# How does money supply affect inflation

## Money and Inflation

So far, we studied the determinants of real variables: Y, C, S. I, r, W/P, N (See Chapter 5 ).

We should now consider the determination of nominal variables: the price level P, the nominal wage W, the inflation rate, the nominal interest rate i.

Basic idea: the price level (and the nominal wage rate) depend on the level of the money supply. The rate of inflation depends on the rate of growth of the money supply.

In the classical theory, money is a veil that does not affect real variables. It affects only nominal variables.

**The Quantity Theory of Money**

Example of the neutrality of money: the government replaces every dollar with two new dollars. Effect: the prices of all goods in terms of new dollars would be twice as high.

Quantity theory of money and prices:

1. Money is not fundamental for real variables.

2. The usefulness of money is in executing transactions.

Suppose:

Y = All transactions in the economy in a period of time

PY = Value of all transactions (sales revenues)

So, we need M dollars to make all these transactions each period:

M = PY

So, if we double M, we double PY.

Reinterpret:

Y = Real GDP

P = GDP deflator index

PY = Nominal GDP

Slight generalization: money can be used several times each period for transactions, as it goes from one person to the other:

MV = PY

or: V = PY/M

where V is the velocity of money, the number of times each period a unit

of money is in a transaction.

Assumption of the quantity theory: V is constant so that changes in M are associated with proportional changes in PY.

In principle, the increase in PY could be in P or Y or both.

For now assume that Y (real output) is not affected by M. This means that a fundamental real variable such as Y is not affected by money since it is determined by the production function and labor market equilibrium (as seen in the Classical Theory).

Then, only P (the price level) can change when M changes.

Implication: changes in the stock of money lead to proportional changes in the price level.

The same theory can be reinterpreted in terms of the inflation rate. Take, the quantity equation at two dates and divide, to get:

This leads (approximately):

or: **m + v = p + y**

where lower case characters represent the rate of growth of upper case characters (i.e. m is the rate of growth of money M).

If velocity is constant, we get approximately, the growth rate of money equals the growth rate of prices (inflation) plus the growth rate of output:

or. **m = p + y**

Implication: if higher money growth does not affect output, higher money growth leads to higher inflation.

**Open Market Operations**

How do governments increase the money supply.

One way is to print money to finance budget deficits:

i.e. each dollar of deficit is financed by dM_{t} new dollar bills.

Other way to change the money supply: changes in the composition of the balance sheet of the government:

Source: people.stern.nyu.eduCategory: Bank

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