The quantity theory of money describes inflation and has a long history dating back to thinkers in the Renaissance. Coepernicus among others noted that as gold arrived from the New World the price of goods rose. Thus the theory expounds that there is a positive relationship between increases in the money supply and prices of goods and services.
An easy example would be coffee. Imagine a Dunkin Donuts as it started in the 1950s, it charged a nickel. Now to buy that same cup of joe it costs 2 pieces of silver ($2.00.) Is it because the coffee is better, or because people enjoy it more? Nope, according to the theory, your dollar's value is less, so before a 20th of a dollar got you some warm goodness now it costs two. So how did the dollar come to be valued less? Isn't monetary policy off the gold standard?
It wouldn't be economics if supply and demand were not involved. The money supply is based on the Federal Reserve through its operations including its open market operations. Again, it buys bonds to increase the money supply and it sells them to decrease the money supply. For the next example it is assumed that the Federal Reserve keeps the money supply constant. The money demand however is controlled by people. Some factors that affect how much money people want to hold are: that availability of credit through credit cards, the availability of withdrawing funds either through an ATM or from a bank's teller. Underlying this idea though is the cost of goods/services because as they are priced higher than people must carry more cash for daily transactions. Since the people carry higher balances with higher prices than the demand for money is greater.
Here is a chart.
The blue line is the fixed money supply. The Red line is the Money Demand. The demand line curves downward because as the value of money falls or conversely the price level is higher people desire a larger quantity of money. The equilibrium is shown by the dotted line it is where the price level and the value of money intersect.
Now as the Fed performs open market operations, say buying treasury bonds, it will increase the money supply. The next chart shows the money supply parallel shifting out (from blue to orange.) This cause the value of money to fall and thus price levels to rise.
It is important to note that the fundamental economy has not been affected by this injection of money. The capital level has not changed, the labor productivity has not changed, knowledge is static, everything in short is held constant. However, because there is now more money chasing the same amount of goods then prices must therefore rise.
This brings up another point, that prices should not matter or restated that there exists a monetary neutrality. If prices double, then so should wages because the inputs for the good/services include labor, thus everything should be equal in the long run.
Now back to MV=PY or V=(PY/M) so the velocity of money should equal the price level times real output divided by the quantity of money. During most times V is stable, however, during financial crises this does not have to be so.
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