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Reading: AB, chapter 7, section 4.

Recall, inflation is simply the growth rate of some aggregate price index like the CPI or the GDP deflator. If P(t) denotes the aggregate price level in year t then, symbolically, annual inflation from year t-1 to year t is given as: = %P(t) = (P(t) - P(t-1))/P(t-1).

We build a link between money growth and inflation through our model of money market equilibrium. In money market equilibrium, real money supply is equal to real money demand: M/P = L^d(Y, i). If we assume that the aggregate price level is free to adjust to keep the money market in equilibrium then we can use the money market equilibrium condition to solve for the aggregate price level: P = M/L^d(Y, i). That is, the price level is directly related to the nominal money supply and to real money demand (which is a function of real income and the nominal interest rate).

A) Nominal money is the amount of money measured in dollars. B) The quantity of nominal money demanded is proportional to the price level — a 10 percent rise in the price level increases the quantity of nominal money demanded by 10 percent. The interest rate is the opportunity cost of holding wealth in the form of money rather than. The equilibrium between money supply (which is set by the fed) and money demand (which is set by economic factors) generates the interest rate for the economy at a given time. The fed thus has power to affect the interest rate by increase or decrease the real money supply in order to maintain an interest rate.

Using the above relationship between the aggregate price level, nominal money supply and real money demand we may derive a link between inflation, growth in the money supply and growth in money demand. Inflation is just the growth rate of aggregate prices and from the relationship P = M/L^d(Y, i) we get, using the fact that the growth rate of a A/B is equal to the growth rate of A minus the growth rate of B, = %P = %M - %L^d(Y,i). That is, inflation is equal to the growth rate in the nominal money supply (controlled by the Fed) minus the growth rate in real money demand.

Notice that if the growth rate of the nominal money supply is equal to growth rate of money demand then inflation is equal to zero. Now money demand grows over time primarily because the real economy grows over time (average real growth is about 2.5% per year on average). As Y grows individuals consume more and thus need more money to conduct transactions. Since money demand is a function of both Y and i we can use a trick from calculus - the total derivative - to decompose the growth of money demand as follows: %L^d(Y,i) = e_Y*%Y + e_i*%i, where e_Y = income elasticity of money demand and e_i = nominal interest rate elasticity of money demand. Economists estimate that e_Y is approximately 2/3, for the U.S., and that e_i is approximately -1/10 so that money demand is much more sensitive to changes in income than to changes in the nominal interest rate. Further, the growth rate of the nominal interest rate is on average about zero (interest rate on average do not tend to go up or down). These data facts tell us that the nominal interest component does not contribute much to the growth rate of money demand and a reasonable good prediction model for inflation become: = %P = %M - (2/3)*%Y.

An example

Suppose the Fed sets money growth, %M, equal to 6% per year, the annual real economic growth, %Y, is 3% and that the income elasticity of money demand is 2/3. Then our prediction for inflation is given by: = %M - (2/3)*%Y = 6% - (2/3)*3% = 4%.

Empirical relationship between money growth and inflation

The tables below show the relationship between actual inflation and money growth in low money growth countries and high money growth countries.

Inflation in low money growth countries: 1986-1989
Country	money growth (% per year)	inflation (% per year)
Chad	-2.1%	-2.7%
Switzerland	4.1%	1.8%
Belgium	5.0%	1.8%
France	5.5%	3.0%
United States	7.0%	3.6%

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Inflation in high money growth countries: 1986-1989
Country	money growth (% per year)	inflation (% per year)
Peru	425%	545%
Yugoslavia	358%	305%
Mexico	71%	82%
Poland	47%	68%
Nepal	20%	11.2%

Real Money Supply Nominal Interest Rate Calculator

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Last updated on July 18, 1996 by Eric Zivot.

Real versus Nominal Rates of Interest: Fisher Equation- Basic Macroeconomics

1. Learning Outcomes
2. Introduction
   1. Nominal interest rate
   2. Real interest rate
3. Relation between Real and Nominal interest rate
4. Relationship between Real and nominal interest rate and Expected Inflation: Fisher equation
5. Different applications of Real and Nominal interest rate
   1. Real versus Nominal interest rate and Present values
   2. Real versus Nominal interest rate and the IS-LM model
6. Fisher effect in economics
7. Summary

Nominal Interest Rate Formula

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