With M = 1000 and P = 2, the real money supply is 500. The real money supply is independent of the interest rate and is, therefore, represented by the vertical line. What is the equilibrium interest rate? Set the supply and demand for real balances equal to each other: 500 = 1000 – 100r r = 5, so the real interest rate is 5%.

Assume that the demand for real money balance ( M / P) is M / P = 0.6 Y - 100 i, where Y is national income, and i is the nominal interest rate (in percent). The real interest rate r is fixed at 3 percent by the investment and saving functions. The expected inflation rate equals the rate of nominal money growth. The interaction of the demand for real money balances, L, and the supply of real money balances, M/P, in the money market determines. The equilibrium real GDP and employment.

Nouriel Roubini

Undestanding theWorld Macroeconomy

Handout for Chapter 6:

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 nominalinterest rate i.

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

In the classical theory, money is a veil that does notaffect real variables. It affects only nominal variables.

The Quantity Theory of Money

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

Casnio real money games. 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 eachperiod:

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 timeseach 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 timeseach period a unit of money is in a transaction.

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

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

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

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

Real Money Balances Meaning

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

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

(M_t / M_t-1) (V_t / V_t-1)= (P_t / P_t-1) (Y_t / Y_t-1)

This leads (approximately):

(M_t - M_t-1)/M_t-1 + (V_t- V_t-1)/V_t-1 = (P_t - P_t-1)/P_t-1+(Y_t - Y_t-1)/Y_t-1

or: m + v = p + y

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

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

(M_t - M_t-1)/M_t-1 = (P_t- P_t-1)/P_t-1+ (Y_t - Y_t-1)/Y_t-1

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:

P_t(G_t-T_t) = dM_t= M_t - M_t-1

i.e. each dollar of deficit is financed by dM_tnew dollar bills.

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

Government Debt	4,000
Bonds	3,800
Currency	200

Suppose the government (generally the central bank) wantsto increase the quantity of currency in the economy by 20 billion $.

It does this by buying 20b of bonds from someone in theprivate sector, and paying for them in cash.

This is an open market purchase of government securitiesthat increases the money supply:

Government Debt	4,000
Bonds	3,780
Currency	220

Effect of open market operations performed by the Fedon short-term interest rates.

Interest Rates and Inflation

The real interest rate (r) is the difference between thenominal interest rate (i) and the expected inflation rate (p^e):

r = i- p^e

or : i = r + p^e

The real interest rate is determined by savings and investment(see chapter 5) with no relation to money and inflation.

So, for given real interest rate, the nominal interestis determined by the inflation rate: higher p^e leads to higheri.

Evidence on the monetary theory

The complete separation between real and nominal variablesis overly strong in the short-run run, but it is a good approximation ofthe long run effects of money.

First prediction: velocity is constant or the pricelevel follows the money stock adjusted for the level of output. In logarithms:

log P_t = log M_t - log Y_t+ log V_t

i.e. if the money supply grows faster than output, weshould see a comparable increase in the price level. See Figure1: the match is quite good but note that there are ‘wiggles’ in velocity.

If we graphs annual growth rates, we should get that:

(P_t - P_t-1)/P_t-1 = (M_t- M_t-1)/M_t-1 - (Y_t - Y_t-1)/Y_t-1

since velocity is assumed to be constant.

Figure 2: the link between money growthand inflation is much looser for short run mov

Real Money Balances M P