Homework Key Chapter 7

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Instructor: Dr. Nazneen Ahmad Homework KEY Chapter 7: The CPI and the Cost of Living Do the following problems from your textbook: Page 188: # 3 Answer: see page 188 for solution. Page 190 #3 2. The table shows the quantities of the goods that Suzie bought and the prices she paid during two consecutive weeks. Suzie’s CPI market basket contains the goods she bought in Week 1. Calculate the cost of Suzie’s CPI market basket in Week 1 and in Week 2. What percentage of the CPI market basket is gasoline? Calculate the value of Suzie’s CPI in Week 2 and her inflation rate in Week 2. Answer: Susie’s CPI market basket contains 11 cups of coffee, 1 DVD, and 15 gallons of gasoline. The cost of her market basket in Week 1 is (11cups *$3.25 a cup) + (1 DVD*$25 each) + (15 gallons of gasoline *$2.50 a gallon), which is $35.75 + $25.00 + $37.50, or $98.25 . The cost of her market basket in Week 2 is (11 cups *$3.25 a cup) + (1 DVD*$12.50 each) + (15 gallons of gasoline *$3.00 a gallon), which is $35.75 + $12.50 + $45.00, or $93.25 . Gasoline accounted for $37.50 of her $98.25 market basket, which is ($37.50 ÷ $98.25) × 100 or 38.2 percent. Her CPI in Week 2 is equal to [$93.25/$98.25] *100, which is equal to 94.9 . The CPI in the base week is 100, so the inflation rate in week 2 equals {[94.9 - 100.0] / 100} * 100, which is -5.1 percent. 1 Item Week 1 Week 2 Quantity Price (per unit) Quantity Price (per unit) Coffee 11 cups $3.25 11 cups $3.25 DVDs 1 $25.00 3 $12.50 Gasoline 15 gallons $2.50 5 gallons $3.00 Concert 1 ticket $95.00

3) Suppose in 2009 the United Congress passes a minimum wage law that increases the minimum wage to $7.25 per hour and has a provision that increases the minimum wage at the beginning of each year based on the CPI for the previous year. a) If the CPI increases 3 percent for each of the next four years (so that the inflation rate is 3 percent for each of the next four years), find the minimum wage for 2010, 2011, and 2012. b) If the CPI overstates inflation by 1 percentage point, calculate a revised minimum wage for each year 2010 to 2012 removing the CPI bias. c) How much does the CPI bias affect the minimum wage in 2010, 2011, and 2012? Minimum rate in 2010: $(7.25*1.03) = $7.47 In 2011: $(7.47*1.03) = $7.69 In 2012: $(7.69*1.03) = $7.92 b) Once the CPI is adjusted out, the adjusted CPI increases by 2%; i.e., 2010: $(7.25*1.02) = $7.40 2011: $(7.40*1.02) = $7.55 2012: $(7.55*1.02) = $7.70 c) Biases in CPI: in 2010: 7 cents, in 2011: 14 cents and in 2012 it is 22 cents. 4) In 2012, Annie, an 80-year old, is telling her granddaughter Suzie about the good old days. Annie says that in 1932, when she was a child, you could buy a nice house for $15,000 and a jacket for $5. Suzie looks up some current prices and finds that a house that costs $200,000 and jacket that costs $50 are today’s equivalent of the ones that Annie says cost so little when she was a child. Suzie, an economics student, looks up the CPI for 1932 and discovers that it was 13.7. The reference base is 1982-84. The CPI for 2012 was 180.3. a) What is the 2012 price that is equivalent to $15,000 in 1932? b) Which is the lower cost: $15,000 in 1932 or $200,000 in 2012? c) Which is the lower cost: $5 in 1932 or $50 in 2012? d) Is Annie correct about the good old days? Explain your answer. 2

Answer: 4 a) The 2012 price that is equivalent to $15,000 in 1932 equals the CPI in 2012 divided by the CPI in 1932 and then multiplied by $15,000. So the 2012 price is ( 180.3 / 13.7) * $15,000 , which is $197,409 . 4b. The $15,000 in 1932 is the slightly lower cost. 4c. The 2012 price that is equivalent to $5 in 1932 equals the CPI in 2012 divided by the CPI in 1932 and then multiplied by $5. So the 2007 price is (180.3 / 13.7) * $5 , which is $66 . So, $50 in 2012 is the lower cost. 4d. Annie is probably a bit off in her description of the good old days. Houses are a little cheaper in 1932 but the jacket is more expensive. To the extent that most goods are similar to the jacket rather than the house, real prices are lower in 2012. In addition, likely there has been substantial quality improvement over the years, which is another reason Annie is a bit mistaken. 3

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