6.8: Problem Sets

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Problem Set 1: Inflation Adjustment

Year	CPI-U (1982-84=100)
1970	38.8
1980	82.4
1990	130.7
2000	172.2
2010	218.1
2016	240.0

Exercise $\PageIndex{1}$

Given the following:

The nominal price in 2000 was $120.

The nominal price in 2016 was $520.

Express these prices in constant 1990 dollars.

Answer

The real price in 2000 was $91.08.

The real price in 2016 was $283.18.

Exercise $\PageIndex{2}$

Given the following:

The nominal price in 2000 was $220.

The nominal price in 2016 was $670.

Express these prices in constant 1970 dollars.

Answer

The real price in 2000 was $49.57.

The real price in 2016 was $108.32.

Exercise $\PageIndex{3}$

Given the following:

The nominal price in 2000 was $310.

The nominal price in 2016 was $320.

Express these prices in constant 2016 dollars.

Answer

The real price in 2000 was $432.06.

The real price in 2016 was $320.

Exercise $\PageIndex{4}$

Given the following:

The nominal price in 2000 was $415.

The nominal price in 2016 was $670.

Express these prices in constant 1982-84 dollars.

Answer

The real price in 2000 was $241.

The real price in 2016 was $279.17.

Exercise $\PageIndex{5}$

Given the following:

The nominal price in 2000 was $520.

The nominal price in 2016 was $560.

Express these prices in constant 1980 dollars.

Answer

The real price in 2000 was $248.83.

The real price in 2016 was $192.27.

Exercise $\PageIndex{6}$

Given the following:

The nominal price in 2000 was $370.

The nominal price in 2016 was $400.

Express these prices in constant 2000 dollars.

Answer

The real price in 2000 was $370.

The real price in 2016 was $287.01.

Exercise $\PageIndex{7}$

Given the following:

The nominal price in 2000 was $320.

The nominal price in 2016 was $360.

Express these prices in constant 2010 dollars.

Answer

The real price in 2000 was $405.32.

The real price in 2016 was $327.15.

Exercise $\PageIndex{8}$

Given the following:

The nominal price in 2000 was $870.

The nominal price in 2016 was $910.

Express these prices in constant 1990 dollars.

Answer

The real price in 2000 was $660.34.

The real price in 2016 was $495.56.

Exercise $\PageIndex{9}$

The nominal price in 2000 was $425.

The nominal price in 2016 was $415.

Express these prices in constant 2016 dollars.

Answer

The real price in 2000 was $592.33.

The real price in 2016 was $415.

Exercise $\PageIndex{10}$

Given the following:

The nominal price in 2000 was $425.

The nominal price in 2016 was $415.

Express these prices in constant 1982-84 dollars.

Answer

The real price in 2000 was $246.81.

The real price in 2016 was $172.92.

Problem Set 2: Multiple Choice

Exercise $\PageIndex{1}$

Which scenario is most likely to give rise to seasonal price patterns in a prices series?

a) Storage costs for a storable agricultural commodity

b) Production lags (e.g., biological lags)

c) Random factors that shock supply or demand

d) A consistent and sustained general growth in market demand over a long period of time

Answer: a

Exercise $\PageIndex{2}$

Which scenario is most likely to give rise to cyclical price patterns in a price series?

a) Storage costs for a storable agricultural commodity

b) Production lags (e.g., biological lags)

c) Random factors that shock supply or demand

d) A consistent and sustained general growth in market demand over a long period of time

Answer: b

Exercise $\PageIndex{3}$

Which scenario is most likely to give rise to a trend in a price series?

a) Storage costs for a storable agricultural commodity

b) Production lags (e.g., biological lags)

c) Random factors that shock supply or demand

d) A consistent and sustained general growth in market demand over a long period of time

Answer: d

Exercise $\PageIndex{4}$

Production lags, such as the biological lag or the psychological lag are likely to give rise to

a) Spatial patterns in a time series of prices

b) Cyclical patterns in a time series of prices

c) Seasonal patterns in a time series of prices

d) All of the above

Answer: b

Exercise $\PageIndex{5}$

Which best describes inflation?

a) Inflated statements such as “our product is the most delicious”

b) An effort to set the selling price above the break-even point

c) A general increase in calorie consumption as foods have become cheaper over time

d) A general increase in price levels across the economy

Answer: d

Exercise $\PageIndex{6}$

What best describes a four-period moving average?

a) An average of the four periods with the largest values

b) An average of the four periods with the smallest values

c) An average of the four most recent periods

d) All of the above

Answer: c

Exercise $\PageIndex{7}$

Which is not one of the four components of a time series?

a) The trend component

b) The random component

c) The spatial component

d) The seasonal component

Answer: c

Exercise $\PageIndex{8}$

If a price index number is 103, we can say:

a) That prices are 103 percent higher than they were in the base year.

b) That price levels are 3 percent higher than they were in the base year.

c) Nothing, unless we first convert to nominal dollars.

d) That relative to the base year, prices have fallen slightly.

Answer: b

Exercise $\PageIndex{9}$

If you were to adjust a monetary time series for inflation using the Consumer Price Index with 1982-84 = 100 you would get

a) nominal prices.

b) real prices in 1982-84 dollars.

c) prices that are always equal to 100.

d) current prices.

Answer: b

Exercise $\PageIndex{10}$

If you have weekly data and wanted to remove seasonality, you could

a) Use a 52-period moving average

b) Use a 7-period moving average

c) Use a 5-period moving average (assuming weekends are not included)

d) Estimate the biological lag model

e) Choices (b) and (c) only

Answer: a

Exercise $\PageIndex{11}$

Fluctuations in prices over time that cannot be explained by a trend, a cycle, or a seasonal pattern are called

a) the market component of the time series.

b) the demand-induced component of the time series.

c) the equilibrium component of the time series.

d) the random component of the time series.

Answer: d

Exercise $\PageIndex{12}$

If a price index has a value of 0.96 then we know that

a) We are probably looking at the base period since this number is close to 100.

b) Relative to the base period prices are 4 percent lower.

c) Relative to the base period prices are 96 percent higher.

d) We are dealing with a producer price index and not a consumer price index.

Answer: b

Exercise $\PageIndex{13}$

If you are presented with ‘nominal’ prices then you know that:

a) Prices are in US dollars as opposed to some other currency

b) These prices have not been adjusted for inflation

c) These prices have been adjusted for inflation

d) These prices reflect the trade-off between two physical commodities, for example the price of one nominal product such as corn as a ratio to the price of another nominal product such as soybeans.

Answer: b

Exercise $\PageIndex{14}$

If you see a table indicated that prices are in constant 2010 dollars then you know that

a) You are looking at current prices.

b) Prices have been adjusted for inflation.

c) Prices have not been adjusted for inflation.

d) Both (a) and (c).

Answer: b

Exercise $\PageIndex{15}$

A price cycle is most likely to be observed

In areas of the United States, such as Colorado, where cycling is an especially popular pastime.
When there has been a general increase in long run demand over the period being analyzed.
When there has been a general decrease in long run supply over the period being analyzed.
When there is a significant biological lag (e.g., tree fruits, livestock).

Answer: d

Exercise $\PageIndex{16}$

If we have monthly time series data that is highly seasonal, the best way to remove the seasonal component would be to

Employ the time series seasonal decompression model that has been the main topic of the course since we returned from Spring Break.
Apply a 12-period moving average to the data.
Throw out observations from August and December. In most cultures, these months usually contain aberrations that are due to summer vacations and major winter holidays.
Do none of the above. We must first determine whether the seasonal component is supply induced or demand induced.

Answer: b

Exercise $\PageIndex{17}$

In the base year, the value of a price index is

100
0
Indeterminate unless you are using inflation adjusted numbers
The highest point in the index series

Answer: a

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