VI. The Quantity Theory of Money

• The quantity theory of money is the proposition that in the long run, an increase in the quantity of money brings an equal percentage increase in the price level.
• The velocity of circulation is the average number of times a dollar of money is used annually to buy the goods and services that make up GDP. Nominal GDP equals real GDP, Y, multiplied by the price level, P, or GDP=PY. So the velocity of circulation, V, is given by V = PY/M.
• The equation of exchange states that the quantity of money, M, multiplied by the velocity of circulation, V, equals GDP: MV = PY. The equation of exchange is a definition and so is always true. It becomes the quantity theory of money by adding two assumptions:

· The velocity of circulation is not influenced by the quantity of money.

· Potential GDP is not influenced by the quantity of money.

• The equation of exchange can be rearranged as P = M(V/Y). This equation, together with the assumptions about velocity and potential GDP, implies that in the long run, the price level is determined by the quantity of money.

· In growth rates, the equation of exchange is: (Money growth rate) + (Growth rate of velocity) = (Inflation rate) + (Real GDP growth rate). Rearranging this equation gives (Inflation rate) = (Money growth rate) + (Growth rate of velocity) - (Real GDP growth rate). If velocity does not grow, then in the long run the inflation rate equals the growth rate of the quantity of money minus the growth rate of potential GDP.

Evidence on the Quantity Theory of Money

The predictions of the quantity theory can be tested using evidence on money growth and inflation across time. On the average, the money growth rate and the inflation rate are correlated, supporting the quantity theory. The predictions of the quantity theory also can be tested using the evidence on money growth and inflation across countries. As predicted, rapid money growth is correlated with high inflation.

MATHEMATICAL NOTE

The mathematical note derives the formula for the money multiplier.

• Money is M.

M = Deposits + Currency

• The monetary base is MB.

MB = Currency+ Reserves.

· Currency = a ´ Deposits. The fraction “a” is the currency drain ratio, which is equal to C/D where C is currency and D is deposits..

· Reserves = b ´ Deposits. The fraction “b” is the reserve ratio, which is equal to R/D where R is reserves..

• Using these definitions for desired currency holdings and desired reserves shows that:

M = Deposits + a ´ Deposits = (1 + a) ´ Deposits

MB = a ´ Deposits + b ´ Deposits = (a + b) ´ Deposits

• Using “D” for “change in,” these last two equalities show that:

DM = (1 + a) ´ DDeposits

DMB = (a + b) ´ DDeposits

• The money multiplier is the ratio of DM to DMB. So dividing the top equation by the bottom gives:

Money multiplier = .

• The formula shows that the size of the money multiplier depends on the reserve ratio and the currency drain.
• In 2008, when times were more “normal,” for M1 the currency drain ratio, a, was equal to 1.24 and the reserve ratio, b, was equal to 0.28, so the money multiplier for M1 was = 1.47. In 2008, for M2 the currency drain ratio, a, was equal to 0.12 and the reserve ratio, b, was equal to 0.03, so the money multiplier for M2 was = 7.5.
• In 2010, when times banks are holding substantially more reserves than in past decades, for M1 the currency drain ratio, a, is equal to 1.06 and the reserve ratio, b, is equal to 1.32, so the money multiplier for M1 was = 0.87. In 2010, for M2 the currency drain ratio, a, is equal to 0.11 and the reserve ratio, b, is equal to 0.14, so the money multiplier for M2 was = 4.44.

Date: 2015-12-11; view: 802