The Fed and the money supply
The Federal Reserve system (Fed) serves as the central bank of the United States. As such, it functions as a bank for commercial banks (receiving deposits and making loans), and it is also charged with carrying out monetary policy. This entails controlling (varying the growth of) the supply of money in circulation, which in turn influences interest rates and real GDP.
In conducting monetary policy, the Fed seeks to achieve multiple (and at times conflicting) goals: keeping inflation under control and thereby maintaining the purchasing power of money; reaching and maintaining full employment; smoothing the impact of fluctuations in economic activity (moderating the business cycle), and stimulating and maintaining adequate long-term growth. Typically, in times of conflict among these goals, the Fed has come down on the side of controlling inflation even at the cost of exacerbating cyclical fluctuations (e.g., Volcker in the early 1980s).
The Fed's principal policy tools consist of the discount rate and open market operations (can also vary reserve requirements, but this tool is not ordinarily used). The discount rate is the interest rate at which the Fed lends reserves to commercial banks. An increase in the discount rate raises the cost of borrowing reserves from the Fed, and thereby encourages banks to reduce their lending activity (so they won't need as much in reserves). This in turn results in a reduction in the money supply. This policy tool is most effective when banks have a shortage of reserves and are borrowing from the Fed (likely in an expansionary period when demand for loans is high).
Open market operations consist of the purchase or sale of U.S. Treasury bills and bonds by the Fed in the open market -- i.e, buying or selling these government securities from commercial banks and the general public. When the Fed sells government securities on the open market, it is paid with bank deposits and bank reserves, and this reduction in reserves held by banks results in a decline in bank lending and hence in the money supply. Conversely, purchases of these securities by the Fed add to bank reserves and permit an expansion of lending activity and the money supply. Such open market operations are the principal policy tool of the Fed (i.e., the most actively used tool).
There is a multiplier effect associated with the Fed's open market operations, similar to the deposit multiplier effects that were discussed in recitations last week. For our purposes, we need not go into the details; rather, it is sufficient to note that when the Fed changes the discount rate or engages in open market operations this results ultimately in an increase in the supply of money.
The Fed normally does not seek to change the money supply as an end in itself, but rather as a means of influencing interest rates and ultimately economic activity (real GDP). To see this, we must first look at the demand for money.
Demand for money
When we speak of the demand for money, we are talking about the demand for the stock of money that we hold in currency or on deposit in a bank. The factors that influence the quantity of money that individuals wish to hold are the price level, the interest rate, the level of real GDP, and financial innovation. We need to distinguish between the quantity of money in current dollars (nominal money) and the quantity in constant dollars (real money). As the price level changes, there will be corresponding changes in the quantity of nominal money that people wish to hold, but no changes in the quantity of real money that is desired to be held (how much do you usually carry around in your pocket?; how would that amount change if all prices were doubled?).
We argued earlier that the interest rate serves as a measure of the opportunity cost of consumption; it is also the opportunity cost of holding money. Hence, the higher the opportunity cost of holding money, the lower is the quantity of real money demanded.Note that since several components of M2 do bear interest, this point seems more strongly pertinent with respect to M1 than M2; however, note further that interest rates on various financial assets such as savings bonds or Treasury bills typically are higher and more variable than interest rates on time and saving deposits -- components of M2. Hence, the argument holds for M2 as well as for M1.
Individuals with higher incomes have higher ongoing consumption expenditures, and hence typically carry higher cash balances. In the aggregate, a similar relationship holds true: the quantity of real money demanded by households and firms tends to vary positively with the level of real GDP.
Finally, financial innovation (including developments such as checking with interest, ATMs, and credit cards) also influence the demand for money. In general, it appears that financial innovation tends to reduce the demand for money.
We define the demand for money as the relationship between the quantity of real money demanded and the interest rate, holding constant all other influences on the quantity of real money demanded. With this definition, We can identify a demand
for money curve, with the quantity of real money demanded on the horizontal axis and the interest rate on the vertical axis. Based on the discussion above, this curve would have a negative slope; changes in interest rates would entail movements along the curve; and changes in real GDP or in financial innovation would result in shifting of the curve (i.e., changes in money demand).

Determination of interest rates
Interest rates are determined by the demand for money and the supply of money. The latter is determined by the Fed, and at any given moment may be considered as fixed (a vertical line in the interest rate-real money space). Money market equilibrium
occurs when the quantity of money demanded equals the quantity of money supplied.

At interest rates above this equilibrium level, there will be an excess supply of money, and firms and households will buy bonds, causing the price of bonds to rise and hence interest rates to fall. Likewise, at interest rates below the money market equilibrium, there will be an excess demand for money and bond prices will fall and interest rates rise.
Two key aspects here: 1) bonds and money are substitutes, and 2) bond prices and interest rates are inversely related.
Given the demand for money, then, changes in the supply of money initiated by the Fed will result in corresponding changes in interest rates. Such changes, occurring through open market operations, are how the Fed influences the state of the economy.

Monetary policy
As Parkin notes, the link between the supply and demand for money and interest rates that we've just examined was fairly tight up until 1990. Since then, however, further financial innovation -- and in particular, development of new substitute ways of holding wealth such as bond and equity mutual funds -- has weakened the relationship between M2 and short-term interest rates.
Note that there are multiple effects (what Parkin describes as ripple effects) of monetary policy. When the Fed buys securities in the open market and thereby increases bank reserves and the quantity of money, the consequent fall in interest rates stimulates aggregate demand via increased consumption (especially of consumer durable goods, purchases of which tend to be more sensitive to interest rates) and increased investment. In addition, declining interest rates also tend to reduce the value of the dollar on foreign exchange markets (the dollar is no longer as profitable to hold), and this increases net exports.
Increased consumption, investment, and net exports all contribute to increased real GDP and put upward pressure on prices. If, by contrast, the Fed sells securities on the open market, aggregate demand contracts and real GDP growth and inflation tend to slow down.
The link between interest rates and real GDP growth is evident from Parkin's Fig. 14.15, which shows that fluctuations in short-term interest rates tend to be followed (roughly a year later) with inverse changes in the growth of real GDP.
A final point of note is the relevance of expectations of Fed policy actions. As Parkin notes, if a money supply change is unanticipated, interest rates change when the money supply changes. However, if a money supply change is anticipated, interest rates will change even before the change in the money supply, as agents attempt to "beat the Fed" (e.g., if an increase in the money supply is anticipated, bondholders anticipating a decline in interest rates and hence an increase in bond prices will buy bonds and thereby push down interest rates even before the change in the money supply).
The relevance of this phenomenon will be apparent when we get to Ch. 17 ("Macroeconomic Policy Challenges").