Some preferatory remarks:

To have a low interest rate, you need a larger money supply. You can't change one without the other. Increased money supply always shows up as inflation. We will see how the money supply is controlled.

Velocity of Money

V = PY/M = nominal GDP / M

Recall: GDP deflator (P) = Nominal GDP / Real GDP (Y)

Therefore, nominal GDP = PxY

Velocity is how many times the money changes hands to get to GDP.

Latest data: 2006 nominal GDP 13.2Tr. V or M1 = 9.6. V of M2 = 1.96.

Quantity equation: M x V = P x Y

Assume V is constant

(i) M x Vbar = P x Y

(ii) In the long run, Y = AxF(K,L)

If the money supply M increases, it must show up in an increase in P, prices. (Unless K and/or L work to increase Y)

This is known as the quantity theory of money.

In %Δ - %DM + %DV = %DP + %DY

%DP is inflation, denoted at Π

Therefore, Π = %DM - %DY

%DY has historically been about 3% in the US.

Any money supply increase over the GDP growth rate will show up as inflation. This is the primary driver of inflation - excessive monetary growth. Other sources of inflation are: Cost-push inflation, demand-pull inflation (seen after the collapse of Soviet Union).

The assumption was that the velocity of money is constant. Data shows (Table 1) that %DY is about 0.1% on average from 1960-2006. Monetary innovations such as debit cards and ATM

machines have impacted the velocity of money.

Friedman: Inflation is always and everywhere monetary phenomenon.

So why can't we easily control inflation through monetary policy?

Forecasting - We'd need to know the growth rate accurately in order to control the money supply correspondingly.

Time Lag - money supply changes effect the economy with about a year lag

Cross-country data supports the connection between money supply and inflation.

Nominal and Real Interest Rates

Fisher Equation: i = r + Π

i = nominal interest rate

r = real interest rate

Π = actual inflation rate

In practice, i = r + Π^{e}, where Π^{e} = expected inflation rate, since Π is not known in real time

The Fisher effect: one-for-one relationship between the inflation and niominal interest rates.

Using the Fisher equation, we see that monetary growth leads to inflation which leads to interest rates rising. Data since 1980 shows this correlation.

Liquidity Preference Theory

Determinants of money demand: (i, Y)

(i) i = opportunity cost of holding cash (nominal interest rate). We can graph this relationship - negative correlation between i and Md (money demand) If interest rates go down, money demand goes up.

What's the main purpose of holding cash? As a medium of exchange.

Dividing M by P (price level) makes this graph more meaningful.

If Y goes up, income goes up, and real money demand goes up and the (M/P)^{d} curve shifts to the right.

Money Market Equilibrium

See graph 3

Equilibrium is achieved when (M/P)^{s} = (M/P)^{d}

This occurs at interest rate i*.

At i_{1}, there are high interest rates and there is excess supply of money. Eventually, this excess supply will drive interest rates down.

Similarly, at i_{2}, there are low interest rates there is excess demand.

Notation: Real Monday Demand = L (i,Y)

If the Fed increases the money supply, the money supply vertical shifts to the right (monetary expansion). A new equilibrium point is achieved, with a lower interest rate. (see graph 4)

Timeline: Over time, other things will change and interest rates will not remain low after a monetary expansion.

(i) in the intermediate run (around 5 yrs), low interest rate will encourage consumption up, net exports up(via e down) and investments up. Therefore, output Y will increase because Y = C+I+G+NX. This causes a rightward shift to the money deman curve and a new equilibrium (3) is achieved.

(ii) in the long run, MxV=PxY and the ultimate result of increase money supply will show up in increased prices, P. This will drive interest rates even higher (i4 on graph).

Monetary policy is used to control and prevent these escalating interest rates in the intermediate and long run.

Refer to US Monetary Aggregate M2 (annual percent change) vs Federal Funds Rates 1960-2007 graph. It shows that they move in opposite directions.

## Wednesday, May 14, 2008

### Lecture 7 - Money (continued)

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