• Inflation
  • Definitions

Inflation

Inflation is the rise of prices of goods and services (reduction in purchasing power) over time.

Inflation rate can apply to:

• individual items: an orange today costs $0.69 costs $0.64 last year; the inflation rate is 7.8%
• commodity: inflation rate of bread is taken from average prices
• basket of goods: general consumer prices

Example: average inflation rate

Given the base price of $100 in year 0, inflation rate in year 1 is 5%, year 2 is 3%, what is average inflation rate over two years?

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First, find the real price at the end of year 2:

\[100(1+0.05)(1+0.03)=108.15\]

Then take average inflation rate \(f\) which is constant and plug it into the equation:

\[100(1+f)^n=108.15\]

where \(n=2\) for 2 years. \(f=3.995\%\).

Definitions

• Inflation Rate (\(f\)): annual rate of increase of cost to the same goods and services
• Real Interest Rate (\(i_R\) or \(i'\)): real growth of money (:x: excluding effect of inflation)
• Real / Constant Dollars ($R$$ or \(R_N\)): dollar with constant purchasing power, expressed using base year (:x: excluding inflation)
• Nominal / Market Interest Rate (\(i\)): rate that one obtains in general market place (:white_check_mark: includes inflation and real interest)
• Nominal / Actual Dollars ($A$$ or \(A_N\)): money at face-value

The relationship between real and nominal interest rate is:

\[(1+i)=(1+i')(1+f)\]

The relationship between real and nominal dollar is:

\[R_N=\frac{A_N}{(1+f)^N}\]

or simply:

\[R_N=A_N(P/F, f, N)\]