16.8 The price of gasoline. The yearly average price of unleaded regular gasoline has fluctuated as follows:

Give the gasoline price index numbers (2004 = 100) for 1994, 2004, and 2014.

16.9 The cost of college. The part of the CPI that measures the cost of college tuition (1982–84 = 100) was 796.2 in July 2015. The overall CPI was 238.7 that month.

16.10 The price of gasoline. Use your results from Exercise 16.8 to answer these questions.

You see that the point change and the percentage change in an index number are the same if we start in the base period, but not otherwise.

16.11 Toxic releases. The Environmental Protection Agency requires industry to report releases of any of a list of toxic chemicals. The total amounts released (in thousands of pounds, total on- and offsite disposal or other releases, all chemicals, all industries) were 6,939,299 in 1988, 6,655,831 in 2000, and 4,137,328 in 2013. Give an index number for toxic chemical releases in each of these years, with 1988 as the base period. By what percentage did releases increase or decrease between 1988 and 2000? Between 1988 and 2013?

16.12 How much can a dollar buy? The buying power of a dollar changes over time. The Bureau of Labor Statistics measures the cost of a “market basket” of goods and services to compile its Consumer Price Index (CPI). If the CPI is 120, goods and services that cost $100 in the base period now cost $120. Here are the average values of the CPI for the years between 1970 and 2014. The base period is the years 1982 to 1984.

16.13 Los Angeles and New York. The Bureau of Labor Statistics publishes separate consumer price indexes for major metropolitan areas in addition to the national CPI. The CPI (1982–84 = 100) in July 2015 was 247.1 in Los Angeles and 261.2 in New York.

16.14 The Food Faddist Price Index. A food faddist eats only steak, rice, and ice cream. In 1995, he bought:

After a visit from his mother, he adds oranges to his diet. Oranges cost $0.56/pound in 1995. Here are the food faddist’s food purchases in 2015:

Find the fixed market basket Food Faddist Price Index (1995 = 100) for the year 2015.

16.15 The Guru Price Index. A guru purchases only olive oil, loincloths, and copies of the Atharva Veda, from which he selects mantras for his disciples. Here are the quantities and prices of his purchases in 1985 and 2015:

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From these data, find the fixed market basket Guru Price Index (1985 = 100) for 2015.

16.16 The curse of the Bambino. In 1920, the Boston Red Sox sold Babe Ruth to the New York Yankees for $125,000. Between 1920 and 2004, the Yankees won 26 World Series and the Red Sox won 1 (and that occurred in 2004). The Red Sox victory in 2004 supposedly broke the curse. How much is $125,000 in 2004 dollars?

16.17 Dream on. When Julie started college in 2010, she set a goal of making $50,000 when she graduated. Julie graduated in 2014. What must Julie earn in 2014 in order to have the same buying power that $50,000 had in 2010?

16.18 Living too long? If both husband and wife are alive at age 65, in half the cases at least one will still be alive at age 93, 28 years later. Myrna and Bill retired in 1986 with an income of $30,000 per year. They were quite comfortable—that was about the median family income in 1986. How much income did they need 28 years later, in 2014, to have the same buying power?

16.19 Microwaves on sale. The prices of new gadgets often start high and then fall rapidly. The first home microwave oven cost $1300 in 1955. You can now buy a better microwave oven for $100. Find the latest value of the CPI (it’s on the BLS website, www.bls.gov/cpi/home.htm) and use it to restate $100 in present-day dollars in 1955 dollars. Compare this with $1300 to see how much microwave oven real prices have come down.

16.20 Good golfers. In 2007, Tiger Woods won $10,867,052 on the Professional Golfers Association tour. The leading money winner in 1946 was Ben Hogan, at $42,566. Jack Nicklaus, the leader in 1972, won $320,542 that year. How do these amounts compare in real terms?

16.21 Joe DiMaggio. Yankee center fielder Joe DiMaggio was paid $32,000 in 1940 and $100,000 in 1950. Express his 1940 salary in 1950 dollars. By what percentage did DiMaggio’s real income change in the decade?

16.22 Calling London. A 10-minute telephone call to London via AT&T cost $12 in 1976 and $14.10 in July 2015 using an occasional calling plan. Compare the real costs of these calls. By what percentage did the real cost go down between 1976 and July 2015? The CPI in July 2015 was 238.7.

16.23 Paying for Harvard. Harvard charged $5900 for tuition, room, and board in 1976. The 2014 charge was $59,607. Express Harvard’s 1976 charges in 2014 dollars. Did the cost of going to Harvard go up faster or slower than consumer prices in general? How do you know?

16.24 The minimum wage. The federal government sets the minimum hourly wage that employers can pay a worker. Labor wants a high minimum wage, but many economists argue that too high a minimum makes employers reluctant to hire workers with low skills and so increases unemployment. Here is information on changes in the federal minimum wage, in dollars per hour:

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Use annual average CPIs from Table 16.1 to restate the minimum wage in constant 1960 dollars. Make two line graphs on the same axes, one showing the actual minimum wage during these years and the other showing the minimum wage in constant dollars. Explain carefully to someone who knows no statistics what your graphs show about the history of the minimum wage.

16.25 College tuition. Tuition for Colorado residents at the University of Colorado, Boulder, has increased as follows (use tuition at your own college if you have those data):

Use annual average CPIs from Table 16.1 to restate each year’s tuition in constant 1985 dollars. Make two line graphs on the same axes, one showing actual dollar tuition for these years and the other showing constant dollar tuition. Then explain to someone who knows no statistics what your graphs show.

16.26 Rising incomes? In Example 4, we saw that the median real income (in 2013 dollars) of all households rose from $50,267 in 1984 to $51,939 in 2013. The real income that marks off the top 5% of households rose from $153,614 to $196,600 in the same period. Verify the claim in Example 4 that median income rose 3.3% and that the real income of top earners rose 28.0%.

16.27 Cable TV. Suppose that cable television systems across the country add channels to their lineup and raise the monthly fee they charge subscribers. The part of the CPI that tracks cable TV prices might not go up at all, even though consumers must pay more. Explain why.

16.28 Item weights in the CPI. The cost of buying a house (with the investment component removed) makes up about 22% of the CPI. The cost of renting a place to live makes up about 6%. Where do the weights 22% and 6% come from? Why does the cost of buying get more weight in the index?

16.29 The CPI doesn’t fit me. The CPI may not measure your personal experience with changing prices. Explain why the CPI will not fit each of these people:

16.30 Seasonal adjustment. Like many government data series, the CPI is published in both unadjusted and seasonally adjusted forms. The BLS says that it “strongly recommends using indexes unadjusted for seasonal variation (i.e., not seasonally adjusted indexes) for escalation.” “Escalation” here means adjusting wage or other payments to keep up with changes in the CPI. Why is the unadjusted CPI preferred for this purpose?

16.31 More CPIs. In addition to the national CPI, the BLS publishes CPIs for four regions and for 37 local areas. Each regional and local CPI is based on just the part of the national sample of prices that applies to the region or local area. The BLS says that the local CPIs should be used with caution because they are much more variable than national or regional CPIs. Why is this?

16.32 The poverty line. The federal government announces “poverty lines” each year for households of different sizes. Households with income below the announced levels are considered to be living in poverty. An economist looked at the poverty lines over time and said that they “show a pattern of getting higher in real terms as the real income of the general population rises.” What does “getting higher in real terms” say about the official poverty level?

16.33 Real wages (optional). In one of the many reports on stagnant incomes in the United States, we read this: “Practically every income group faced a decline in real wages during the 1980s. However, workers at the 33rd percentile experienced a 14 percent drop in the real wage, workers at the 66th percentile experienced only a 6 percent drop, and workers in the upper tail of the distribution experienced a 1 percent wage increase.”

16.34 Saving money? One way to cut the cost of government statistics is to reduce the sizes of the samples. We might, for example, cut the Current Population Survey from 50,000 households to 20,000. Explain clearly, to someone who knows no statistics, why such cuts reduce the accuracy of the resulting data.

16.35 The General Social Survey. The General Social Survey places much emphasis on asking many of the same questions year after year. Why do you think it does this?

16.36 Measuring the effects of crime. We wish to include, as part of a set of social statistics, measures of the amount of crime and of the impact of crime on people’s attitudes and activities. Suggest some possible measures in each of the following categories:

16.37 Statistical agencies. Write a short description of the work of one of these government statistical agencies. You can find information by starting at the FedStats website (https://fedstats.sites.usa.gov) and going to Agencies.