If an unexpected change in the money supply can seemingly have such a profound impact on the economy as did in the 1930s, then perhaps deliberate changes in the money supply might be harnessed to manage the business cycle.  Monetary policy is the deliberate manipulation of the money supply with the intention to increase or decrease aggregate spending. 

For example, assume the US found itself decreasing demand for goods and services and a corresponding increase in unemployment.  Would it be possible for the Federal Reserve Bank to deliberately increase the money supply to stimulate spending? 

Such expansionary policy is used frequently with ambiguous effect.  But here is the underlying idea.  In an effort to stimulate the economy, the Fed begins by buying more financial assets (like bonds).  In exchange for these assets it issues Federal Reserve Notes (i.e. our money) that it creates for the purpose. 

The following supply-demand diagram represents the market for borrowing.  Demand represents those persons who wish to borrow money for one reason or another.  Supply represents savers looking to loan money.  The interest rate is the effective price of borrowing money.  And so, the intersection of demand and supply determine the equilibrium interest rate.  Of course, there are many interest rates (e.g. mortgage rates, car loan rates, credit card rates, etc.). But all of these are determined the same way and largely move in unison.  And so, we can get away with pretending there is only the one.   

In practice, the Federal Reserve sets a single target interest rate and continues to increase (or decrease) the supply of Federal Reserve Notes until this interest rate equals the Fed’s target.  The rate the Fed targets is the “Federal Funds” rate.  This is the rate banks charge each other for very short-term loans.  There are reasons the Fed chooses this rate to target, but it could just as easily be mortgage rates, or student loan rates, or anything else. 

Now, what happens to the economy when the Fed creates all this new money?  Since they did so by purchasing financial investments, we might assume the sellers were people interested in saving.  And so, the money the Fed uses to pay for these assets will likely become more supply in our market.  Interest rates will therefore decrease.  Lower interest rates in turn are expected to motivate companies to borrow to build new factories, buy new equipment, etc. 

This is the mechanism underlying our equation of exchange.  An increase in money leads to an increase in GDP by driving down interest rates and so increasing investment in plant and equipment. 

What if the Federal Reserve is concerned about an overheated economy potentially causing inflation?  In this case, the Fed would sell financial securities.  The money it receives (i.e. the Federal Reserve Notes or IOUs) would simply be destroyed.  This in turn would decrease the supply of funds available to borrow driving up interest rates.  The increase in interest rates might then cause a decrease in spending by companies.