 # The price level and the quantity theory of money

## The quantity theory of money

One of the key elements of the classical model is the quantity theory of money. The quantity theory of money connects three important variables: M, P, and Y: the money supply, the price level and the real GDP.

PY is equal to nominal GDP. Suppose that nominal GDP is equal to 100 for a particular year while the money supply is constant and equal to 20 throughout that year. Since we are using money to buy finished goods, we may conclude that every monetary unit (USD or euro or whatever) has been used an average of 5 times during the year (100/20). This value is called the velocity of money and it is denoted by V. We have This is not a theory but a definition. What makes it into a theory - the quantity theory of money - is the assumption that V is a stable variable that does not depend on other economic variables. In the quantity theory, the velocity of money is an exogenous variable.

The quantity theory of money: MV = PY, V exogenous

The main consequence of the quantity theory of money is the direct relationship between M and P if Y is constant. For example, if the money supply increases while real GDP stays the same, P will increase exactly as much as M (in percentage).

## The price level

The price level is determined from the quantity theory of money: P = (M-V)IY

In the classical model, money supply M is an exogenous variable (hence, the growth rate in the money supply nM is exogenous). It is determined by the central bank (as discussed in Chapter 7.4.2). Similarly V is an exogenous variable in agreement with the quantity theory of money. Thus, M- V is exogenous and given.

Remember that Y is determined by the labour market and the production function. If we combine this with the quantity theory of money, we can determine the price level P: P = (M- V)/Y.

Now, suppose that GDP is constant over time. Since V is stable (let’s say it too is constant), the percentage change in P is equal to the percentage change in M. That is, inflation is equal to the growth rate of money or n = K„,.

Remember that we have removed the trend in Y which means that Y cycles around some average over time. Thus, Y is not constant over time but there is no growth in Y. Therefore, n = nM will still be approximately true even when Y is not constant (it will be true on average and in the long run).

If we do not remove the trend in Y, the result would instead be that inflation is equal to the growth in money supply minus the growth in real GDP.

## Aggregate demand

P and Y are both endogenous variables and according to the quantity theory of money we need P-Y = constant. If we divide both sides by P we get Y = constant / P. Since Y = YD in the classical model, we can write YD = constant / P. This relationship is sometimes called "classical aggregate demand" as it relates the real aggregate demand for goods and services YD to the price level P. Fig. 10.4: Determination of price level.

However, it is important to remember that it is not price adjustments that make aggregate demand equal to aggregate supply in the chart above. Aggregate demand is always equal to the aggregate supply by Say’s Law. In the classical model, YD is not determined by P but rather the opposite; P is determined by YD (which is equal to YS) and the money supply (which is included in the constant).

## Nominal wages

The nominal wage Is equal to the real wage times the price level.

Since the real wages W/P is determined in the labor market and P is determined by the quantity theory of money, we can also determine the nominal wage in the classical model: W = (W/P) P. From the labor market, Say’s Law and the quantity theory, we have now determined W, P, Y and L. We can also demonstrate how all these four are determined simultaneously: Fig. 10.5: Determination of W, P, Y and L.