Inflation Rates and Interest Rates (Mankiw)

INTERMEDIATE MACRO-ECONOMICS
CHAPTER 4 (MANKIW)
INFLATION RATES AND INTEREST RATES: THE FISHER EQUATION
NOTES by: Chadia Mathurin

Economists differentiate between real and nominal interest rates where: real interest: is defined as the increase or decrease in a consumer’s purchasing power experienced as a result of changes in the interest rate. nominal interest: is defined as the interest payed by the bank.

Let: i denote the nominal interest rate r the real interest rate pi , the inflation rate

The equation for the real interest rate is r = i - pi

Tutorial Sheet 2: Question 3

Assume in Jamaica, the velocity of money is constant. Real GDP grows by 5 percent per year, the money stock grows by 14 percent per year, and the nominal interest rate is 11 percent. What is the real interest rate?

Using the Quantity Equation in its percentage form, we get: %∆M + %∆V = %∆P + %∆Y, where %∆P is equal to the inflation rate. In this equation it is assumed that velocity is constant, thus %∆V = 0. Therefore let:
%∆M = 14
%∆V = 0
%∆P = pi
%∆Y = 5

Solving for P, we find that %∆P = %∆M + %∆V - %∆Y. Thus, %∆P = 14 - 0 - 5. %∆P = 9%

Using the Fisher Equation we find that: r = i - pi, where r denotes the real interest rate, i denotes the nominal interest rate and pi denotes the inflation rate. In the above mentioned question i = 11% and using the quantity equation it was found that pi = 9%. Thus the real interest rate is equal to 2%

THE FISHER EQUATION AND FISHER EFFECT

When the equation for finding real interest rates is rearranged, making nominal interest the subject of the formula, the Fisher equation is derived. The fisher equation is therefore as: i = pi + r

The Fisher Equation states that the nominal interest can be affected by either changes in the real interest rate or changes in the price level (inflation). The Fisher Effect shows a one-on- one relationship between the inflation rate and the nominal interest rate. According to the