Milton Friedman has famously claimed once - inflation is everywhere and without exception a monetary phenomenon. Many have agreed, many have disagreed and a small subset on either side have understood. I don't know which group i belong to!
In theory, it is quite straightforward to understand that if the money supply in the economy is growing at the same rate as the output, the average price level in the economy will be constant - zero inflation. Hence any economy wide price increase has to be attributed to the prevalence of more money than that is needed to buy all the goods and services produced. The issue becomes perpelxing when one thinks of the so-called supply side inflationary shocks. If the oil price goes through the roof, prices of most things tend to go up. This is also easy to understand and in fact to see in practice. What happens to money supply in this case? As in, if money supply were constant and the price of a key commodity went up due to supply side issues, what explains the resultant inflation?
One can go back to first principles and device a thought experiment. Say a closed economy has wheat as the primary commodity and a host of manufactured goods and services. For simplicity let us assume that the economy is not growing in real terms and has constant money supply. Hence one can effectively point to the total amount money in the market (including notes, coins and bank deposits). Now if the wheat harvest of one year turns out to be quite bad and the stocks dwindle. The demand for wheat has remained same and hence by the laws of supply and demand, the price of wheat will go up. Insofar as there is no change in the money supply, one would expect a deflationary pressure on the price of other commodities. As in the haircuts and electricity should become cheaper since more money is now being sent the way of purchasing wheat. Would it happen in real life? If not, where would the excess money to pay for more wheat come from?
In a real life scenario, there might be a linkage to the asset markets and credit generation. Ultimately money supply is primarily affected by the rate of credit growth in the economy. If the supply shock leads to change (effectively increase) of the credit in the economy, it can lead to inflation through a forced change in money supply. Forced in the sense that it comes from outside the monetary policy controller of the economy (central bank). In this sense Friedman may be right in the final observation - it is through the money supply route that the supply shocks also get to increase inflation. But the statement has been often abused by monetary policy critics who directly translate that statement into a blame for all inflation onto monetary policy. That is clearly not the case.
One can only say that supply side or demand side, inflation comes through increase of money supply. Not always can the increased money supply be attributed to the monetary policy. However only active monetary policy can quell the increased money supply.
Another important factor in considering the impact of money supply on inflation is the growth rate in asset markets. It is not only goods and services that are purchased with money. Equities, bonds and real estate are as well. Hence the linkage of money supply to inflation is not complete without understanding the balancing figures of asset price changes. More on that later.