Initial Publication Date: April 12, 2016
Calculating Percentage Change: Practice Problems
Problem 1:
During one year in 1980, gas prices rose from $0.75 per gallon to $1.50 per gallon. In 2010, prices increased from $3.50 to $4.50. When did consumers face the biggest price increase in percentage terms?
In 1980:
- change in price was $1.50 - $0.75 = $0.75
- percent change was (0.75/ 0.75) x 100 = 100%
In 2010:
- change in price was $4.50 - $3.50 = $1.00
- percent change was (1.00 / 3.50) x 100 = 28%.
Even though prices increased by $1.00 in 2010 and only $0.75 in 1980, on a percentage basis, the 1980s increase was much more.
Problem 2:
In which year was inflation the highest? The lowest?
Year CPI
============
1980 82
1981 91
1982 97
1983 100
For 1981:
- change in CPI was 91-82 = 9
- percent change was (9/82) x 100 = 11%
For 1982:
- change in CPE was 97 - 91 = 6
- percent change was (6/91) x 100 = 7%
For 1983:
- change in CPE was 100 - 97 = 3
- percent change was (3/97) x 100 = 3%
Inflation was highest in 1981.
Inflation was lowest in 1983.
Problem 3:
Gross Domestic Product (GDP) for the U.S. and China in 2004 and 2005 are given below:
2004 GDP:
- China 16,000 billion RMB
- U.S. $11,900 billion
2005 GDP:
- China 18,300 billion RMB
- U.S. $12,600 billion
Which country had the faster growth rate?
For China:
- change in GDP was 18,300 - 16,000 = 2,300 billion RMB
- percent change was (2,300/16,000) x 100 = 14%.
For U.S.:
- change in GDP was $700 billion
- percent change was (700/11,900) x 100 = 6%.
China had the faster growth rate.
Problem 4:
At the start of 2011, Apple stock was valued at $322 per share, and Bank of America stock was valued at $13.50 per share. At the end of 2011, Apple stock was worth $456 per share, and Bank of America was worth $7.10 per share. How much did an investor gain or lose by owning each stock?
For Apple:
- change in value was $456-$322 = $132
- percent change was (132/$322) x 100 = 41.6%.
For Bank of America:
- change in value was $7.10-$13.50 = -$6.40
- percent change = (6.40/13.50) x 100 = -47.4% loss for Bank of America.
Apple stock had a big gain of 41.6%.
Bank of America stock suffered a large loss of 47.4%.
Problem 5:
A 20 percent increase in income causes water consumption for a typical U.S. household to increase from 800 to 840 gallons per week. What is the income elasticity of demand (that is: percent change in demand / percent change in income)?
Demand for water:
- change = 840 - 800 = 40 gallons per week
- percent change = (40/800) x 100 = 5%.
Income elasticity = (percent change in quantity demanded)/(percent change in income) = 5%/20% = 0.25
The income elasticity of demand is 0.25
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