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The CPI and the Cost of Living

7. The CPI and the Cost of Living. CHECKPOINTS. Checkpoint 7.1. Checkpoint 7.2. Checkpoint 7.3. Problem 1. Problem 1. Problem 1. Problem 2. Problem 2. Problem 2. Problem 3. Problem 3. Problem 3. Problem 4. Problem 4. Problem 4. Practice Problem 1

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The CPI and the Cost of Living

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  1. 7 The CPI and the Cost of Living CHECKPOINTS

  2. Checkpoint 7.1 Checkpoint 7.2 Checkpoint 7.3 Problem 1 Problem 1 Problem 1 Problem 2 Problem 2 Problem 2 Problem 3 Problem 3 Problem 3 Problem 4 Problem 4 Problem 4

  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. Table 1 sets out the prices of juice and cloth. Calculate the CPI market basket and the percentage of household budget spent on juice in the base year. CHECKPOINT 7.1

  4. Solution The CPI market basket is thequantities bought during thereference base 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 7.1

  5. 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 7.1

  6. 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. Table 1 sets out the prices of juice and cloth in 2008 and 2010. Calculate the CPI in 2010 and inflation between 2008 and 2010. CHECKPOINT 7.1

  7. Solution To calculate the CPI in 2010, find the cost of theCPI basket in 2008 and 2010. In 2008, the CPI basket costs $65 ($40 for juice + $25 for cloth). In 2010, the CPI basket costs $70 (10 bottles of juice at $4 a bottle + 5 yards at $6 a yard). The CPI in 2010 is ($70 ÷ $65) x 100 = 107.7. The inflation between 2008 and 2010 is [(107.7 – 100) ÷ 100] x 100, which is 7.7 percent. CHECKPOINT 7.1

  8. 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 7.1

  9. 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 7.1

  10. Practice Problem 4 Consumer prices rise less than expected in May The CPI in May 2009 was 212.9, 0.1% higher than the April CPI. The gasoline price rose 9.6% in May 2009, but gasoline was still cheaper than in May 2008 when it exceeded $4 a gallon. Because of the lower gas price, the CPI fell by 1.3% in the year to May 2009, the steepest drop since 1950. Source: USA Today, June 17, 2009 Use the information in the news clip to distinguish between the price level and the inflation rate. Explain why the reason suggested for the fall in the CPI can’t be entirely correct. CHECKPOINT 7.1

  11. Solution The CPI is the price level. The percentage change in the CPI is the inflation rate. Gasoline is one component of the transportation item in the CPI basket. The entire transportation item is only 15.3 percent of the CPI basket, so gasoline represents a small part of the CPI basket. For the CPI to have fallen in the year to May 2009, many other prices must also have fallen. The fall in gas prices is not the only or even the main reason why the CPI fell. CHECKPOINT 7.1

  12. 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 2008 and 2009. The table shows the results of the survey: the items that consumers buy and their prices. Calculate the CPI in 2009 using the 2008 CPI market basket. CHECKPOINT 7.2 • The Statistics Bureau fixes the reference base year as 2008.

  13. Solution The table shows the calculation of the CPI in 2009 using the 2008 basket. The cost of the 2008 basket at 2008 prices is $60. The cost of the 2008 basket at 2009 prices is $90. So the CPI in 2009 using the 2008 basket is ($90 ÷ $60) x 100, which is 150. CHECKPOINT 7.2

  14. Practice Problem 2 The Statistics Bureau decides to check the substitution bias in the CPI. It conducts a Consumer Expenditure Survey in both 2008 and 2009. The table shows the results of the survey: the items that consumers buy and their prices. Calculate the CPI in 2009 using the 2009 CPI market basket. CHECKPOINT 7.2 • The Statistics Bureau fixes the reference base year as 2008.

  15. Solution The table shows the calculation of the CPI in 2009 using the 2009 basket. The cost of the 2009 basket at 2008 prices is $65. The cost of the 2009 basket at 2009 prices is $85. So the CPI in 2009 using the 2009 basket is ($85 ÷ $65) x 100, which is 131. CHECKPOINT 7.2

  16. Practice Problem 3 The Statistics Bureau decides to check the substitution bias in the CPI. It conducts a Consumer Expenditure Survey in both 2008 and 2009. The table shows the results: the items that consumers buy and their prices. Is there any substitution bias in the CPI that uses the 2008 basket? Explain. CHECKPOINT 7.2 • The Statistics Bureau fixes the reference base year as 2008.

  17. Solution There is some substitution bias in the CPI that uses the 2008 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 7.2

  18. CHECKPOINT 7.2 • 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 2009 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.

  19. Practice Problem 4 News release Personal consumption expenditures (PCE) increased from $9,978.2 billion in May to $10,019.6 billion in June, an increase of 0.4%. Real personal consumption expenditures decreased from $9,185.5 billion in May to $9,173.5 billion in June, a decrease of 0.1%. Source: Bureau of Economic Analysis, August 4, 2009 Calculate the PCE price index in May 2009 and June 2009. How can real personal consumption expenditures decrease when personal consumption expenditures increases? CHECKPOINT 7.2

  20. Solution The PCE price index = (Nominal PCE ÷ Real PCE) x 100. In May 2009, the PCE price index equaled($9,978.2 billion ÷ $9,185.5 billion) x 100, or 108.63. In June 2009, the PCE price index equaled($10,019.62 billion ÷ $9,173.5 billion) x 100, or 109.22. The PCE price index rose by 0.55 percent, which exceeded the 0.4 percent increase in nominal PCE, so real PCE fell by 0.13 percent. CHECKPOINT 7.2

  21. 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 7.3

  22. 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 7.3

  23. 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 7.3

  24. 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 7.3

  25. 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 7.3

  26. 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 7.3

  27. 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 7.3

  28. Practice Problem 4 Inflation can act as a safety valve Workers will more readily accept a real wage cut that arises from an increase in the consumer prices than a cut in their nominal wage rate. Source: FT.com, May 28. 2009 Explain why inflation influences a worker’s real wage rate. Why might this observation be true? CHECKPOINT 7.3

  29. Solution The real wage rate in 2009 equals(Nominal wage rate ÷ CPI in 2009) x 100. Inflation occurs when the CPI increases. If inflation during 2009 is 3 percent, then the CPI at the end of 2009 is 3 percent higher than at the start of 2009, and the real wage rate has fallen by 3 percent during 2009. Inflation gradually lowers the real wage rate over the year, while a cut in the nominal wage rate lowers the real wage rate at a point in time. CHECKPOINT 7.2

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