Główna zawartość

Kurs: Makroekonomia > Rozdział 2

Lekcja 1: Mierzenie kosztów utrzymania – inflacja i indeks cen konsumpcyjnych (CPI)

Śledzenie inflacji

Kiedy słyszysz, że ktoś mówi o gospodarce, jest bardzo prawdopodobne, że powie coś o inflacji. A czym jest inflacja?

Kluczowe pojęcia

Price level is measured by constructing a hypothetical basket of goods and services—meant to represent a typical set of consumer purchases—and calculating how the total cost of buying that basket of goods increases over time.
The rate of inflation is measured as the percentage change between price levels over time.
An index number is a unit-free number derived from the price level over a number of years that makes computing inflation rates easier.
Inflation is the general and ongoing rise in the level of prices in an economy.

Tracking inflation

When you hear about inflation at the dinner table, it's often a conversation about how everything seemed to cost so much less in the past, how you used to be able to buy three gallons of gasoline for a dollar and then go see an afternoon movie for another dollar.

The table below compares some prices of common goods in 1970 and 2014—but keep in mind that the average prices shown may not reflect the prices where you live. The cost of living in New York City is much higher than in Houston, Texas, for example. In addition, certain products have evolved over recent decades. A new car in 2014—loaded with antipollution equipment, safety gear, computerized engine controls, and many other technological advances—is a more advanced machine and more fuel efficient than your typical 1970s car.

Let's put details like these to one side for the moment, however, and look at the overall pattern. The primary reason behind the price increases in the table—and increases in prices of other products in the economy not shown here—is not specific to the market for housing or cars or gasoline or movie tickets. Instead, it is part of a general rise in the level of all prices.

In 2014, one dollar had about the same purchasing power in overall terms of goods and services as 18 cents did in 1972 because of the amount of inflation that has occurred over that time period.

Price comparisons, 1970 and 2014
Item	1970	2014
Pound of ground beef	$0.66	$4.16
Pound of butter	$0.87	$2.93
Movie ticket	$1.55	$8.17
Sales price of new home, median	$22,000	$280,000
New car	$3,000	$32,531
Gallon of gasoline	$0.36	$3.36
Average hourly wage for a manufacturing worker	$3.23	$19.55
Per capita GDP	$5,069	$53,041.98

Additionally, the power of inflation does not affect just goods and services but wages and income levels, too. The second-to-last row of the table above shows that the average hourly wage for a manufacturing worker increased nearly six-fold from 1970 to 2014. Sure, the average worker in 2014 is better educated and more productive than the average worker in 1970—but not six times more productive. And yes, per capita gross domestic product increased substantially from 1970 to 2014, but is the average person in the US economy really more than eight times better off in just 44 years? Not likely.

A modern economy has millions of goods and services whose prices are continually quivering in the breezes of supply and demand. How can all of these shifts in price be boiled down to a single inflation rate? As with many problems in economic measurement, the conceptual answer is reasonably straightforward. Prices of a variety of goods and services are combined into a single price level. The inflation rate is the percentage change in the price level. Applying the concept, however, involves some practical difficulties.

The price of a basket of goods

To calculate the price level, economists begin with the concept of a basket of goods and services that consists of the different items individuals, businesses, or organizations typically buy. The next step is to look at how the prices of those items change over time.

In thinking about how to combine individual prices into an overall price level, many people find that their first impulse is to calculate the average of the prices. Such a calculation, however, could easily be misleading because some products matter more than others.

Changes in the prices of goods for which people spend a larger share of their incomes will matter more than changes in the prices of goods for which people spend a smaller share of their incomes. For example, an increase of 10% in the rental rate on housing matters more to most people than whether the price of carrots rises by 10%. To construct an overall measure of the price level, economists compute a weighted average of the prices of the items in the basket, where the weights are based on the actual quantities of goods and services people buy.

Imagine a simple basket of goods containing only the three items shown in the table below. Say that in any given month, a college student spends money on 20 hamburgers, one bottle of aspirin, and five movies. Prices for these items over four years are given in the table through each time period.

Prices of some goods in the basket may rise while others fall. In this example, the price of aspirin does not change over the four years, while movies increase in price and hamburgers bounce up and down. Each year, the cost of buying the given basket of goods at the prices prevailing at that time is shown.

A college student’s basket of goods
Items	Hamburger	Bottle of Asprin	Movies	Total	Inflation rate
Quantity	20	1	5	-	-
Period one
Price	$3.00	$10.00	$6.00	-	-
Amount spent	$60.00	$10.00	$30.00	$100.00	-
Period two
Price	$3.20	$10.00	$6.50	-	-
Amount spent	$64.00	$10.00	$32.50	$106.50	6.5%
Period three
Price	$3.10	$10.00	$7.00	-	-
Amount spent	$62.00	$10.00	$35.00	$107.00	0.5%
Period four
Price	$3.50	$10.00	$7.50	-	-
Amount spent	$70.00	$10.00	$37.50	$117.50	9.8%

Now, let's calculate the annual rate of inflation.

Step 1. Find the percentage change in the cost of purchasing the overall basket of goods between the time periods. The general equation for percentage change between two years, whether in the context of inflation or in any other calculation, is below.

\begin{array}{ccc} \frac{(Level in new year - Level in previous year)}{Level in previous year} & = & Percentage change \end{array}

Step 2. From period one to period two, the total cost of purchasing the basket of goods rises from $100 to $106.50. The percentage change over this time—which we also call the inflation rate—can be calculated as shown below:

\begin{array}{ccccc} \frac{(106.50 - 100)}{100.0} & = & 0.065 & = & 6.5 % \end{array}

Step 3. From period two to period three, the overall change in the cost of purchasing the basket rises from $106.50 to $107. Again, we calculate the percentage change:

\begin{array}{ccccc} \frac{(107 - 106.50)}{106.50} & = & 0.0047 & = & 0.47 % \end{array}

Step 4. From period three to period four, the overall cost rises from $107 to $117.50. The inflation rate is

\begin{array}{ccccc} \frac{(117.50 - 107)}{107} & = & 0.098 & = & 9.8 % \end{array}

This calculation of the change in the total cost of purchasing a basket of goods takes into account how much is spent on each good. Hamburgers are the lowest-priced good in this example, and Aspirin is the highest priced. If an individual buys a greater quantity of a low-price good, then it makes sense that changes in the price of that good should have a larger impact on the buying power of that person’s money. The larger impact of hamburgers shows up in the amount spent row, where—in all time periods—hamburgers are the largest item within the amount spent row.

Index numbers

The numerical results of a calculation based on a basket of goods can get a little messy. To simplify the task of interpreting the price levels for realistically complex baskets of goods, the price level in each period is typically reported as an index number, rather than as the dollar amount for buying the basket of goods.

Price indices are created to calculate an overall average change in relative prices over time. To convert the money spent on the basket to an index number, economists arbitrarily choose one year to be the base year, or starting point from which we measure changes in prices. The base year, by definition, has an index number equal to 100.

This might sound strange, but it's really just a math trick to simplify things. Let's try it out. Let's say we choose a base year in which $107 is spent. We divide that amount by itself—$107—and multiply by 100, which gives us an index in the base year of 100. Note that the index number in the base year always has to have a value of 100.

Then, to figure out the values of the index numbers for the other years, we divide the dollar amounts for the other years by 1.07—the amount spent during the base year divided by 100. Note also that the dollar signs cancel out, so index numbers have no units.

Take a look at the table below. You'll see that in our example, we've chosen period three as our base year—notice that total spending is $107. The index numbers for the other three periods in the table were calculated using the same method we used above. And—because the index numbers are calculated so that they are in exactly the same proportion as the total dollar cost of purchasing the basket of goods—the inflation rate can be calculated based on the index numbers, using the percentage change formula.

Let's give it a try! The inflation rate from period one to period two can be calculated using the formula for percentage change:

\begin{array}{ccccc} \frac{(99.5 - 93.4)}{93.4} & = & 0.065 & = & 6.5 % \end{array}

You can see that the inflation rates for the other periods in the table were calculated using the same formula.

	Total spending	Index number	Inflation rate since previous period
Period 1	$100	$\frac{100}{1.07} = 93.4$ ‍
Period 2	$106.50	$\frac{106.50}{1.07} = 99.5$ ‍	$\frac{(99.5 - 93.4)}{93.4} = 0.065 = 6.5 %$ ‍
Period 3 – base year	$107	$\frac{107}{1.07} = 100.0$ ‍	$\frac{(100 - 99.5)}{99.5} = 0.005 = 0.5 %$ ‍
Period 4	$117.50	$\frac{117.50}{1.07} = 109.8$ ‍	$\frac{(109.8 - 100)}{100} = 0.098 = 9.8 %$ ‍

If we can calculate inflation rate correctly using either dollar values or index numbers, then why bother with the index numbers?

The advantage is that indexing allows easier eyeballing of the inflation numbers. If you glance at two index numbers like 107 and 110, you know automatically that the rate of inflation between the two years is about, but not quite exactly equal to, 3%. By contrast, imagine that the price levels were expressed in absolute dollars of a large basket of goods, so when you looked at the data, the numbers were $19,493.62 and $20,009.32. Most people find it difficult to eyeball those kinds of numbers and say that it is a change of about 3%—even though the proportions are exactly the same.

A word of warning: When a price index moves from, say, 107 to 110, the rate of inflation is not exactly 3%. Remember, the inflation rate is not derived by subtracting the index numbers, but rather through the percentage-change calculation. The precise inflation rate as the price index moves from 107 to 110 is calculated as (110 – 107) / 107 = 0.028 = 2.8%. When the base year is fairly close to 100, a quick subtraction is not a terrible shortcut to calculating the inflation rate—but when precision matters down to tenths of a percent, subtracting will not give the right answer.

Two final points about index numbers are worth remembering. First, index numbers have no dollar signs or other units attached to them. Although index numbers can be used to calculate a percentage inflation rate, the index numbers themselves do not have percentage signs. Index numbers just mirror the proportions found in other data. They transform the other data so that the data are easier to work with.

Second, the choice of a base year for the index number—that is, the year that is automatically set equal to 100—is arbitrary. It is chosen as a starting point from which changes in prices are tracked. In official inflation statistics, it is common to use one base year for a few years and then to update it so that the base year of 100 is relatively close to the present. But any base year that is chosen for the index numbers will result in exactly the same inflation rate.

To see this in the previous example, imagine that period one—when total spending was $100—was chosen as the base year and given an index number of 100. At a glance, you can see that the index numbers would now exactly match the dollar figures, the inflation rate in the first period would be 6.5%, and so on.

Podsumowanie

Price level is measured by constructing a hypothetical basket of goods and services—meant to represent a typical set of consumer purchases—and calculating how the total cost of buying that basket of goods increases over time.
The rate of inflation is measured as the percentage change between price levels over time.
An index number is a unit-free number derived from the price level over a number of years that makes computing inflation rates easier.
Inflation is the general and ongoing rise in the level of prices in an economy.

Pytania do samodzielnego sprawdzenia swojej wiedzy

The table below shows the prices of fruit purchased by the typical college student from 2001 to 2004. What is the amount spent each year on this hypothetical basket of fruit with the quantities shown in column two?

Items	Quantity	2001 price	2002 price	2003 price	2004 price	2004 amount spent
Apples	10	$0.50	$0.75	$0.85	$0.88
Bananas	12	$0.20	$0.25	$0.25	$0.29
Grapes	2	$0.65	$0.70	$0.90	$0.95
Raspberries	1	$2.00	$1.90	$2.05	$2.13	$2.13
Total

To calculate the amount spent on each fruit in each year, multiply the quantity of each fruit by the price.

10 apples \times $ 0.5 = $ 5.00 spent on apples in 2001

12 bananas \times $ 0.20 = $ 2.40 spent on bananas in 2001

2 bunches of grapes \times $ 0.65 = $ 1.30 spent on grapes in 2001

1 pint of raspberries \times $ 2 = $ 2.00 spent on raspberries in 2001

Adding up the amounts gives you the total cost of the fruit basket:

$ 5.00 + $ 2.40 + $ 1.30 + $ 2.00 = $ 10.70

The total costs for all the years are shown in the following table.

2001	2002	2003	2004
$10.70	$13.80	$15.35	$16.31

Construct the price index for a hypothetical fruit basket in each year using 2003 as the base year.

If 2003 is the base year, then the index number has a value of 100 in 2003. To transform the cost of a fruit basket each year, we divide each year’s value by $15.35—the value of the base year—and then multiply the result by 100. The price index is shown in the following table.

2 001	2 002	2 003	2 004
69,71	89,90	100,00	106,3

Note that the base year has a value of 100. Years before the base year have values less than 100. Years after the base year have values more than 100.

Calculate the inflation rate for fruit prices from 2001 to 2004.

The inflation rate is calculated as the percentage change in the price index from year to year. For example, the inflation rate between 2001 and 2002 is

(84.61 - 69.71) / 69.71 = 0.2137 = 21.37 %

The inflation rates for all the years are shown in the last row of the following table, which includes the two previous answers.

Items	Quantity	2001 price	2001 amount spent	2002 price	2002 amount spent	2003 price	2003 amount spent	2004 price	2004 amount spent
Apples	10	$0.50	$5.00	$0.75	$7.50	$0.85	$8.50	$0.88	$8.80
Bananas	12	$0.20	$2.40	$0.25	$3.00	$0.25	$3.00	$0.29	$3.48
Grapes	2	$0.65	$1.30	$0.70	$1.40	$0.90	$1.80	$0.95	$1.90
Raspberries	1	$2.00	$2.00	$1.90	$1.90	$2.05	$2.05	$2.13	$2.13
Total			$10.70		$13.80		$15.35		$16.31
Price index			69.71		89.90		100.00		106.3
Inflation rate					28.97%		11.23%		6.25%

Edna is living in a retirement home where most of her needs are taken care of, but she has some discretionary spending. Based on the basket of goods in the table below, by what percentage does Edna’s cost of living increase between time one and time two?

Items	Quantity	Time one Price	Time two price
Gifts for grandchildren	12	$50	$60
Pizza delivery	24	$15	$16
Blouses	6	$60	$50
Vacation trips	2	$400	$420

Begin by calculating the total cost of buying the basket in each time period, as shown in the following table.

Items	Quantity	Time one price	Time one total cost	Time two price	Time two total cost
Gifts	12	$50	$600	$60	$720
Pizza	24	$15	$360	$16	$384
Blouses	6	$60	$360	$50	$300
Trips	2	$400	$800	$420	$840
Total cost			$2,120		$2,244

The rise in cost of living is calculated as the percentage increase:

(2244 - 2120) / 2120 = 0.0585 = 5.85 % .

Pytania do powtórzenia

How is a basket of goods and services used to measure the price level?
Why are index numbers used to measure the price level rather than dollar value of goods?
What is the difference between the price level and the rate of inflation?

Pytanie rozwijające myślenie krytyczne

Inflation rates, like most statistics, are imperfect measures. Can you identify some ways that the inflation rate for fruit does not perfectly capture the rising price of fruit?

Zadania

Problem one

The index number representing the price level changes from 110 to 115 in one year, and then from 115 to 120 the next year. Since the index number increases by five each year, is five the inflation rate each year? Is the inflation rate the same each year? Explain your answer.

Problem two

The total price of purchasing a basket of goods in the United Kingdom over four years is shown in the table below:

Year one	Year two	Year three	Year four
£940	£970	£1000	£1070

Calculate two price indices:

One using year one as the base year—set equal to 100.
One using year four as the base year—set equal to 100.

Then, calculate the inflation rate based on the first price index. If you had used the other price index, would you get a different inflation rate? If you are unsure, do the calculation and find out.

Źródło

This article is a modified derivative of "Tracking Inflation" by OpenStaxCollege, CC BY 4.0.

Zmodyfikowany artykuł może być używany zgodnie z licencją CC BY-NC-SA 4.0.

Bibliografia

"Average Movie Ticket Prices Increase to

$ 8.17

for 2014." Variety. January 20, 2015. http://variety.com/2015/film/news/movie-ticket-prices-increased-in-2014-1201409670/

"Average Retail Food and Energy Prices, U.S. and Midwest Region." Buereau of Labor Statistics. http://www.bls.gov/ro3/apmw.htm

"Consumer Price Index-Average Price Data" Bureau of Labor Statistics. http://data.bls.gov/cgi-bin/surveymost?ap

"Median and Average Sales Prices of New Homes Sold in United States." United States Census Bureau. https://www.census.gov/construction/nrs/pdf/uspricemon.pdf

"Weekly Retail Gasoline and Diesel Prices." US Energy Information Administration. 2016. http://www.eia.gov/dnav/pet/pet_pri_gnd_a_epmr_pte_dpgal_w.htm

"Table B-8. Average hourly and weekly earnings of production and nonsupervisory employees on private nonfarm payrolls by industry sector, seasonally adjusted(1)." Bureau of Labor Statistics. October 7, 2016. http://www.bls.gov/news.release/empsit.t24.htm

US Inflation Calculator. "Historical Inflation Rates: 1914-2013." Accessed March 4, 2015. http://www.usinflationcalculator.com/inflation/historical-inflation-rates/.

"Who Can Afford The Average Car Price? Only Folks In Washington, D.C." Autoblog. March 12, 2014. http://www.autoblog.com/2014/03/12/who-can-afford-the-average-car-price-only-folks-in-washington/

Chcesz dołączyć do dyskusji?

Zaloguj się

Sortuj według

Na razie brak głosów w dyskusji

Rozumiesz angielski? Kliknij tutaj, aby zobaczyć więcej dyskusji na angielskiej wersji strony Khan Academy.