Week 3 · Chapter

Chapter 3 — Measuring Inflation & Unemployment

Principles of Macroeconomics Free sample edition

The module's primary reading · ~35–45 minutes · Objective 3 (measure the price level and the labor market — compute and interpret the CPI, the inflation rate, a real wage change, the unemployment rate, and the labor-force participation rate — and classify frictional, structural, and cyclical unemployment) · Read it first this week; the lecture, the tutorial, the quiz, and the Model Workshop all build on it.

In plain language

This week is about the two numbers behind most money headlines: how fast prices are rising, and how many people cannot find work. Economists track prices with the Consumer Price Index, or CPI (one number that tells you how much a fixed list of everyday purchases costs compared with a starting year). They turn that number into an inflation rate (how fast prices rose from one year to the next, in percent). They also count people, sorting adults into those with jobs, those looking for jobs, and those doing neither. From those counts come the unemployment rate (the share of job seekers and workers who have no job) and two other measures you will compute by hand.

Why you already care about this

Think about the last time a price you pay all the time went up. Maybe your coffee went from 3 dollars to 3.30, or a slice of pizza went from 8 dollars to 9. You noticed, because you buy those things over and over. Now imagine noticing every price in the country at once. That is the job the CPI does.

Paychecks have the same story hiding inside them. Suppose your boss gives you a 4 percent raise. It feels like good news. But if the things you buy cost 5 percent more than last year, your new paycheck buys a little less than the old one did. To know whether you are ahead, you need both numbers.

Jobs work the same way. A headline says the unemployment rate fell. Did more people find work, or did some people stop looking? In this chapter you will see that both stories can produce the same drop, and you will learn to tell them apart. You will work with an illustrative campus basket that costs 200 dollars in the base year, and an illustrative labor market of 200 million adults.

By the end of this chapter you will be able to:

compute the CPI for a fixed basket in any year and say what the number means;
compute an inflation rate between two years and tell a CPI level from an inflation rate;
estimate the real change in a paycheck from a raise and an inflation rate;
compute the labor force, the unemployment rate, and the labor-force participation rate from counts of people;
explain why a discouraged worker can make the unemployment rate fall, and sort a job loss into frictional, structural, or cyclical unemployment.

Carry this sentence with you: a level says where prices are; a rate says how fast they moved.

Where we are

Already covered: Week 1, The Macro Perspective, taught you to see the economy as a whole and to read an idle point inside the frontier as a first look at unemployment. Week 2, Measuring Output, taught you to add up GDP and to strip price changes out with real GDP and the GDP deflator.
This week: a second price index, the Consumer Price Index; the inflation rate; real versus nominal wages; and how the labor market is counted.
How they connect: the real-versus-nominal split you used on GDP now applies to prices and paychecks, and the idle workers you met inside the frontier now get counted.
Where we're going next: Week 4, Economic Growth & Productivity, uses the same percentage-change formula you learn here to measure how fast an economy grows.

Week 2 is the one this chapter leans on most. Recall that a price index compares the overall level of prices in a period with the level in a base year, which is set to 100. A reading of 110 means prices sit 10 percent above the base year. The GDP deflator was one price index. This week you build a second one from a shopping list, and you learn to turn a level into a rate.

1. Define the CPI: one basket, priced twice

Picture a student's regular week. A few pizzas with friends, a coffee most mornings, and a textbook or two each term. If you wrote down exactly what you bought and then priced that same list again a year later, you would know how much your own cost of living changed. The list stays fixed. Only the prices move.

That fixed list is the heart of the CPI.

A market basket is a fixed list of goods and services, with a set quantity of each, whose total cost is tracked from year to year so that only changes in prices, not changes in what is bought, move the total.
The Consumer Price Index (CPI) is a price index that compares the cost of a fixed market basket of goods and services that households buy in a given year with the cost of the same basket in the base year, times 100.

As a formula, CPI = (cost of the basket in a year ÷ cost of the basket in the base year) × 100. In the base year, the top and the bottom are the same number, so the CPI equals 100 by definition.

The real CPI follows this idea at national scale. It tracks the average change over time in the prices that urban consumers pay for a fixed market basket of consumer goods and services. Your version this week has three items, and the arithmetic is the same.

Why keep the basket fixed? Suppose you bought more pizza this year than last. If the list changed too, a bigger bill could mean you bought more, not that prices rose. Holding the list still means the only thing that can change the total is price. That is the same idea as real GDP from Week 2, where holding prices still meant only quantities could move the total.

Misconception check. Students often think the CPI measures how much people spent. It does not. Spending can rise because people buy more. The CPI asks a narrower question: what does the same basket cost now? The cure: whenever you see a CPI, say "the same basket now costs this much compared with the base year."

2. Price the basket: computing the CPI

Now put numbers on the student's week. This basket is illustrative, constructed for this course, not real data. All prices are in dollars.

The illustrative campus basket: quantities and prices in dollars, base year and year 2
Item	Quantity in the basket	Base-year price	Year-2 price
Pizzas	10	8	9
Coffees	20	3	3.30
Textbooks	4	15	15

Worked example — the base-year basket. Start with the prices in the first price column.

Cost of each item. Pizzas: 10 × 8 = 80. Coffees: 20 × 3 = 60. Textbooks: 4 × 15 = 60.
Add them up. 80 + 60 + 60 = 200 dollars.
The CPI. (200 ÷ 200) × 100 = 100.

In words: the basket costs 200 dollars in the base year, and the CPI is 100 there, as it must be.

Worked example — the year-2 basket. Keep the same quantities and switch to the year-2 prices.

Cost of each item at year-2 prices. Pizzas: 10 × 9 = 90. Coffees: 20 × 3.30 = 66. Textbooks: 4 × 15 = 60.
Add them up. 90 + 66 + 60 = 216 dollars.
The CPI. (216 ÷ 200) × 100 = 108.

In words: the same basket that cost 200 dollars now costs 216 dollars, so the CPI is 108. The basket costs 8 percent more than it did in the base year.

Notice the units. A CPI is a level, so it carries no percent sign. You write 108, not 108%.

In practice (your tools). In Google Sheets, put the quantities in B2 to B4 (10, 20, 4), the base-year prices in C2 to C4 (8, 3, 15), and the year-2 prices in D2 to D4 (9, 3.30, 15). The base-year cost is =SUMPRODUCT(B2:B4,C2:C4), which shows 200. The year-2 cost is =SUMPRODUCT(B2:B4,D2:D4), which shows 216. In another cell, =D6/C6*100 gives the CPI of 108 if the two costs sit in C6 and D6.

Misconception check. Students often add up the prices instead of the costs: 9 + 3.30 + 15 against 8 + 3 + 15. That ignores how much of each item the basket holds, so a price change on something you buy 20 of counts the same as one on something you buy 4 of. The cure: multiply each price by its quantity first, then add.

3. Turn a level into a rate: the inflation rate

Think of a road trip. The mile marker tells you where you are. Your speed tells you how fast you are moving. Both matter, and they are different numbers. The CPI is the mile marker. The inflation rate is the speed.

The inflation rate is the percentage change in a price index from one period to the next: the new level minus the old level, divided by the old level, times 100.

As a formula, inflation rate = (new CPI − old CPI) ÷ old CPI × 100.

Worked example — from the base year to year 2. Use the two CPI readings, 100 and 108.

The change in the index. 108 − 100 = 8.
Divide by the starting level. 8 ÷ 100 = 0.08.
Turn it into a percent. 0.08 × 100 = 8%.

So (108 − 100) ÷ 100 × 100 = 8%. You get the same answer from the basket costs: (216 − 200) ÷ 200 × 100 = 8%. In words: prices rose 8 percent from the base year to year 2.

Worked example — from year 2 to year 3. In year 3 the same basket costs 226.80 dollars.

The year-3 CPI. (226.80 ÷ 200) × 100 = 113.4.
The change in the index. 113.4 − 108 = 5.4.
Divide by the starting level, year 2's. 5.4 ÷ 108 = 0.05.
Turn it into a percent. 0.05 × 100 = 5%.

So (113.4 − 108) ÷ 108 × 100 = 5.4 ÷ 108 × 100 = 5%. In words: prices rose 5 percent from year 2 to year 3. Inflation slowed, even though the CPI kept climbing.

That last sentence is worth a second look. A CPI that keeps rising does not mean inflation is speeding up. It means prices are still going up. Inflation measures how fast.

Index points are the plain difference between two readings of a price index, such as 113.4 minus 108; they measure distance on the index, not a percentage change.

The gap of 5.4 is index points, not a rate. It becomes a rate only after you divide by the starting level.

Misconception check. Students often read a CPI level of 108 as "8% inflation this year." That works only once. A CPI of 108 says the basket costs 8 percent more than in the base year. It says nothing about this year alone. "CPI − 100" equals the inflation rate only in the first year after the base year, because only then is the starting level 100. The cure: always find two CPI readings, one for each end of the period, and compute the percentage change between them.

Misconception check — the forgotten division. Students often compute year-3 inflation as 113.4 − 108 = 5.4, and call it 5.4%. That skips the step that makes it a rate. The cure: divide the change by the old level, 5.4 ÷ 108 × 100 = 5%. The bigger the index gets, the further apart these two numbers drift.

In practice (your tools). In Google Sheets, put the three CPI readings in a column, 100, 108, and 113.4, in B2 to B4. In C3, type =(B3-B2)/B2*100 and copy it down to C4. C3 shows 8 and C4 shows 5. The formula always divides by the cell above, which is the starting level for that year.

Pause and reflect — choose one. Pick either prompt; they count the same.

(a) Think of one price you pay often. Describe how you would turn two years of that price into an inflation rate for that one item, and say what the number would and would not tell you about all prices.
(b) Think of a headline that reports a price index level. Explain in two sentences why that level alone cannot tell you how fast prices rose this year.

4. Protect your paycheck: real versus nominal wages

Picture two paychecks, one from last year and one from this year. This year's has more dollars on it. Whether you can buy more depends on what happened to prices. Economists give each view of the paycheck its own name.

A nominal wage is pay measured in the dollars a worker receives at the time, with no adjustment for what those dollars can buy.
A real wage is pay measured by the goods and services it can buy, found by removing the effect of price changes; a real wage change is about the nominal wage change minus the inflation rate.

This is the real-versus-nominal split from Week 2, moved from GDP to your pay.

Worked example — the 4 percent raise. This example is illustrative. A worker gets a 4% raise. Over the same year, prices rise 5%.

Write the rule. Real wage change ≈ nominal wage change − inflation rate.
Put in the numbers. 4% − 5% = −1%.
Read the sign. The result is negative.

In words: the raise was a real pay cut of about 1 percent. The paycheck has more dollars, but those dollars buy about 1 percent less than last year's paycheck did.

The symbol ≈ means "approximately." The subtraction rule is a shortcut that works well when both rates are small, as they are here. It is close, not exact, which is why the result is said as "about 1 percent."

Worked example — a paycheck in base-year dollars. Here is a second, illustrative way to see the same idea, using the campus basket's CPI. Suppose a weekly paycheck is 540 dollars in year 2, when the CPI is 108.

Divide by the CPI and multiply by 100. 540 ÷ 108 × 100.
Divide first. 540 ÷ 108 = 5.
Then multiply. 5 × 100 = 500.

In words: 540 dollars in year 2 buys what 500 dollars bought in the base year. That 500 is the paycheck's value in base-year dollars, its real value.

Misconception check. Students often treat any raise as a gain. A raise in dollars is a nominal gain. Whether it is a real gain depends on inflation. The cure: before you celebrate a raise, subtract the inflation rate from it. If the result is negative, your buying power fell.

Two honest caveats about the CPI

Here is a caveat about the basket itself. Because the basket is fixed, the CPI can overstate inflation when shoppers switch to cheaper goods or when the quality of goods improves. A second limitation is about scope: the GDP deflator from Week 2 prices everything counted in GDP, while the CPI prices what households buy. The two indexes answer different questions, so they need not move together.

5. Count the labor market: three rates from three counts

Now leave the store and walk into a job fair. Some people there already have jobs and are looking for better ones. Some have no job and are looking hard. Others in the town never come to the fair at all: retirees, full-time students, people caring for family. To measure unemployment, economists first sort every adult into one of three groups.

Employed describes a person who has a job and works for pay or profit, whether part-time or full-time.
Unemployed describes a person who has no job, is available to work, and has actively looked for work recently; a person without a job who is not looking does not count.
The labor force is all the people who are either employed or unemployed: everyone who is working or actively looking for work.

Everyone else, adults with no job who are not looking, is outside the labor force. That group is not counted as unemployed.

From those counts come two rates.

The unemployment rate is the number of unemployed people divided by the labor force, times 100, which gives the share of people working or looking for work who have no job.
The labor-force participation rate is the labor force divided by the adult population aged 16 and over, times 100, which gives the share of adults who are working or looking for work.

Worked example — the illustrative labor market. These counts are illustrative, constructed for this course, not real data.

Adults in the illustrative labor market, by group, in millions and in people
Group	Millions of people	Number of people
Adult population, 16 and over	200	200,000,000
Employed	114	114,000,000
Unemployed	6	6,000,000
Labor force	120	120,000,000
Outside the labor force	80	80,000,000

The labor force. Employed + unemployed = 114 + 6 = 120 million people.
The unemployment rate. 6 ÷ 120 = 0.05, and 0.05 × 100 = 5%.
The participation rate. 120 ÷ 200 = 0.6, and 0.6 × 100 = 60%.
Outside the labor force. 200 − 120 = 80 million adults.

In words: 5 of every 100 people in the labor force are looking for work and do not have it, and 60 of every 100 adults are either working or looking. The other 80 million adults, including retirees and full-time students not seeking work, are outside the labor force.

In practice (your tools). In Google Sheets, type the adult population in B2 (200), the employed in B3 (114), and the unemployed in B4 (6). In B5, =B3+B4 gives the labor force, 120. In B6, =B4/B5*100 gives the unemployment rate, 5. In B7, =B5/B2*100 gives the participation rate, 60. Look at the two denominators: B5 for unemployment, B2 for participation.

Misconception check. Students often divide the unemployed by the whole adult population: 6 ÷ 200 × 100 = 3%. That is the wrong base. The unemployment rate asks, "Of the people in the job market, what share has no job?" Retirees and full-time students are not in the job market. The cure: the unemployment rate divides by the labor force, 120, and only the participation rate divides by all adults, 200.

6. Spot who is left out: discouraged workers

Picture someone who lost a job months ago. At first, they sent out applications every week. Nothing came back. Eventually they stopped applying, because they came to believe no job was out there for them. They still want work. But they are no longer looking.

A discouraged worker is a person who wants a job but has stopped looking because they believe none is available; the survey counts such a person as outside the labor force, not as unemployed.

That rule has a strange side effect. When a jobless person stops looking, they leave the unemployed count and the labor force. Both the top and the bottom of the unemployment rate shrink. The rate can fall even though nobody found a job.

Worked example — the illustrative town. This town is illustrative, constructed for this course. Its labor force is 4,800 people, and 240 of them are unemployed.

The rate before. 240 ÷ 4,800 × 100 = 5%.
Fifty people stop looking. The unemployed count falls to 240 − 50 = 190. The labor force falls to 4,800 − 50 = 4,750.
The rate after. 190 ÷ 4,750 × 100 = 4%.

In words: the town's unemployment rate fell from 5% to 4%, and not one person was hired. The drop came from people giving up.

This is a known limitation of the measured rate. It is why careful readers also check the participation rate. In the town, participation would fall too, because the labor force shrank. A falling unemployment rate alongside a falling participation rate is a sign to look closer.

Misconception check. Students often count a discouraged worker as unemployed, since that person wants a job and has none. The survey does not. To be unemployed, a person must be actively looking. The cure: ask two questions in order. Does this person have a job? If not, are they actively looking? Only a "no" and then a "yes" makes someone unemployed.

Pause and reflect — choose one. Pick either prompt; they count the same.

(a) A news report says the unemployment rate fell. Write two questions you would ask before deciding it is good news, and say which number would answer each one.
(b) Describe, in your own words, someone who is out of work but would not be counted as unemployed. Explain which part of the definition leaves them out.

7. Sort the jobless: three types of unemployment

Not every job loss has the same cause. Think of three people without work. One quit to move closer to family and is now interviewing. One spent years in a trade that new technology replaced. One was laid off when a downturn cut customer spending everywhere. Economists sort these into three types, because each one has a different cause.

Frictional unemployment is joblessness that comes from the ordinary time it takes workers and employers to find and match with each other, such as a new graduate searching for a first job.
Structural unemployment is joblessness that comes from a lasting mismatch between the skills or locations of workers and the jobs on offer, such as when new technology replaces a trade.
Cyclical unemployment is the extra joblessness that appears when spending across the economy falls in a recession and that shrinks again in an expansion.

Worked example — sorting four cases. These cases are illustrative. Run each through one question: why is this person without a job?

A nursing graduate is spending a few weeks choosing between hospital offers. The jobs exist; matching takes time. That is frictional.
A film-photo lab technician lost work when cameras went digital, and the nearby openings need different skills. The jobs that remain do not match the skills on offer. That is structural.
A hotel housekeeper was laid off when travel spending fell during a recession, and the hotel plans to rehire once guests return. That is cyclical.
A software tester moved across the country for a partner's job and is now applying for local roles. The search after a move is frictional.

In words: two of the four are frictional, one is structural, and one is cyclical. The question "why?" sorts them, not the person's industry.

Frictional unemployment is not a sign of trouble. Some search time is healthy: it means workers are finding jobs that fit. Structural unemployment can last longer, because a worker may need new training or a move. Cyclical unemployment rises and falls with the business cycle, which you will meet in Week 6.

Misconception check. Students often think any long spell without work must be cyclical. Length does not decide the type; the cause does. A trade replaced by technology stays structural even in a boom. The cure: ask whether the job would come back if spending across the economy recovered. If yes, it is cyclical. If the job is gone for good, it is structural.

Key terms

Market basket — A fixed list of goods and services, with a set quantity of each, whose total cost is tracked from year to year so that only changes in prices, not changes in what is bought, move the total. (first used: 1. Define the CPI: one basket, priced twice)
Consumer Price Index — A price index that compares the cost of a fixed market basket of goods and services that households buy in a given year with the cost of the same basket in the base year, times 100; it is written CPI. (first used: 1. Define the CPI: one basket, priced twice)
Inflation rate — The percentage change in a price index from one period to the next: the new level minus the old level, divided by the old level, times 100. (first used: 3. Turn a level into a rate: the inflation rate)
Index points — The plain difference between two readings of a price index, such as 113.4 minus 108; it measures distance on the index, not a percentage change. (first used: 3. Turn a level into a rate: the inflation rate)
Nominal wage — Pay measured in the dollars a worker receives at the time, with no adjustment for what those dollars can buy. (first used: 4. Protect your paycheck: real versus nominal wages)
Real wage — Pay measured by the goods and services it can buy, found by removing the effect of price changes; a real wage change is about the nominal wage change minus the inflation rate. (first used: 4. Protect your paycheck: real versus nominal wages)
Employed — Describes a person who has a job and works for pay or profit, whether part-time or full-time. (first used: 5. Count the labor market: three rates from three counts)
Unemployed — Describes a person who has no job, is available to work, and has actively looked for work recently; a person without a job who is not looking does not count. (first used: 5. Count the labor market: three rates from three counts)
Labor force — All the people who are either employed or unemployed: everyone who is working or actively looking for work. (first used: 5. Count the labor market: three rates from three counts)
Unemployment rate — The number of unemployed people divided by the labor force, times 100, which gives the share of people working or looking for work who have no job. (first used: 5. Count the labor market: three rates from three counts)
Labor-force participation rate — The labor force divided by the adult population aged 16 and over, times 100, which gives the share of adults who are working or looking for work. (first used: 5. Count the labor market: three rates from three counts)
Discouraged worker — A person who wants a job but has stopped looking because they believe none is available; the survey counts such a person as outside the labor force, not as unemployed. (first used: 6. Spot who is left out: discouraged workers)
Frictional unemployment — Joblessness that comes from the ordinary time it takes workers and employers to find and match with each other, such as a new graduate searching for a first job. (first used: 7. Sort the jobless: three types of unemployment)
Structural unemployment — Joblessness that comes from a lasting mismatch between the skills or locations of workers and the jobs on offer, such as when new technology replaces a trade. (first used: 7. Sort the jobless: three types of unemployment)
Cyclical unemployment — The extra joblessness that appears when spending across the economy falls in a recession and that shrinks again in an expansion. (first used: 7. Sort the jobless: three types of unemployment)

Summary

The CPI is the cost of a fixed basket in a year divided by its cost in the base year, times 100.
A CPI level has no percent sign; it equals 100 in the base year.
The inflation rate is (new CPI − old CPI) ÷ old CPI × 100.
A gap in index points becomes a rate only after you divide by the starting level.
A real wage change is about the nominal raise minus the inflation rate.
The labor force is the employed plus the unemployed.
The unemployment rate divides by the labor force; the participation rate divides by all adults.
Discouraged workers sit outside the labor force, so the measured rate can fall with no one hired.
Frictional, structural, and cyclical unemployment differ by cause, not by length.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

An illustrative commuter's basket holds 5 bus passes and 10 lunches. In the base year a pass costs 20 dollars and a lunch costs 6. In year 2 a pass costs 22 dollars and a lunch costs 6.60. Compute the basket's cost in both years, the year-2 CPI, and the inflation rate from the base year to year 2.
The same commuter's CPI reaches 121 in year 3. A friend says inflation from year 2 to year 3 was 11%. Find the actual inflation rate and explain the friend's slip.
An illustrative county has 40,000 adults aged 16 and over. Of them, 25,200 are employed and 2,800 are unemployed. Compute the labor force, the unemployment rate, and the labor-force participation rate, and say each result in words.
A server earns a 6% raise in a year when prices rise 2%. About how much did the server's real wage change? Then classify this illustrative case: a bank teller whose branch closed after customers moved to phone banking, and whose town has no teller openings left.

Answers (worked reasoning — read after attempting)

Base-year cost: 5 × 20 + 10 × 6 = 100 + 60 = 160 dollars. Year-2 cost: 5 × 22 + 10 × 6.60 = 110 + 66 = 176 dollars. Year-2 CPI: (176 ÷ 160) × 100 = 110. Inflation: (110 − 100) ÷ 100 × 100 = 10%. In words, the same commuter basket costs 10 percent more in year 2. Here "CPI − 100" works, because year 2 is the first year after the base year.
Inflation from year 2 to year 3 is (121 − 110) ÷ 110 × 100 = 11 ÷ 110 × 100 = 10%. The friend took the gap in index points, 11, and called it a rate. Prices rose 10 percent that year, not 11 percent. The slip is the forgotten division by the starting level.
Labor force: 25,200 + 2,800 = 28,000 people. Unemployment rate: 2,800 ÷ 28,000 × 100 = 10%, so 10 of every 100 people in the county's job market have no job. Participation rate: 28,000 ÷ 40,000 × 100 = 70%, so 70 of every 100 adults are working or looking. If you got 7% for unemployment, you divided by all adults instead of the labor force.
Real wage change ≈ 6% − 2% = 4%, so the server's pay buys about 4 percent more than last year. The teller's job loss is structural: the work was replaced by a change in how people bank, and the town's openings do not match. It would not come back if spending across the economy recovered, which is what separates it from cyclical unemployment.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the rule of 70 turns a growth rate into the years it takes an economy to double.

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