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Course: AP®︎/College Macroeconomics > Unit 2

Lesson 4: Price Indices and inflation

Lesson summary: Price indices and inflation

In this lesson summary review and remind yourself of the key terms and calculations used in measuring inflation. Topics include the consumer price index (CPI), calculating the rate of inflation, the distinction between inflation, deflation, and disinflation, and the shortcomings of the CPI as a measure of the cost of living.

Lesson overview

You just got a raise! But wait: was that raise really a raise? The third of our three key macroeconomic indicators, the inflation rate, can help you figure that out. Inflation is an increase in the overall price level. The official inflation rate is tracked by calculating changes in a measure called the consumer price index (CPI). The CPI tracks changes in the cost of living over time. Like other economic measures it does a pretty good job of this. But it does have some limitations, such as substitution bias, which can overstate how much the cost of living really has changed.

Key Terms

Key Term	Definition
inflation	a sustained increase in the overall price level in the economy, which reduces the purchasing power of a dollar
inflation rate	the pace at which the overall price level is increasing; this is the percentage increase in the price level from one period to the next.
deflation	a sustained decrease in the overall price level in the economy; deflation occurs if the inflation rate is negative.
disinflation	a slowing of the rate of inflation; for example if the rate of inflation is $5 %$ ‍ in 2016 and $3 %$ ‍ in 2017, there is still inflation in 2017.Prices are just not rising as fast as they were before.
aggregate price level	a single number that summarizes all prices in an economy; price indices are frequently used to represent the aggregate price level.
price index	a measure that calculates the changing cost of purchasing a particular (and unchanging) combination of goods (called a “market basket”) each year; the consumer price index and the producer price index are examples.
consumer price index (CPI)	an index that calculates the cost of a market basket of goods purchased by a typical family that lives in an urban area; the purpose of the CPI is to track changes in the cost of living over time.
market basket	the combination of goods that are used to calculate a price index; the goods stay the same from year to year.
base year	a reference year to which variables are compared; for example, the current CPI in the United States uses 1983 as its base year, so all values of the CPI compare the current to 1983.
real variables	variables that are adjusted for the rate of inflation that represent the true value of something (such as real interest, real income, or real GDP); for example if your boss gives you a $10 %$ ‍ raise, but the purchasing power of your money has decreased by $8 %$ ‍ because of inflation, your raise is really only worth $2 %$ ‍.
nominal variables	variables such as wages, income, or interest that have not been adjusted for the rate of inflation; you can think of nominal variables as the “sticker price.” The bank tells you they will pay you $3 %$ ‍ interest, but the real interest rate that tells you what you are actually earning.
purchasing power	what can actually be bought with money; if you walk into a store with $$ 10$ ‍ and want to buy apples that cost $$ 1$ ‍ each, the purchasing power of your $$ 10$ ‍ is $10$ ‍ apples; If the next day the price of apples increases to $$ 2$ ‍, you can only buy $5$ ‍ apples, so the purchasing power of your $$ 10$ ‍ has decreased.
real interest rate	the interest rate earned that reflects the actual purchasing power of that interest; for example if a bank pays $3 %$ ‍ interest, but there is $2 %$ ‍ inflation, you really have only gained $1 %$ ‍ interest because the purchasing power of your interest has decreased.

Key takeaways

The Consumer Price Index (CPI)

The Consumer Price Index (CPI) measures the change in income a consumer needs to maintain the same standard of living over time. The CPI is meant to reflect changes in the cost of living for a typical urban household.

For example, suppose every household buys

2

bottles of cod liver oil,

10

loaves of bread, and

8

dog treats every week. A consumer price index tracks changes in the price of this unchanging collection of goods over time to measure changes in the cost of living for this household. Once the CPI is calculated for two years, we can to calculate the rate of inflation.

How the CPI is calculated

Let’s use the example above of the “basket of goods” consisting of 2 bottles of cod liver oil, 10 loaves of bread, and 8 dog food treats. Once the prices of the goods are calculated, the price of the basket in that year is compared to the price of the basket in some base year.

Let’s take that basket of goods our example family buys every week. Suppose that 1995 is the base year. We want to calculate the CPI for 2016.

To calculate the consumer price index we 1) calculate the price of the basket in the base year, 2) then the price of the basket in the year we want the CPI for, then finally 3) apply this formula:

C P I = \frac{Price of goods in 2016}{Price of goods in 1995} \times 100

We collect the prices that these goods sold for in 1995 and 2016, as shown in the table below:

Year	Price of cod liver oil	Quantity of cod liver	Price of a loaf of bread	Quantity of bread	Price of doggy treats	Quantity of doggy treats
1995	$$ 5$ ‍	$2$ ‍	$$ 1$ ‍	$10$ ‍	$$ 2$ ‍	$8$ ‍
2016	$$ 7$ ‍	$2$ ‍	$$ 2$ ‍	$10$ ‍	$$ 4$ ‍	$8$ ‍

Using our prices to calculate the CPI in the base year (1995) and the year for which we want to calculate the CPI (2016):

\begin{aligned} Price of bundle in 1995 & = ($ 5 \times 2) + ($ 1 \times 10) + ($ 2 \times 8) \\ = $ 36 \\ Price of bundle in 2016 & = ($ 7 \times 2) + ($ 2 \times 10) + ($ 4 \times 8) \\ = $ 66 \end{aligned}

CPI is then calculated as:

\begin{aligned} CPI & = \frac{$ 66}{$ 36} \times 100 \\ = 183 \end{aligned}

How the CPI is used to calculate the rate of inflation

The inflation rate is determined by calculating the percentage change in a price index (such as CPI or the GDP deflator). The inflation rate tells us the percentage by which the price level is changing from period to period.

To calculate the rate of inflation, you implement this formula:

inflation rate = \frac{C P I_{2} - C P I_{1}}{C P I_{1}} \times 100 %

Think of this formula this way—any rate of change (such as the rate of change of prices, which is what the inflation rate is measuring) can be calculated as: “new minus old, over old”:

Rate of change = \frac{new value - old value}{old value} \times 100 %

Suppose that you had previously calculated that the CPI in 2015 is 175 and the CPI in 2016 is 183. We calculate the rate of inflation between 2015 and 2016 as

\begin{aligned} Rate of inflation & = \frac{183 - 175}{175} \\ = 4.57 % \end{aligned}

Adjusting nominal variables into real variables

Real variables are nominal variables deflated by the price level. Examples of real variables are a real wage or a real interest rate. For instance, the sign at the bank says that they are paying

8 %

interest, but what are really earning?

If we want to find the real interest rate (the one that reflects what people are actually earning on money deposited in the bank), then we want to take away the effect of inflation. We do so because inflation reduces the purchasing power of the money deposited.

If the interest rate the bank gives us (the nominal interest rate) is

8 %

, but the rate of inflation is

5 %

, we are really earning

8 % - 5 % = 3 %

on the money that we put in the bank. Why? Because that is how much more we can buy when we take our money out after a year.

Let’s apply this approach to adjusting nominal wages to real wages. Nominal wages are what your contract says you make, but real wages are what you actually can do with that money.

Suppose your mom made a salary of $50,000 in 2010 and $55,000 in 2015. On the surface, it looks like she is earning more than she used to. But is she really? That depends on whether the purchasing power of her earnings has stayed the same.

Let's say we know that the GDP deflator for 2010 is 1.20 and the GDP deflator for 2015 is 1.40. We can use these values to deflate the salaries in each year to their real purchasing power and then compare them:

\begin{aligned} Real earnings in 2010 & = \frac{$ 50, 000}{1.20} \\ = $ 41, 666.67 \\ Real earnings in 2015 & = \frac{$ 55, 000}{1.40} \\ = $ 39, 285.71 \end{aligned}

As it turns out, in real terms, you mom’s salary has actually decreased! Uh oh!

The shortcomings of CPI as a measure of the cost of living

Using the CPI as a measure of inflation has some shortcomings. That can cause the CPI to overstate the true inflation rate. For example,

causes the CPI to overstate increases in the cost of living. When the prices of goods go up, people will substitute other similar goods in place of the good that is now more expensive. But because the CPI assumes that the basket of goods never changes, it makes it appear that people always buy the same amount of a good that is now more expensive.

Another shortcoming of CPI is that it fails to account for changes in quality. For example, one of the reasons a 2013 Volvo Station Wagon costs more than a 1973 Volvo Station Wagon is that the newer model has things like seatbelts in the backseat, FM radio, and air conditioning. The CPI, however, treats these vehicles as identical, which overstates the true rate of inflation.

Key Equations

For any year,

t

\begin{aligned} C P I_{t} & = \frac{Cost of basket in year t}{Cost of basket base year} \times 100 \\ Inflation rate & = \frac{C P I_{n e w} - C P I_{o l d}}{C P I_{o l d}} \times 100 \end{aligned}

Common Misperceptions

If there is $2 %$ ‍ inflation every year for five years, then after ten years the price level has gone up to $20 %$ ‍, right? No! Inflation compounds over time. For example, suppose a chicken coop costs $$ 100$ ‍ and there is $2 %$ ‍ inflation, that means that after a year the chicken coop will cost $$ 102$ ‍. If inflation continues at $2 %$ ‍ for another year, the $$ 102$ ‍ grows by $2 %$ ‍, not the original price. In fact, if there is $2 %$ ‍ inflation every year for 10 years, the chicken coop will cost $$ 121.90$ ‍, $21.9 %$ ‍ more than the original price.
The term “index” might sound strange, but an index is simply any measure that compares a value in one period to the value in a base year.
Another common misperception is that once we calculate the CPI, we have the rate of inflation between any two years. That is a necessary step, but it is not the final step. We must then use the CPI in both years to calculate the rate of inflation.
There are actually several different price indices used to calculate the rate of inflation. The CPI is the one that is used to calculate the official rate of inflation, which is why you’ll often hear it reported in the news.

Discussion Questions:

What are some reasons that the CPI might not capture the true rate of inflation?
How might changes in spending habits of households over a 20 year period change? How does this impact CPI as a measure of the cost of living?
The CPI in the nation of Montrose was 220 in 2016 and 200 in 2015. What is the rate of inflation between 2015 and 2016?

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Allan
Posted 4 years ago. Direct link to Allan's post “Discussion Question 1: So...”
Discussion Question 1: Some reasons that the CPI might not capture the true rate of inflation are the substitution bias and the quality bias.

Discussion Question 2: Households might substitute more expensive items for cheaper items. This does not impact CPI unless they change the basket of goods.

Discussion Question 3: The rate of inflation is around 10%
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lqiming2
Posted 4 years ago. Direct link to lqiming2's post “Why we must use the CPI i...”
Why we must use the CPI in both years to calculate the rate of inflation? Can we just use "inflation rate = (prices of goods in the current year - prices of goods in the base year)/ price of the goods in base year" to calculate the inflation rate?
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- Bryan
  Posted 4 years ago. Direct link to Bryan's post “You could. That would cal...”
  You could. That would calculate the inflation rate going from the base year to the current year. Calculating percent change in the CPI from the base year to the current year will give u the same answer.
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graveliner25
Posted 7 months ago. Direct link to graveliner25's post “What does CPI not include...”
What does CPI not include?
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Ivan Bogush
Posted 8 months ago. Direct link to Ivan Bogush's post “*What are the biggest fac...”
What are the biggest factors that contribute to inflation rate?

For example, if I want to buy 10-year bonds with a fixed coupon and intend to not sell them all these 10 years what should I definitely look at to understand my risk of investment in terms of inflation?
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Siddhant
Posted 4 years ago. Direct link to Siddhant's post “Since the prices of goods...”
Since the prices of goods keep fluctuating over time, which prices are considered for CPI calculations.
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- Jeremy S
  Posted 4 years ago. Direct link to Jeremy S's post “All prices as part of the...”
  All prices as part of the CPI calculation are based upon a set market basket. To calculate CPI, the current market basket price (of all goods within the market basket) is divided by the price of the market basket in the base year. Thus, the CPI is still grounded in base year prices from 1982-1984. However, the changing prices of goods found across the domestic economy is indicative of one problem of the CPI calculations because these calculations do not account for quality or quantity changes, or the change in preferences of certain goods through an increased variety of products.
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preytong1000
Posted 11 days ago. Direct link to preytong1000's post “What does CPI not include...”
What does CPI not include?
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mayahamid
Posted a year ago. Direct link to mayahamid's post “Can someone please explai...”
Can someone please explain how to calculate the 2% inflation every year for 10 years, the chicken coop will cost $121.90, 21.9% more than the original price?
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- Hecretary Bird
  Posted 10 months ago. Direct link to Hecretary Bird's post “When you want to calculat...”
  When you want to calculate how the value of a good will change thanks to inflation over a long time, think about how inflation affects the value of something in say one year. 2% inflation every year means that prices will increase by 2% from one year to the next, or that you have to multiply the previous year's prices by 1.02 to get the next year. If we want to do this for 10 years, we have to repeat this process. Repeated multiplication is the same thing as using an exponent, so we can find the price of a chicken coop that originally costed $100 by multiplying it by 1.02 10 times:
  100 * 1.02^10 = 121.90
  Here you can see the same percent increase that you described. Does this help?
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akon.pachecomontes
Posted a month ago. Direct link to akon.pachecomontes's post “The CPI might not fully c...”
The CPI might not fully capture the true rate of inflation due to factors such as substitution bias, quality changes, new goods and services, geometric weighting, different spending patterns, regional differences, exclusion of asset prices, and measurement errors.
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akon.pachecomontes
Posted a month ago. Direct link to akon.pachecomontes's post “1. Why might the CPI not ...”
1. Why might the CPI not capture the true rate of inflation?
Factors like substitution bias, quality changes, new goods, and outlet substitution can distort CPI's accuracy.

2. How can changes in household spending habits affect CPI's reliability as a cost of living measure?
Shifting preferences, demographics, economic conditions, and inflationary pressures alter spending patterns, impacting CPI's representativeness.

3. Given Montrose's CPI of 220 in 2016 and 200 in 2015, what's the inflation rate between those years?
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bhold114
Posted 4 years ago. Direct link to bhold114's post “If something like a gallo...”
If something like a gallon of milk was included in the market basket used to calculate CPI, would it be a specific brand used in the calculation, or an average of all available options for a gallon of milk with brands represented for the geographic area?
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- Eirian
  Posted 3 years ago. Direct link to Eirian's post “"How do US government sta...”
  "How do US government statisticians measure the Consumer Price Index?
  First, they decide on a basket of goods that is representative of the purchases of the average household. This is done by using the Consumer Expenditure Survey, a national survey of about 7,000 households that provides detailed information on spending habits.
  
  Consumer expenditures are broken up into eight major groups which in turn are broken up into more than 200 individual item categories. For each of these 200 individual expenditure items, the BLS chooses several hundred very specific examples of that item and looks at the prices of those examples. The specific products and sizes and stores chosen are statistically selected to reflect what people buy and where they shop.
  
  The basket of goods in the CPI thus consists of about 80,000 products—several hundred specific products in over 200 broad-item categories. About one quarter of these 80,000 specific products are rotated out of the sample each year and replaced with a different set of products."
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