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## The Quantity Theory of Money

The quantity theory of money basically explains how the quantity of money in the economy affects the price level. The quantity theory is usually explained simply in the identity MV = PT. This means quantity of money (M) multiplied by velocity (V) equals price level (P) multiplied by the number of transactions (T). The velocity of money describes the rate at which money circulates round the economy – for instance if you were to follow the life of one pound coin, velocity tells us how many times that pound changes hands in a given time period.

Because this is an identity, the left hand side always equals the right. Suppose you had an economy existing solely of cars, and there were 100 cars bought and sold in a year at a price of £3000 each, and the overall quantity of money in the economy was £50000

The number of transactions (T) is 100, the average price level of transaction is (P) is £3000 per car, so PT = £300000. M is £50000, so MV = PT means 50000V = 300000, so V = 6. This means the velocity of money is 6, each pound must change hands 6 times a year.

Usually when using the quantity theory of money model we make a couple of assumptions:

1 – The number of transactions is proportional to the total output in the economy. This is fairly logical – if the economy grows then more stuff is produced so more stuff changes hands. So we can roughly substitute output (Y) for transactions (T) and express the quantity theory identity in a more useful form: MV = PY. You can think of velocity now as being the income velocity (number of times a pound enters someone’s income in a given period of time).

2 – Velocity of money is constant. This is a simplification of reality because the money demand function will change depending on the interest rate. The velocity of money is related to the money demand functon – by assuming the velocity is constant we are assuming a money demand function of $\frac{M}{P}=kY$ where k is a constant. This can be rewritten as $\frac{M}{k}=PY$ which is the same as MV = PY when V = (1/k). If k is large then people have a high demand for money and want to hold a lot of money for each pound of income, so money does not change hands very much, V is small. If k is small then people have a low demand for money and want to hold little money for each pound of income, in this case money changes hands quickly and V is large. Assuming k is constant means V is constant which makes the identity a lot more informative as if one part is fixed it allows to see how certain elements of the identity will adjust in response to changes to the others.

So if we call the quantity theory of money $M\bar{V}=PY$ where V is now fixed, then it leads us to important conclusions:

– If the quantity of money in the economy (M) increases faster than output (Y) increases, then the price level (P) has to rise.
– If the quantity of money (M) increases slower than output (Y) increases, then the price level (P) has to fall.

In the real world prices tend to adjust upwards more easily than they adjust downwards (known as being sticky downwards) so if the price level cannot adjust downwards quickly enough, then output itself may decrease in response to an excessively slow increase in M. In this case you have a recession rooted in monetary factors – people are not spending due to a lack of available money to facilitate transactions, so demand drops. This type of recession can be addressed by increasing the money supply.