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I. The Quantity Theory of Money
This theory, developed by the classical economists over 100 years ago, related the amount of money in the economy to nominal income. Economist Irving Fisher is given credit for the development of this theory. It begins with an identity known as the equation of exchange:
MV = PY
Where M is the quantity of money, P is the price level, and Y is aggregate output (and aggregate income). V is velocity, which serves as the link between money and output. Velocity is the number of times in a year that a dollar is used to purchased goods and services.
The equation of exchange is an identity because it must be true that the quantity of money, times how many times it is used to buy goods equals the amount of goods times their price.
To move towards the quantity theory of money, Fisher makes two key assumptions: 1. Fisher viewed velocity as constant in the short run. This is because he felt that velocity is affected by institutions and technology that change slowly over time. 2. Fisher, like all classical economists, believed that flexible wages and prices guaranteed output, Y, to be at its full-employment level, so it was also constant in the short run.
Putting these two assumptions together let’s look again at the equation of exchange:
MV = PY
If both V and Y are constant, then changes in M must cause changes in P to preserve the equality between MV and PY. This is the quantity theory of money: a change in the money supply, M, results in an equal percentage change in the price level P.
We can further modify this relationship by dividing both sides by V:
M = (1/V) x PY
Since V is constant we can replace (1/V) with some constant, k, and when the money market is in equilibrium, Md = M. So our equation becomes
Md = k x PY
So under the quantity theory of money, money demand is a function of income and does not depend on interest rates.
Is Velocity Constant?
A constant V is key to the quantity theory of money. For Fisher, the

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