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## CPI and the Cost of Living

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**6**CPI and the Cost of Living CHAPTER CHECKPOINTS**Checkpoint 6.1**Checkpoint 6.2 Checkpoint 6.3 Problem 1 Problem 1 Problem 1 Problem 2 Problem 2 Problem 2 Problem 3 Problem 3 Problem 3**Practice Problem 1**A Consumer Expenditure Survey in Sparta shows that people buy only juice and cloth. In 2008, the year of the Consumer Expenditure Survey and also the reference base year, the average household spent $40 on juice and $25 on cloth. In 2008, juice was $4 a bottle and cloth was $5 a yard. In the current year, 2009, juice is $4 a bottle and cloth is $6 a yard. Calculate the CPI market basket and the percentage of household budget spent on juice in the reference base year. CHECKPOINT 6.1**Solution**The CPI market basket is the quantities bought during the Consumer Expenditure Survey year, 2008. Households spent $40 on juice and at $4 a bottle, so the quantity of juice bought was 10 bottles. Households spent $25 on cloth at $5 a yard, so the quantity of cloth bought was 5 yards. The CPI market basket is 10 bottles of juice and 5 yards of cloth. CHECKPOINT 6.1**In the reference base year, the average household spent $40**on juice and $25 on cloth, so the household budget was $65. Expenditure on juice was 61.5 percent of the household budget: ($40 ÷ $65) x 100 = 61.5 percent. CHECKPOINT 6.1**Practice Problem 2**A consumer Expenditure Survey in Sparta shows that people buy only juice and cloth. In 2008, the year of the Consumer Expenditure Survey and also the reference base year, the average household spent $40 on juice and $25 on cloth. The price of juice in 2008 was $4 a bottle, and the price of cloth was $5 a yard. In the current year, 2009, juice is $4 a bottle and cloth is $6 a yard. Calculate the CPI in 2009 and the inflation rate in 2009. CHECKPOINT 6.1**Solution**To calculate the CPI in 2009, find the cost of the CPI basket in 2008 and 2009. In 2008, the CPI basket costs $65 ($40 for juice + $25 for cloth). In 2009, the CPI basket costs $70 (10 bottles of juice at $4 a bottle plus 5 yards of cloth at $6 a yard), which is $70. The CPI in 2009 is ($70 ÷$65) x 100 = 107.7. The inflation rate in 2009 is [(107.7 – 100) ÷ 100] x 100, which is 7.7 percent. CHECKPOINT 6.1**Practice Problem 3**The table shows the CPI in Russia. Calculate Russia’s inflation rate in 2006 and 2007. Did the price level rise or fall in 2007? Did the inflation rate increase or decrease in 2007? CHECKPOINT 6.1**Solution**The inflation rate in 2006 is [(219 – 200) ÷ 200] x 100 = 9.5 percent. The inflation rate in 2007 is [(237 – 219) ÷ 219] x 100 = 8.2 percent. In 2007, the price level increased, but the inflation rate decreased. CHECKPOINT 6.1**Practice Problem 1**The Statistics Bureau decides to check the substitution bias in the CPI. To do so, it conducts a Consumer Expenditure Survey in both 2005 and 2006. The table shows the results of the survey: the items that consumers buy and their prices. Calculate the CPI in 2006 using the 2005 CPI market basket. CHECKPOINT 6.2 • The Statistics Bureau fixes the reference base year as 2005.**Solution**The table shows the calculation of the CPI in 2006 using the 2005 basket. The cost of the 2005 basket at 2005 prices is $60, and the cost of the 2005 basket at 2006 prices is $90. So the CPI in 2006 using the 2005 basket is ($90 ÷ $60) x 100, which is 150. CHECKPOINT 6.2 • The Statistics Bureau fixes the reference base year as 2005.**Practice Problem 2**The Statistics Bureau decides to check the substitution bias in the CPI. It conducts a Consumer Expenditure Survey in both 2005 and 2006. The table shows the results of the survey: the items that consumers buy and their prices. Calculate the CPI in 2006 using the 2006 CPI market basket. CHECKPOINT 6.2 • The Statistics Bureau fixes the reference base year as 2005.**Solution**The table shows the calculation of the CPI in 2006 using the 2006 basket. The cost of the 2006 basket at 2005 prices is $65, and the cost of the 2006 basket at 2006 prices is $85. So the CPI in 2006 using the 2006 basket is ($85 ÷ $65) x 100, which is 131. CHECKPOINT 6.2 • The Statistics Bureau fixes the reference base year as 2005.**Practice Problem 3**The Statistics Bureau decides to check the substitution bias in the CPI. It conducts a Consumer Expenditure Survey in both 2005 and 2006. The table shows the results: the items that consumers buy and their prices. Is there any substitution bias in the CPI that uses the 2005 basket? Explain. CHECKPOINT 6.2 • The Statistics Bureau fixes the reference base year as 2005.**Solution**There is some substitution bias in the CPI that uses the 2005 basket. The price of broccoli remains constant, whereas the price of carrots rises by 100 percent. So consumers cut the quantity of carrots consumed and increase the quantity of broccoli consumed. They end up spending $85 on vegetables, but they would have spent $90 if they had not substituted the now relatively less costly broccoli. CHECKPOINT 6.2**CHECKPOINT 6.2**• The cost of vegetables does not rise by 50 percent as shown by the CPI. • Instead, because of substitution, the cost of vegetables increases by only 42 percent ($85 is 42 percent greater than $60). • When we calculate the increase in the price of vegetables using the 2006 CPI market basket, the increase is only 31 percent ($85 compared with $65). • So the CPI is biased upward because it ignores the substitutions that people make in response to changes in the price of one item relative to the price of another.**Practice Problem 1**The table shows the gas price and the CPI for four years. The reference base period is 1982–1984. Calculate the real price of gasoline in each year in 1982–1984 cents. In real terms, in which year was gasoline the most costly and in which year was gasoline the least costly? CHECKPOINT 6.3**Solution**To calculate the real price of gasoline in 1982–1984 cents, divide by the CPI and multiply the nominal price by 100. The table shows the calculations. CHECKPOINT 6.3**In real terms, gasoline was the most costly in 1981, when it**was 152 cents (1982–1984 cents) per gallon. Gasoline was the least costly in real terms in 2001, when it was 83 cents (1982–1984 cents) per gallon. CHECKPOINT 6.3**Practice Problem 2**Amazon.com agreed to pay its workers $20 an hour in 1999 and $22 an hour in 2001. The CPI for these years was 166 in 1999 and 180 in 2001. Calculate the real wage rate in each year. Did these workers really get a pay raise between 1999 and 2001? CHECKPOINT 6.3**Solution**The real wage rate in 2001, expressed in dollars of the reference base year, was ($22 ÷ 180) X 100 = $12.22 an hour. The real wage rate of these workers increased between 1999 and 2001. CHECKPOINT 6.3**Practice Problem 3**Sally worked hard all year so that she could go to school full time the following year. She put her savings into a mutual fund that paid a nominal interest rate of 7 percent a year. The CPI was 165 at the beginning of the year and 177 at the end of the year. What was the real interest rate that Sally earned? CHECKPOINT 6.3**Solution**The inflation rate during the year that Sally worked was equal to (177 – 165) ÷ 165) x 100 = 7.3 percent. Her savings in the mutual fund for the full year her earned a real interest rate equal to the nominal interest rate minus the inflation rate, which is 7.0 – 7.3 = – 0.3 percent. Sally’s real interest rate was negative. (If Sally had just kept her savings in cash, her nominal interest rate would have been zero, and her real interest rate would have been -7.3 percent. She would have been worse off.) CHECKPOINT 6.3