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Depository institutions (commercial banks, savings and loan associations, and credit unions) borrow savers money balances and lend them to individuals, businesses, or government. By pooling the funds of many small savers and investing in a diversi ed portfolio of nancial instruments, these institutions reduce the transaction costs and risks associated with lending to a borrower. In the U.S., the Federal Deposit Insurance Corporation (FDIC) insures the liabilities of deposit intermediaries. Savers therefore readily hold these liquid liabilities because they normally offer a higher interest return than money. Because the liabilities are liquid and therefore good stores of value, the Federal Reserve presents an M1, M2, and M3 de nition of money. The M1 de nition is a transaction de nition and consists of currency and checking accounts, while M2 and M3 add other liquid nancial instruments to the M1 de nition. Current measures of the money supply appear in Table 7.1. Small time deposits are certi cates of deposit (CDs) issued by these same nancial intermediaries in amounts less than $100,000, and large time deposits exceed this dollar amount. CDs are classi ed as time deposits since the depositor agrees to keep these funds on deposit for a speci ed period of time or incur an interest penalty. Repurchase agreements (RPs) are large (at least $1 million) overnight, collateralized loans.

public static void main(String[] args) { for (int n = 0; n < 16; n++) { System.out.println("fib(" + n + ") = " + fib(n)); } }

TRACING A RECURSIVE CALL Hand tracing the execution of a method usually helps clarify it. EXAMPLE 9.7 Tracing the Recursive Factorial Function

Here is a trace of the call f(5) to the recursive factorial function defined in Example 9.2:

The call originates in the main() function, passing 5 to the f() function. There, the value of the parameter n is 5, so it calls f(4), passing 4 to the f() function. There the value of the parameter n is 4, so it calls f(3), passing 3 to the f() function. This process continues (recursively) until the call f(1) is made from within the call f(2). There, the value of the parameter n is 1, so it returns 1 immediately, without making any more calls. Then the call f(2) returns 2*1 = 2 to the call f(3). Then the call f(3) returns 3*2 = 6 to the call f(4). Then the call f(4) returns 4*6 = 24 to the call f(5). Finally, the call f(5) returns the value 120 to main().

When a bank lends, it gives the borrower a check drawn upon itself. The Federal Reserve controls the banking system s ability to issue checkwriting deposits by imposing a reserve requirement on checking deposits. U.S. bank reserves consist of currency held by banks and deposits that banks have at the Federal Reserve. The reserve requirement (r) on checkwriting deposits is currently 10 percent (r = 0.10); it requires that a bank hold $1 in reserves for each $10 in checking account liability it has. Since U.S. banks are managed to maximize pro ts, they usually expand loans and issue checkwriting deposits when they have more reserves than they are required to hold. Even when a bank has no excess reserves, it can lend and create new checking deposits if it can borrow the excess reserves of other banks. With banks behaving in this manner, there is a tendency for the excess reserves of the banking system to approximate zero and for the combined sum of check-writing deposits to be a multiple of the amount of reserves held by all banks. When excess reserves for the combined banking system equal zero, the relationship of check-writing deposits (D) and reserves (R) can be presented as Dmax = dR, where d, the check-writing deposit multiplier, equals 1/r. It therefore follows that the Federal Reserve can control the maximum amount of check-writing deposits by controlling the amount of reserves held by banks and by setting the reserve requirement on checking deposits. Example 7.1 Suppose the reserve requirement on check-writing deposits is 0.10 and reserves held by all banks total $500,000. The maximum amount of check-writing deposits for the banking system is $5,000,000. Dmax = dR; d = 1/r; d = 1/0.10 = 10; since R = $500,000, Dmax = (10)$500,000 = $5,000,000.