MECH 431

# Inflation

Updated 2018-08-08

# 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? 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:

$R_N=A_N(P/F, f, N)$