Question

If volatility of a variable during 2000 - 2014 is defined as
$\frac{Maximumvalue-Minimumvalue}{Averagevalue}$, then which of the following is true?

• A. Price per unit has the highest volatility
• B. Cost per unit has the highest volatility
• C. Total profit has the highest volatility
• D. Revenue has the highest volatility
• E. None of the above

Answer 1

The correct option is C Total profit has the highest volatility

Checking option (a),
Volatility per unit $=\frac{15-8}{\frac{126}{11}}=\frac{77}{126}=0.611$ Checking of option (b),
Total cost = Revenue - Profit
= (700 + 1400 + 1200 + 900 + 1100 + 400 + 200 + 700 + 600 + 800 + 900) - (0 + 100 + 300 + 150 + 0 + 150 + 100 + 200 + 0 + 400 + 300) = 8900 - 1700 = 7200
Average cost per unit $=\frac{7200}{11}$
Volatility cost per unit $=\frac{(1400-100)-(200-100)}{7200}$ $=\frac{1300-100}{7200}\times 11=1.833$
Checking option (c),
Average profit $=\frac{1700}{11}$
$\therefore$ Profit volatility $=\frac{400-0}{\frac{1700}{11}}=\frac{44}{17}=2.588$
Checking option (d),
Average revenue $=\frac{8600}{11}$
$\therefore$ Revenue volatility $=\frac{1400-200}{\frac{8600}{11}}$
$=\frac{132}{86}=1.535$
$\therefore$ Total profit has highest volatility.