Chapter 15 Index Numbers

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Chapter 15

Index Numbers

True/False

1. An index number is a percent that measures the change in price, quantity, value, or some other item of interest from one time to another.

Answer: True

2. An index of 239.2 and an index of 86.4 are actually percents.

Answer: True

3. All indexes have the same base, namely 1982-84, written 1982-84=100.

Answer: False

4. The base period for one index might be 1982-84, while the base period for another index might be

1990.

Answer: True

5. The base number for most indexes is 1.

Answer: False

6. No systematic approach to collecting and reporting data an index was evident in the United States until about 1900.

Answer: True

7. An Italian, G.R. Carli, has been credited with originating the first index numbers in 1764.

Answer: True

8. An index is a convenient way of comparing changes for different variables, i.e., average income and food prices.

Answer: True

9. Most business and economic indexes are carried either to the nearest whole percent, such as 312 or 96, or to the nearest 10th of a percent, such as 97.5 and 178.6.

Answer: True

10. Converting data to indexes makes it easier to compare the trend in a series composed of exceptionally large numbers.

Answer: True

11. The base-period price is designated as p n

and the price for the given period is designated p

0

.

Answer: False

12. Etienne Laspeyres developed a method in the latter part of the 18th century to determine a weighted index using base-period weights.

Answer: True

13. Two methods of computing a weighted price index are the Laspeyres' method and Paasche's method.

Answer: True

14. The Laspeyres' method uses the amounts consumed in the base period, q

0

, as weights to determine a price index.

Answer: True

15. If we are constructing a weighted index of the price of food for 2007 using the Laspeyres' method and

1982-84 = 100, we use the amounts consumed in the base period, q

0

, as weights.

Answer: True

16. The CPI serves only one major function: as an economic indicator of the rate of inflation in the

United States.

Answer: False

17. To construct a special-purpose index designed to measure general business activity, the weights are based on the judgments of the statistician and assigned to each series.

Answer: True

18. The Consumer Price Index measures the change in prices of a fixed market basket of goods and services from one period to another.

Answer: True

19. One function of the CPI is to allow consumers to determine the degree to which their purchasing power is being eroded by price increases.

Answer: True

20. The CPI is used as a yardstick for revising wages, pensions and other income payments to keep pace with changes in prices or inflation.

Answer: True

21. The Consumer Price Index originated in 1913 and has been published regularly since 1921.

Answer: True

22. The CPI is not just one index, but includes a large number of groups, subgroups and selected items, such as a food index, a medical care index and an entertainment index.

Answer: True

23. The first of two Consumer Price Indexes is for all urban consumers and covers about 80 percent of the total non-institutional population, while the second one is for urban wage earners and clerical workers and covers about half the population.

Answer: True

24. The concept of real income is sometimes called deflated income or income expressed in constant dollars and the CPI is called the deflator.

Answer: True

25. To deflate sales, the actual sales are multiplied by the wholesale price index and the result multiplied by 100.

Answer: False

26. Social security, pensions, many apartment leases and many labor contracts are tied to the change in the CPI.

Answer: True

27. Millions of employees in automobile, steel, and other industries have their wages adjusted upward when the CPI increases. The specifics are in the management-union contracts. These clauses in the contracts are referred to as "escalator clauses."

Answer: True

28. If two or more series of index numbers have the same year as the base period, then they can be compared directly.

Answer: True

29. When two or more series of index numbers to be compared do not have the same base period, we select a common base period for all series. Then we use the respective base numbers as the denominators and convert each base to the new base.

Answer: True

Multiple Choice

30. If the average hourly earnings in mining in 1998 was $7.67 and for the most recent month it was

$14.90, what is the index of hourly earnings for the most recent month based on 1998?

A) 100.0

B) 186.9

C) 151.5

D) 194.3

Answer: D

31. The Bureau of the Census reported that the farm population dropped from 30.5 million in 1940 to 6.5 million in 1999. What is the index for 1999 based on 1940?

A) 469.7

B) 100.0

C) 21.3

D) 78.7

Answer: C

32. Besides measuring change in the prices of goods and services, the consumer price index has a number of other applications such as:

A) To determine real disposable personal income,

B) To deflate sales or other data series,

C) To find the purchasing power of the dollar

D) Establish cost of living increases.

E) All of the above.

Answer: E

33. Sean McCarthy earns $20,000 a year; John Nowak, $35,000. What is John's income as an index using

Sean's income as the base?

A) 1.75

B) 75.0

C) 100.0

D) 57.1

E) None of the above

Answer: E

34. The wholesale price of a straight back desk chair in 2004 was $70; in 2005, $80.50; and in 2006, $63.

What were the indexes for 2005 and 2006 using 2004 = 100?

A) 115.0 and 90.0

B) 1.15 and 0.9

C) 1150.0 and 900.0

D) 87.0 and 111.1

Answer: A

35. An index of clothing prices for 2006 based on 1985 is to be constructed. The prices for 1985 and

2006 and the quantity consumed in 1985 are shown below.

Assuming that the number sold remained constant, i.e., the same number were sold in 2006 as in 1985, what is the weighted index of price for 2006 using 1985 as the base?

A) 206.7

B) 214.5

C) 48.4

D) 46.6

Answer: B

36. Real income is computed by

A) Dividing money income by the CPI and multiplying by 100.

B) Dividing the CPI by money income and multiplying by 100.

C) Multiplying money income by the CPI.

D) Subtracting the CPI from money income.

Answer: A

37. Prices and the number produced for selected agricultural items are:

Using the Laspeyres method, what price index of agricultural production for 2006 (1980 = 100)?

A) 42.5

B) 129.7

C) 117.1

D) 85.3

Answer: B

38. The number of items produced and the price per item for the Duffy Manufacturing Company are:

What is the value index of production for 2006 using 1990 as the base period?

A) 115.2

B) 72.9

C) 110.6

D) 127.1

Answer: D

39. As chief statistician for the county, you want to compute and publish every year a special-purpose index, which you plan to call Index of County Business Activity. Three series seem to hold promise as the basis for the index; namely, the price of cotton, the number of new cars sold, and the rate of money turnover for the county (published by a local bank). Arbitrarily you decide that money turnover should have a weight of 60 percent; number of new cars sold, 30 percent; and the price of cotton, 10 percent.

What is the Index of County Business Activity for 1981 (the base year) and for 2006?

A) 100 for 1981, 139 for 2006

B) 139 for 1981, 100 for 2006

C) 100 for 1981, 61 for 2006

D) 100 for 1981, 100 for 2006

Answer: A

40. The Consumer Price Index in June 2006 was 159.3 (1982-84 = 100). What does this indicate about prices from 1982-84 to June 2006?

A) Rose 59.3%

B) Rose 100.0%

C) Rose 159.3%

D) Declined 159.3%

Answer: A

41. Below is Jim Walker's income for 1995 and 2007.

What was Jim's real income for 2007?

A) $37,000

B) $67,000

C) $34,387

D) $38,908

Answer: D

42. The take home pay of an employee working in an urban area for 1993and 2007are:

If the CPI rose from 159 in 1993 to 210 in 2007 (1982-84 = 100), what was the "real" take home pay of the employee in 2007?

A) $5,000

B) $15,000

C) $113,200

D) $53,904

Answer: D

43. How is the purchasing power of the dollar computed?

A) ($1/CPI) (100)

B) ($1 - CPI) (100)

C) ($1 x CPI) (100)

D) (CPI/$1) (100)

Answer: A

44. If the Consumer Price Index in June 2006 was about 202.9 (1982-84 = 100), what was the purchasing power of the dollar?

A) $1.00

B) $0.33

C) $0.58

D) $0.49

Answer: D

45. An index number is a percent that measures the change from one period of time to another in terms of?

A) Value

B) Price

C) Quantity

D) All of the above

Answer: D

46. How can indexes be classified?

A) Price

B) Quantity

C) Value

D) Special purpose

E) All of the above

Answer: E

47. The CPI for "personal computers and peripheral equipment" in June 2006 was 10.7 (1982-

1984=100). Interpret this index.

A) There was no significant increase in the price of "personal computers and peripheral equipment"

B) The price of "personal computers and peripheral equipment" increased 10.7%.

C) The price of "personal computers and peripheral equipment" decreased 89.3%.

D) If the average price of a computer in 1982-1984 was $3000.00, the CPI for "personal computers and peripheral equipment" would predict that the price of a computer in June 2006 would be $893.

Answer: C

48. The CPI for "educational books and supplies" in June of 2006 was 386.7 (1982-1984=100). Interpret this index.

A) There was no significant increase in the price of "educational books and supplies".

B) The price of "educational books and supplies" increased 386.7 times.

C) If the average price of a textbook in 1982-1984 was $25.00, the CPI for "educational books and supplies" would predict that the price of the textbook in June 2006 would be $71.68.

D) If the average price of a textbook in 1982-1984 was $25.00, the CPI for "educational books and supplies" would predict that the price of the textbook in June 2006 would be $96.68.

Answer: C

49. What does a typical market basket of goods and services include?

A) Bread

B) Beer

C) Milk

D) All of the above

Answer: D

Fill-in-the-Blank

50. There are several indexes that reflect the overall economic activity in the United States. The federal government puts out an index of leading economic indicators. It includes such diverse economic indicators as stock prices, new orders for plants and equipment, and building permits issued. What are these indexes usually referred to as? _______________________

Answer: special purpose

51. What is the base year for the Consumer Price Index currently? _______

Answer: 1982-84

52. What is the index that measures the average change in prices received in the primary markets of the

United States by producers of commodities? _________________________________

Answer: producers price index

53. What is a price index for a single commodity called? __________

Answer: relative

54. What is the symbol used to designate a base period price? _______

Answer: p

0

55. What is the usual index number associated with the base period for the CPI? ______

Answer: 100

56. What is a major disadvantage of the unweighted price index? ______________________________

Answer: extremely large or small values overly influence the index

57. Which method for computing a weighted price index uses current year weights? _____________

Answer: Paasche

58. What is another name for the unweighted method of computing an index? _____________________

Answer: simple aggregate

59. Which method of computing index numbers has the advantage that the consumption pattern is always up-to-date? _____________________

Answer: Paasche

60. Which index is computed using base year prices and quantities and current year prices and quantities together? _____________

Answer: value

61. Which index measures the change in the prices of a fixed market basket of goods and services from one time period to another? ___________

Answer: Consumer Price Index (CPI)

62. What is another term for real income? _______________

Answer: deflated income

63. What is the CPI called when it determines real income? ___________

Answer: deflator

64. If we divide one dollar by the CPI and multiply it this result by 100, what is the result called?

_________________________

Answer: purchasing power of the dollar

65. What do we call a percent that measures the change in price, quantity, value or some other item of interest from one time period to another? ______________________

Answer: index number

Essay

66. Describe the process of collecting data for the CPI.

Answer: The Consumer Price Index is based on about 400 items, and about 250 part-time and full-time agents collect price data monthly. Prices are collected from more than 18,000 tenants, 24,000 retail establishments and 18,000 housing units in 85 urban areas across the country.

67. List some example items that are included in the CPI that represent a typical "market basket" of goods.

Answer: The prices of baby cribs, bread, beer, cigars and operating-room charges are just a few of the items included in what is often termed a typical "market basket" of goods and services.

Multiple Choice

Use the following to answer questions 68-78:

Data for selected vegetables purchased at wholesale prices for 1995 and 2007 are shown below.

68. What is the unweighted aggregate price index?

A) 98.4

B) 107.0

C) 117.5

D) 128.8

Answer: D

69. What is Laspeyres' price index?

A) 98.4

B) 107.0

C) 108.0

D) 117.5

Answer: A

70. What is Paasche's price index?

A) 98.4

B) 107.0

C) 108.0

D) 117.5

Answer: B

71. What is the value index?

A) 110.3

B) 115.6

C) 108.0

D) 118.5

Answer: B

72. What is the average of Laspeyres' and Paasche's price indexes (Fisher Index)?

A) 107.5

B) 102.7

C) 112.8

D) 103.2

Answer: B

73. What is the interpretation of the value index?

A) Value rose 28.8%

B) Value rose 15.6%

C) Value rose 17.5%

D) Value rose 20.0%

Answer: B

74. What is your interpretation of Laspeyres' price index?

A) Prices rose 98.4%

B) Prices declined 1.6%

C) Prices rose 7.0%

D) Prices rose 8.0%

Answer: B

Fill-in-the-Blank

75. What is the simple price relative for peas? _______

Answer: 90.0

76. What is the simple price relative for broccoli? _______

Answer: 166.7

77. What is the simple price relative for cabbage? _______

Answer: 83.3

78. What is the simple price relative for carrots? _______

Answer: 120.0

Use the following to answer questions 79-83:

Suppose your annual 2001 salary was $40,000 and your 2006 salary was $52,000. Assume the annual

CPI rose from 177.1 to 202.9 during this period of time.

79. What was your real income in 2001? _______

Answer: $22,586

80. What was you real income in 2006? _______

Answer: $25,628

81. What was the purchasing power of the dollar in 2006? _______

Answer: $0.493

82. What was the purchasing power of the dollar in 2001? _______

Answer: $0.565

83. In which year was your "real" income larger? ________

Answer: 2006

84. What is the purpose of an index?_____________________________________

Answer: The purpose of an index is express changes over time as a percent.

85. What do most indexes have in common? ________________________________

Answer: a base period and a current period. Difficulty: Medium Goal: 1

86. In a weighted index, what variable is usually the weight? ________________________

Answer: quantity: Difficulty: Medium Goal: 2

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