given money supply) shifts the money demand curve to the right and generates a new equilibrium with a higher interest rate. The increase in nominal income increases the demand for money at the original interest rate. Since the supply of money has not changed, something must occur to offset the increase in demand. The increase in the interest rate makes bonds more attractive, thereby reducing the demand for money and offsetting the increase in money demand from the increase in income.

Figure 4.1: Equilibrium in the Money Market

How does the central bank control the money supply? Consider the central bank’s balance sheet. Currency held by the public constitutes the central bank’s liabilities. The central bank’s assets are any bonds that it owns. To increase the money supply, the central bank creates currency to purchase bonds, thus increasing assets (through the additional bonds) and liabilities (through the new currency created and exchanged for bonds). To reduce the money supply, the central bank sells bonds for existing currency, thus reducing assets (through the sale of bonds) and liabilities (through the reduction of currency held by the general public). Purchases and sales of bonds by the central bank are called open market operations.

The text also considers open market operations in terms of their effect on bond prices. Suppose a bond promises a payment of $F in one year. Call the current price of the bond $P_B. Then, the interest rate (or rate of return) on this bond is given by

i=($F-$P_B )/$P_B. (4.2)

Equation (4.2) can be solved for the bond price:

$P_B=$F/(1+i). (4.3)

Given fixed nominal bond payments, equation (4.2) shows that the nominal interest rate and the bond price are inversely related. For example, when the central bank purchases bonds, it increases the demand for them and tends to increase their price, which reduces the interest rate.

3. The Determination of the Interest Rate II

Now introduce banks into the model. Banks receive funds from depositors (individuals and firms) and allow their depositors to write checks against (or withdraw) their account balances. These checkable deposits are liabilities of banks. On the asset side, banks hold bonds, loans (which are claims against borrowers), and reserves of some of their deposits. Some bank reserves are held in cash and the rest in accounts at the central bank. Banks hold reserves in part to protect against daily excesses of withdrawals (in currency or check form) over deposits and in part because they are required to do so by the central bank. In the United States, the Federal Reserve may set the required reserve ratio between 7% and 22% of checkable deposits. The actual reserve ratio in the United States is about 10%.

Reconsidering the central bank balance sheet in an economy with banks, the only difference is that central bank liabilities now consist of currency held by the public plus reserves held by banks. Central bank liabilities—the money the central bank has created—are called central bank money.

Now reconsider money market equilibrium in terms of central bank money (H). The demand for money arises from two sources: currency held by the public and reserves held by banks. The supply of money is under the control of the central bank. Thus, equilibrium is given by

H=CU^d+R^d, (4.4)

where CU^d refers to the demand for currency and R^d to the demand for reserves.

On the demand side, assume that overall money demand is determined as before, i.e., M^d=$YL(i), and that the demand for currency (as opposed to checkable deposits) is a fraction c (where 0<c<1) of overall money demand. In addition, assume that banks keep a fixed fraction  of checkable deposits as reserves. Putting these assumptions together with equation (4.4) gives

H= CU^d+R^d=cM^d+ (1-c)M^d=[c+  (1-c)]$YL(i). (4.5)

Equilibrium can be depicted just as in Figure 4.1, with H substituting for M on the horizontal axis. An increase in H (through open market operations) leads to a decrease in the nominal interest rate.