Calculating Percentage Change
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Problem 1:
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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 - Step 1: change in price was $1.50 - $0.75 = $0.75; Step 2: percent change was (0.75/ 0.75) x 100 = 100%
In 2010 - Step 1: change in price was $4.50 - $3.50 = $1.00; Step 2: 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 apercentage 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
Inflation was highest in 1981. Step 1: change in CPI was 91-82 = 9; Step 2: percent change was (9/82) x 100 = 11%; Inflation was lowest in 1983. Step 1: change in CPE was 100 - 97 = 3; Step 2: percent change was (3/97) x 100 = 3%
Problem 3:
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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 - Step 1: change in GDP was 18,300 - 16,000 = 2,300 billion RMB; Step 2: percent change was (2,300/16,000) x 100 = 14%. For U.S. - Step 1: change in GDP was $700 billion; Step 2: percent change was (700/11,900) x 100 =6%.
Problem 4:
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Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
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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 - Step 1: change in value was $456-$322 = $132; Step 2: percent change was (132/$322) x 100 = 41.6%. For Bank of America - Step 1: change in value was $7.10-$13.50 = - $6.40; Step 2: percent change = (6.40/13.50) x 100 = -47.4% loss for Bank of America. Apple stock had a big gain. Bank of America stock suffered a large loss
Problem 5:
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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 - Step 1: change = 840 - 800 = 40 gallons per week; Step 2: percent change = (40/800) x 100 = 5%. Income elasticity = percent change in quantity demanded/percent change in income = 5%)/20% = 0.25
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