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Chapter 6

Measuring the Cost of Living

SOLUTIONS TO TEXTBOOK PROBLEMS

Quick Quizzes

1. Explain briefly what the consumer price index is trying to measure and how it is constructed.

The consumer price index tries to measure the overall cost of the goods and services bought by a typical consumer. It is constructed by surveying consumers to fix a basket of goods and services that the typical consumer buys, finding the prices of the goods and services over time, computing the cost of the basket at different times, and then choosing a base year. To compute the price index, we divide the cost of the market basket in the current year by the cost of the market basket in the base year and multiply by 100.

2. Henry Ford paid his workers $5 a day in 1914. If the U.S. consumer price index was 10 in 1914 and 195 in 2005, how much is the Ford daily paycheque worth in 2005 dollars?

Since Henry Ford paid his workers $5 a day in 1914 and the consumer price index was 10 in 1914 and 195 in 2005, then the Ford daily paycheque was worth $5  195/10 = $97.50 a day in 2005 dollars.

Questions for Review

1. Which do you think has a greater effect on the consumer price index: a 10 percent increase in the price of chicken or a 10 percent increase in the price of caviar? Why?

A 10 percent increase in the price of chicken has a greater effect on the consumer price index than a 10 percent increase in the price of caviar because chicken is a bigger part of the average consumer’s market basket.

2. Describe the three problems that make the consumer price index an imperfect measure of the cost of living.

The three problems in the consumer price index as a measure of the cost of living are: (1) substitution bias, which arises because people substitute toward goods that have become relatively less expensive; (2) the introduction of new goods, which are not reflected quickly in the CPI; and (3) unmeasured quality change.

3. If the price of a military aircraft rises, is the consumer price index or the GDP deflator affected more? Why?

If the price of a military aircraft rises there is no effect on the consumer price index, since military aircraft are not consumer goods. But the GDP deflator is affected, since military aircraft are included in GDP as a part of government purchases.

4. Over a long period of time, the price of a candy bar rose from $0.10 to $0.60. Over the same period, the consumer price index rose from 150 to 300. Adjusted for overall inflation, how much did the price of the candy bar change?

Since the overall price level doubled, but the price of the candy bar rose sixfold, the real price (the price adjusted for inflation) of the candy bar tripled.

5. Explain the meaning of nominal interest rate and real interest rate. How are they related?

The nominal interest rate is the rate of interest paid on a loan in dollar terms. The real interest rate is the rate of interest corrected for inflation. The real interest rate is the nominal interest rate minus the rate of inflation.

Quick Check Multiple Choice

1. The consumer price index measures approximately the same economic phenomenon as which of the following?

a. nominal GDP

b. real GDP

c. the GDP deflator

d. the unemployment rate

2. What is the largest component in the basket of goods and services used to compute the CPI?

a. food and beverages

b. housing

c. transportation

d. apparel

3. If a Manitoba gun manufacturer raises the price of rifles it sells to the Canadian Army, which of the following will be increased by the price hikes?

a. both the CPI and the GDP deflator

b. neither the CPI nor the GDP deflator

c. the CPI but not the GDP deflator

d. the GDP deflator but not the CPI

4. Which of the following occurs because consumers can sometimes substitute cheaper goods for those that have risen in price?

a. the CPI overstates inflation

b. the CPI understates inflation

c. the GDP deflator overstates inflation

d. the GDP deflator understates inflation

5. If the consumer price index was 200 in 1980 and 300 today, then $600 in 1980 has the same purchasing power as what amount today?

a. $400

b. $500

c. $700

d. $900

6. You deposit $2000 in a savings account, and a year later you have $2100. Meanwhile, the consumer price index rises from 200 to 204. In this case, what are the nominal interest rate and the real interest rate, respectively?

a. 1 percent; 5 percent

b. 3 percent; 5 percent

c. 5 percent; 1 percent

d. 5 percent; 3 percent

1. c

2. b

3. d

4. a

5. d

6. d

Problems and Applications

1. Suppose that people consume only three goods, as shown in this table:

a. What is the percentage change in the price of each of the three goods? What is the percentage change in the overall price level?

b. Do tennis racquets become more or less expensive relative to Gatorade? Does the well-being of some people change relative to the well-being of others? Explain.

a. The price of tennis balls increases 0 percent; the price of tennis racquets increases 50 percent [= ($60 – $40)/$40 × 100%]; the price of Gatorade increases 100 percent [= ($2 – $1)/$1 × 100%].

To find the percentage change in the overall price level, follow these steps:

1) Determine the fixed basket of goods: 100 balls, 10 racquets, 200 Gatorades

2) Find the price of each good in each year:

3) Compute the cost of the basket of goods in each year:

2014: (100 × $2) + (10 × $40) + (200 × $1) = $800

2015: (100 × $2) + (10 × $60) + (200 × $2) = $1200

4) Choose one year as a base year (2014) and compute the CPI in each year:

2014: $800/$800 × 100 = 100

2015: $1200/$800 × 100 = 150

5) Use the CPI to compute the inflation rate from the previous year:

2015: (150 – 100)/100 × 100% = 50%

b. Tennis racquets are less expensive relative to Gatorade, since their price rose 50 percent while the price of Gatorade rose 100 percent. The well-being of some people changes relative to the well-being of others. Those who purchase a lot of Gatorade become worse off relative to those who purchase a lot of tennis racquets or tennis balls.

2. Suppose that the residents of Vegopia spend all of their income on cauliflower, broccoli, and carrots. In 2014 they buy 100 heads of cauliflower for $200, 50 bunches of broccoli for $75, and 500 carrots for $50. In 2015 they buy 75 heads of cauliflower for $225, 80 bunches of broccoli for $120, and 500 carrots for $100. If the base year is 2014, what is the CPI in both years? What is the inflation rate in 2015?

To find the percentage change in the overall price level, follow these steps:

1) Determine the fixed basket of goods: 100 heads of cauliflower, 50 bunches of broccoli, 500 carrots.

2) Find the price of each good in each year:

3) Compute the cost of the basket of goods in each year:

2014: (100 × $2) + (50 × $1.50) + (500 × $.10) = $325

2015: (100 × $3) + (50 × $1.50) + (500 × $.20) = $475

4) Choose one year as a base year (2014) and compute the CPI in each year:

2014: $325/$325 × 100 = 100

2015: $475/$325 × 100 = 146

5) Use the CPI to compute the inflation rate from the previous year:

2015: (146 – 100)/100 × 100% = 46%

3. Go to the website of Statistics Canada (www.statcan.gc.ca) and find data on the consumer price index. By how much has the index including all items risen over the past year? For which categories of spending have prices risen the most? The least? Have any categories experienced price declines? Can you explain any of these facts?

Many answers are possible.

4. A small nation of ten people idolizes the TV show Canadian Idol. All that the ten people produce and consume are karaoke machines and CDs, in the following amounts:

a. Using a method similar to the consumer price index, compute the percentage change in the overall price level. Use 2014 as the base year, and fix the basket at 1 karaoke machine and 3 CDs.

b. Using a method similar to the GDP deflator, compute the percentage change of the overall price level. Also use 2014 as the base year.

c. Is the inflation rate in 2015 the same using the two methods? Explain why or why not.

a. The expenditures on the consumption basket in the two years are:

2014: Expenditure = 1 × $40 + 3 × $10 = $70; CPI = 100

2015: Expenditure = 1 × $60 + 3 × $12 = $96; CPI = 96/70 × 100 = 137.1

The inflation rate is 37.1 percent.

b. 2014: GDP = 10 × $40 + 30 × $10 = $700; GDP deflator = 100

2015: Nominal GDP = 12 × $60 + 50 × $12 = $1320;

Real GDP = 12 × $40 + 50 × $10 = $980;

GDP deflator = 1320/980 × 100 = 134.69

Inflation rate = 34.69 percent.

c. The inflation rates calculated in the two different ways are different because one is based on a consumption basket, while the other is on the GDP deflator. The weights in which each price enters the two price indexes (CPI and GDP deflator) are different.

5. Which of the problems in the construction of the CPI might be illustrated by each of the following situations? Explain.

a. The invention of the iPad

b. The introduction of air bags in cars

c. Increased personal computer purchases in response to a decline in the price

d. More scoops of raisins in each package of Raisin Bran

e. Greater use of fuel-efficient cars after gasoline prices increase

1. introduction of new goods

2. unmeasured quality change

3. substitution bias

4. unmeasured quality change

5. substitution bias

6. A single copy of the Ottawa Citizen cost $0.10 in 1970 and $0.50 in 1990. The average wage in manufacturing was $3.01 per hour in 1970 and $14.19 in 1990.

a. By what percentage did the price of a newspaper rise?

b. By what percentage did the wage rise?

c. In each year, how many minutes does a worker have to work to earn enough to buy a newspaper?

d. Did workers’ purchasing power in terms of newspapers rise or fall?

a. ($0.50 – $0.10)/$0.10 × 100% = 400%.

b. ($14.19 – $3.01)/$3.01 × 100% = 371%.

c. In 1970: $0.10/($3.01/60) = 2.0 minutes. In 1990: $0.50/($14.19/60) = 2.1 minutes.

d. Workers’ purchasing power fell in terms of newspapers.

7. The chapter explains that Canada Pension Plan benefits are increased each year in proportion to the increase in the CPI, even though most economists believe that the CPI overstates actual inflation.

a. If the elderly consume the same market basket as other people, does the Canada Pension Plan provide the elderly with an improvement in their standard of living each year? Explain.

b. In fact, the elderly consume more medicine than younger people, and medicine costs have risen faster than overall inflation. What would you do to determine whether the elderly are actually better off from year to year?

a. If the elderly consume the same market basket as other people, the Canada Pension Plan would provide the elderly with an improvement in their standard of living each year because the CPI overstates inflation and Canada Pension Plan payments are tied to the CPI.

b. Since the elderly consume more health care than younger people, and since medicine costs have risen faster than overall inflation, it is possible that the elderly are worse off. To investigate this, you would need to put together a market basket for the elderly, which would have a higher weight on medicine. You would then compare the rise in the cost of the “elderly” basket with that of the general basket for CPI.

8. How do you think the basket of goods and services you buy differs from the basket bought by the typical Canadian household? Do you think you face a higher or lower inflation rate than is indicated by the CPI? Why?

Many answers are possible. A common answer may be that as students, they spend a greater proportion of their income on tuition and books than the typical household. If the prices of tuition and books have risen faster than average prices, students face a higher inflation rate than the typical household.

9. Income tax brackets were not indexed until 2000. When inflation pushed up people’s nominal incomes during the 1970s, what do you think happened to real tax revenue? (Hint: This phenomenon was known as “bracket creep.”)

When bracket creep occurred, inflation increased people’s nominal incomes, pushing them into higher tax brackets, so they had to pay a higher proportion of their incomes in taxes, even though they were not getting higher real incomes. As a result, real tax revenue rose.

10. When deciding how much of their income to save for retirement, should workers consider the real or the nominal interest rate that their savings will earn? Explain.

In deciding how much income to save for retirement, workers should consider the real interest rate, since they care about their purchasing power in the future, not the number of dollars they will have.

11. Suppose that a borrower and a lender agree on the nominal interest rate to be paid on a loan. Then inflation turns out to be higher than they both expected.

a. Is the real interest rate on this loan higher or lower than expected?

b. Does the lender gain or lose from this unexpectedly high inflation? Does the borrower gain or lose?

c. Inflation during the 1970s was much higher than most people had expected when the decade began. How did this affect homeowners who obtained fixed-rate mortgages during the 1960s? How did it affect the banks that lent the money?

a. When inflation is higher than was expected, the real interest rate is lower than expected. For example, suppose the market equilibrium has an expected real interest rate of 3 percent and people expect inflation to be 4 percent, so the nominal interest rate is 7 percent. If inflation turns out to be 5 percent, the real interest rate is 7 percent minus 5 percent equals 2 percent, which is less than the 3 percent that was expected.

b. Since the real interest rate is lower than was expected, the lender loses and the borrower gains. The borrower is repaying the loan with dollars that are worth less than was expected.

c. Homeowners in the 1970s who had fixed-rate mortgages from the 1960s benefited from the unexpected inflation, while the banks that made the mortgage loans were harmed.

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