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# Tracking inflation

When you hear someone talk about the economy, it's pretty likely they'll say something about inflation. What is inflation anyway?

## Key points

• 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
Item19702014
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.

## 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: $\begin{array}{ccccc} \frac{\left (\mathrm{99.5~ -~ 93.4}\right )}{\mathrm{93.4}} & \mathrm{~ =~ } & \mathrm{0.065} & \mathrm{~ =~ } & \mathrm{6.5\% } \end{array}$ You can see that the inflation rates for the other periods in the table were calculated using the same formula. Total spendingIndex numberInflation rate since previous period Period 1$100start fraction, 100, divided by, 1, point, 07, end fraction, equals, 93, point, 4
Period 2$106.50start fraction, 106, point, 50, divided by, 1, point, 07, end fraction, equals, 99, point, 5start fraction, left parenthesis, 99, point, 5, minus, 93, point, 4, right parenthesis, divided by, 93, point, 4, end fraction, equals, 0, point, 065, equals, 6, point, 5, percent Period 3 – base year$107start fraction, 107, divided by, 1, point, 07, end fraction, equals, 100, point, 0start fraction, left parenthesis, 100, minus, 99, point, 5, right parenthesis, divided by, 99, point, 5, end fraction, equals, 0, point, 005, equals, 0, point, 5, percent
Period 4$117.50start fraction, 117, point, 50, divided by, 1, point, 07, end fraction, equals, 109, point, 8start fraction, left parenthesis, 109, point, 8, minus, 100, right parenthesis, divided by, 100, end fraction, equals, 0, point, 098, equals, 9, point, 8, percent 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. 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.

## Summary

• 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.

## Self-check questions

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?
ItemsQuantity2001 price2001 amount spent2002 price2002 amount spent2003 price2003 amount spent2004 price2004 amount spent
Apples10$0.50$0.75$0.85$0.88
Bananas12$0.20$0.25$0.25$0.29
Grapes2$0.65$0.70$0.90$0.95
Raspberries1$2.00$1.90$2.05$2.13$2.13 Total Construct the price index for a hypothetical fruit basket in each year using 2003 as the base year. Calculate the inflation rate for fruit prices from 2001 to 2004. 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? ItemsQuantityTime one PriceTime two price Gifts for grandchildren12$50$60 Pizza delivery24$15$16 Blouses6$60$50 Vacation trips2$400$420 ## Review questions • 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? ## Critical-thinking question 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? ## Problems #### 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 oneYear twoYear threeYear 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. ## Want to join the conversation? • I believe the price index for the self-check questions for the year 2002 is incorrect. (33 votes) • What is the answer to the critical thinking question? Is it that we all tend to consume the same fruits and so the rate may not be representative for all the coconuts and guavas we don't buy? (5 votes) • A large percentage of the price of fruit is derived from the fuel used in the picking, refrigeration, transportation and stocking of the fruit in stores. Also, consider what will happen if immigrant laborers who pick fruit are severely restricted in America causing the cost of picking and packing the fruit to go up, or possibly causing shortages of fruit at the marketplace because there simply isn't enough labor available to pic crops before they rot in the field/on the tree. (4 votes) • Does the price level accounting for only finial goods and services? (2 votes) • 2001 2002 2003 2004$10.70 $13.80$15.35 \$16.31

2001 2002 2003 2004
69.71 84.61 100.00 106.3
I think that the solution is wrong in 2002 index 84.61
I think that the answer is 89.90 but I am not sure .
does anybody can tell me?