Week 12 · Chapter

Chapter 12 — Inflation, the Phillips Curve & Expectations

Principles of Macroeconomics Free sample edition

The module's primary reading · ~35–45 minutes · Objective 8 (analyze the short-run and long-run Phillips curve and the quantity equation of money, and apply open-economy tools — comparative advantage and the gains from trade, the trade balance, exchange rates, and the balance of payments — and weigh the Keynesian and classical / monetarist views of stabilization policy evenhandedly), with 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 slides, the tutorial, the quiz, and the Model Workshop all build on it.

In plain language

This week asks whether a country can buy fewer jobless people by putting up with faster-rising prices. In the short run, the answer often looks like yes: when jobs are plentiful, pay and prices tend to climb faster. That pattern is the short-run Phillips curve (a picture of the link between the unemployment rate and the inflation rate). The catch is expected inflation (the price increases people plan for), because once people expect faster price rises, the deal fades. You will also meet a simple money equation that explains why, over many years, more money mostly means higher prices rather than more goods.

Why you already care about this

Picture three illustrative people this week, with made-up numbers. A line cook at a busy restaurant earns 20 dollars an hour and notices the menu prices going up again. A shop owner is deciding what to charge for next year's haircuts. A nursing student is weighing two job offers in a town where every clinic seems to be hiring. All three are living inside the same story.

When help-wanted signs fill every window, employers compete for workers and raise pay. Firms then pass those costs on in their prices. When jobs are scarce, raises shrink and prices climb more slowly. That pull between jobs and prices is the story of this chapter.

Here is the twist. The line cook does not only react to the prices she sees now. She thinks about prices next year. If she expects the menu to cost 6% more, she will ask for a raise of about 6% to keep up. Her expectation becomes part of tomorrow's prices.

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

read the short-run Phillips curve and state its trade-off forwards;
compute the slope between two points on the curve and say it in words;
find the natural rate of unemployment and draw the long-run Phillips curve as a vertical line there;
explain how a rise in expected inflation shifts the short-run curve up, and why the trade-off does not last;
use the quantity equation M × V = P × Q to find the price level and to measure velocity;
show long-run neutrality: with velocity and real output fixed, a 10% rise in money is a 10% rise in prices;
apply the approximation inflation ≈ money growth − output growth, and lay out both sides of the debate over how fast to bring inflation down.

Carry this line with you: a short-run trade-off, not a permanent menu.

Where we are

Already covered: Week 3, Measuring Inflation & Unemployment, gave you the inflation rate, the real wage, and the three types of unemployment. Week 5, Aggregate Demand & Aggregate Supply, taught you to tell a movement along a curve from a shift of it. Week 6, Business Cycles & Short-Run Fluctuations, showed that expected inflation shifts short-run aggregate supply. Weeks 9, 10, and 11 built the money supply, the Fed's tools, and the chain from money to output.
This week: you put inflation and unemployment on one diagram, see why the short-run trade-off fades once expectations catch up, and meet the quantity equation that ties money to prices in the long run.
How they connect: Week 3's two rates become this week's two axes. Week 11 showed that more money can raise output in the short run; this week asks what is left of that boost in the long run.
Where we're going next: Week 13, International Trade & Comparative Advantage, opens a new unit on the open economy and asks why any country trades at all.

Three earlier ideas carry this chapter. From Week 3, the inflation rate is the percentage change in a price index, and a real wage change is about the nominal raise minus inflation. From Week 3 again, frictional unemployment is the normal time a job search takes, and structural unemployment is a mismatch of skills or places. From Week 6, a rise in expected inflation shifts short-run aggregate supply left, which raises prices and lowers output.

1. Read the short-run Phillips curve: jobs and prices on one diagram

Think back to the help-wanted signs. In a hot job market, unemployment is low, and pay and prices rise fast. In a cold one, unemployment is high, and they rise slowly. Economists put those two facts on one picture.

Picture the graph. The unemployment rate u runs along the horizontal axis, in percent. The inflation rate π runs up the vertical axis, in percent. The curve slopes down from upper left to lower right. High on the left means low unemployment with high inflation. Low on the right means high unemployment with low inflation.

The short-run Phillips curve is a downward-sloping curve with the unemployment rate on the horizontal axis and the inflation rate on the vertical axis, showing that in the short run lower unemployment tends to come with higher inflation for a given level of expected inflation.

The curve is named for A. W. Phillips, whose 1958 study found an inverse relationship between unemployment and the rate of change of money wages in United Kingdom data for 1861–1957. An inverse relationship means that when one goes up, the other tends to go down.

Worked example — two points on the course's curve. The course uses an illustrative curve (Dataset L, constructed for this course, not real data).

First point. (u = 4%, π = 6%): unemployment of 4% comes with inflation of 6%.
Second point. (u = 6%, π = 2%): unemployment of 6% comes with inflation of 2%.
Check the direction. Going from the first point to the second, unemployment goes up and inflation goes down. The curve slopes down.

In words: on this curve, a tighter job market comes with faster-rising prices, and a looser one comes with slower-rising prices.

Misconception check. Students often put inflation on the horizontal axis and unemployment on the vertical one, because the AD–AS diagram had output along the bottom. Then every reading comes out reversed. Fix the axes first: unemployment u along the bottom, inflation π up the side. Then say the pattern out loud: lower unemployment, higher inflation.

Memory hook: u along the floor, π up the wall.

2. Read the trade-off forwards: a slide along the curve

Suppose policymakers want fewer people out of work. On this curve, that choice has a price. Moving left along the curve means less unemployment and more inflation.

The inflation–unemployment trade-off is the short-run pattern in which pushing unemployment lower tends to bring higher inflation, and accepting higher unemployment tends to bring lower inflation; it holds along one short-run Phillips curve and fades once expected inflation adjusts.

Worked example — sizing the trade-off. Use the two points from section 1 (Dataset L, illustrative).

Change in unemployment. From (u = 6%, π = 2%) to (u = 4%, π = 6%), unemployment falls by 6 − 4 = 2, two percentage points.
Change in inflation. Inflation rises by 6 − 2 = 4, four percentage points.
Slope. (2 − 6) ÷ (6 − 4) = −4 ÷ 2 = −2.
Read the slope. Each point less unemployment comes with two points more inflation along this curve.

In words: on this illustrative curve, cutting unemployment by two percentage points costs four percentage points of extra inflation, a trade of 2 for 1.

A "point" here is one percentage point. Going from 6% to 4% is a fall of two percentage points, not a fall of 2%.

Notice what kind of move this is. Nothing about the curve itself changed. The economy slid from one point on it to another. That is a movement along the curve, the same habit you used on aggregate demand in Week 5. A shift of the whole curve is a different event, and section 4 shows what causes one.

Misconception check. Students often state the trade-off backwards: "higher unemployment comes with higher inflation." That is tempting, because unemployment and inflation are both bad news, so it feels like they should rise together. Along one short-run curve they move in opposite directions. Read the two points again: 4% unemployment sits with 6% inflation, and 6% unemployment sits with 2% inflation.

Memory hook: down the slide: fewer jobless, faster prices.

3. Find the natural rate and the vertical long-run curve

Some unemployment never goes away, even in a strong economy. A new graduate takes a few weeks to find the right job. A factory worker whose trade was replaced by a machine needs time to retrain. That leftover unemployment has a name.

The natural rate of unemployment is the unemployment rate that remains when the economy produces at potential output, made up of frictional plus structural unemployment with no cyclical unemployment; it is written u*.

You met the pieces in Week 3. Frictional unemployment is the search time. Structural unemployment is the mismatch. Cyclical unemployment, the extra joblessness of a recession, is zero at the natural rate.

Worked example — the natural rate in the course's economy. Use Dataset L (illustrative).

The rule in the dataset. The natural rate sits midway between the two short-run points.
Compute. u* = (4 + 6) ÷ 2 = 10 ÷ 2 = 5%.
Distance from it. At the first point, 5 − 4 = 1, one point below the natural rate. At the second, 6 − 5 = 1, one point above it.

In words: the illustrative economy's natural rate is 5%, and its two short-run points sit one percentage point on either side of it.

Now the long run. Picture a vertical line rising straight up from 5% on the unemployment axis.

The long-run Phillips curve is a vertical line at the natural rate of unemployment, showing that once expected inflation has caught up, unemployment returns to the natural rate whatever the inflation rate, so there is no lasting trade-off.

Why vertical? In the long run, people's expectations catch up with the inflation they live through. Wages and prices are set to match it. Then inflation no longer surprises anyone, and unemployment drifts back to its natural rate. At any inflation rate, unemployment returns to 5% in the long run in this illustrative economy.

This idea has a history. Milton Friedman (1968) and Edmund Phelps (1967) each argued that the short-run trade-off could not be used forever.

The natural-rate argument is the case, associated with Milton Friedman and Edmund Phelps, that policy can hold unemployment below the natural rate only until people come to expect the higher inflation it brings, after which unemployment returns to the natural rate at a higher inflation rate.

Caveat: the 5% is this course's illustrative number. The real natural rate cannot be seen directly, and economists disagree about its size, so the course never grades a real-world natural rate as a number. What is not in dispute is the shape. That the long-run curve is vertical is an agreed positive result, not a matter of taste.

Misconception check. Students often draw the long-run Phillips curve with a gentle slope, because every other Phillips curve they have drawn slopes down. That is tempting, but it brings back the very trade-off the long run removes. The long-run curve has no slope. It is a vertical line at the natural rate, the same way long-run aggregate supply is a vertical line at potential output.

Memory hook: short run slopes; long run stands straight.

4. Shift the short-run curve: expected inflation catches up

Go back to the line cook. She earns 20 dollars an hour, and she expects prices to rise 6% this year (illustrative, not real data).

Worked example — the cook's raise. Her real wage depends on her raise and on inflation.

A raise that keeps up. To keep pace with 6% inflation she asks for 6%: 20 × 1.06 = 21.20 dollars an hour.
A raise that falls short. If she gets only 2% while prices rise 6%, her real wage change is about 2% − 6% = −4%.
What she does next. She bargains harder next time, and so do her coworkers.

In words: once workers expect 6% inflation, they build it into the wages they ask for, and firms build it into their prices.

That is why the short-run curve is drawn "for a given level of expected inflation." When expected inflation rises, the whole short-run curve shifts up. Every unemployment rate now comes with more inflation than before.

Worked example — chasing 4% unemployment. Use Dataset L (illustrative).

The choice. Policy holds unemployment at 4%, one percentage point below the natural rate.
The short-run price. On the original curve, 4% unemployment comes with 6% inflation.
Expectations catch up. Workers and firms come to expect 6% and build it into wages and prices. The short-run curve shifts up.
Where the economy settles. Unemployment drifts back to 5%, and inflation stays at 6%: the point (u = 5%, π = 6%).

In words: policy bought higher inflation and the same unemployment once expectations caught up. The economy ends on the vertical long-run curve, at the natural rate, with more inflation than it started with.

You have seen this force before. In Week 6, higher expected inflation shifted short-run aggregate supply left. The Phillips curve shows the same event from a different angle: on the AD–AS diagram, prices rise and output slips back toward potential; on the Phillips diagram, the short-run curve shifts up and unemployment slips back toward the natural rate.

Honesty note: how fast expectations catch up is a question economists still argue about. The direction of the shift is agreed. The speed is not.

Misconception check. Students often treat the short-run Phillips curve as a permanent menu, as if a country could pick 4% unemployment with 6% inflation and keep it forever. That is tempting, because the curve looks like a list of options. But the curve itself moves when expected inflation moves. Hold unemployment below the natural rate, and expected inflation keeps climbing, so the curve keeps shifting up.

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

(a) Think of a time you or someone you know asked for a raise, or a price went up at a place you shop. Did expected price increases play a part in that decision?
(b) Imagine you run a small business. If you expected your costs to rise 6% next year, how would that shape the prices you set now?

Memory hook: expect more inflation, and the whole curve climbs.

5. Write the quantity equation: money, velocity, prices, output

Now switch from jobs to money. Picture an illustrative street fair, with made-up numbers. Organizers sell 300 dollars of tokens. A visitor spends a token at a food stall. The stall owner spends it at the craft booth. The craft seller buys a lemonade. By the end of the day, stalls have rung up 1,500 dollars of sales, using the same 300 dollars of tokens: 1,500 ÷ 300 = 5. Each token changed hands 5 times.

That idea scales up to a whole economy.

The quantity equation is the identity M × V = P × Q, which says the money supply times the number of times each dollar is spent equals the price level times real output, the nominal value of what the economy produces.
The velocity of money is the number of times an average dollar is spent on final goods and services in a year, found as nominal output divided by the money supply and written V.

Here M is the money supply. Imports are still written IM, never M, so the two never collide. P is the price level, the average price of one unit of real output. Q is real output, the quantity of final goods and services produced in a year. The left side is the money spent. The right side is the nominal value of what that money bought.

Worked example — the course's quantity equation. Use Dataset M (constructed for this course, not real data), with money in dollars.

Total nominal spending. M × V = 500 × 4 = 2,000.
Price level. P = (M × V) ÷ Q = 2,000 ÷ 1,000 = 2.
Velocity, measured. V = (P × Q) ÷ M = (2 × 1,000) ÷ 500 = 2,000 ÷ 500 = 4.

In words: 500 dollars of money, each dollar spent 4 times a year, buys 1,000 units of real output at an average price of 2 dollars each, and each dollar changes hands 4 times a year.

Misconception check. Students often treat velocity as a fudge factor, a number made up to force the equation to balance. That is tempting, because V is the one letter you cannot see on a price tag. But velocity is measured: divide the nominal value of output by the money supply, as in step 3. At the street fair, 1,500 ÷ 300 gave 5. In the course's economy, 2,000 ÷ 500 gives 4.

Memory hook: money times turnover equals prices times stuff.

6. Test long-run neutrality: more money, same real output

Here is a thought experiment. Suppose the money supply rises and nothing real changes: the same workers, the same machines, the same know-how. More dollars are now chasing the same goods.

Worked example — a 10% rise in money. Use Dataset M (illustrative), holding V and Q fixed.

New money supply. 500 × 1.10 = 550.
New spending. M × V = 550 × 4 = 2,200.
New price level. P = 2,200 ÷ 1,000 = 2.2.
Inflation from the money increase. (2.2 − 2) ÷ 2 × 100 = 0.2 ÷ 2 × 100 = 10%.
Real output. Still 1,000, because Q was held fixed.

In words: the money supply rose 10%, the price level rose the same 10%, and real output did not change at all.

Long-run neutrality of money is the result that, in the long run, a change in the money supply changes the price level and other nominal values but leaves real output and unemployment unchanged.
The quantity theory of money is the use of the quantity equation with velocity and real output held steady, which predicts that the price level changes in proportion to the money supply.

Notice how this fits the long-run Phillips curve. In the long run, money moves prices and leaves real output and unemployment where they were. In the Phillips picture, that is a vertical line at the natural rate.

Caveat: velocity does not always hold still. People and firms change how fast they spend, and unpredictable swings in velocity are one of the hazards of monetary policy. That is why the fixed-V case is a model, not a promise.

Misconception check. Students often conclude that "MV = PQ says money does not matter." That is tempting, because real output did not move in the worked example. But the result is narrower. Money is neutral for real output in the long run. In Weeks 10 and 11 you saw the short run: a bond purchase lowered the interest rate, raised investment, and shifted aggregate demand right, so real output rose. Both are true, on different clocks.

Memory hook: in the long run, money moves prices, not output.

7. Approximate inflation from money growth, and weigh how fast to bring it down

Most economies grow, so real output does not hold still either. A handy shortcut handles growth in money and in output at the same time.

The money growth rate is the percentage change in the money supply over a year; when velocity is stable, the inflation rate is approximately the money growth rate minus the growth rate of real output.

Worked example — the growth-form approximation. Use the course's pinned rates (Dataset M, illustrative).

Money growth. 8% a year.
Output growth. 3% a year.
Approximate inflation. inflation ≈ money growth − output growth = 8% − 3% ≈ 5%.

In words: if money grows 8% a year while real output grows 3%, and velocity is stable, prices rise about 5% a year. Of the 8% money growth, the extra goods absorb 3%; the other 5% shows up in prices.

This shortcut is an approximation. It holds when velocity is stable. If velocity falls, the same money growth brings less inflation; if it rises, more.

Now tie the threads together. Steady money growth above output growth sets the inflation people come to expect. That expected inflation is the force that shifts the short-run Phillips curve up. So once inflation is high, a hard question follows: how fast should a central bank bring it down? Bringing it down means slowing money growth, and in the short run that can mean a slide down the short-run curve toward higher unemployment.

The Keynesian case, at full strength. Wages and prices are sticky, and expectations adjust slowly. A sharp squeeze on money growth would push unemployment well above the natural rate while expectations catch up, and that means real families losing real paychecks. A gradual path spreads out the pain and gives contracts time to adjust.

The classical and monetarist case, at full strength. Inflation in the long run is a monetary matter, so it ends only when money growth slows. A firm and believable commitment can bring expectations down faster, which shortens the painful stretch. A slow path risks letting high inflation settle into wages and prices, so the eventual cure costs more.

Now separate the two kinds of claims, as the course asks you to every week.

Positive and normative claims in the debate over how fast to bring inflation down
Claim	Kind	Which side leans on it
The long-run Phillips curve is vertical at the natural rate.	Positive, agreed by both	Both
Sustained high inflation is, in the long run, a monetary matter.	Positive, agreed by both	Both
Expectations adjust slowly, so a fast squeeze costs many jobs.	Positive, disputed evidence	Keynesian
A believable commitment brings expectations down quickly.	Positive, disputed evidence	Classical and monetarist
Spreading out the job losses is worth a longer spell of inflation.	Normative	Keynesian
Ending inflation quickly is worth a sharper spell of unemployment.	Normative	Classical and monetarist

Notice that the first two rows are not up for debate. The disagreement lives in how fast expectations move, which is a question for evidence, and in how to weigh jobs now against stable prices later, which is a question of values. This course gives you both columns and leaves the verdict to the evidence and your own values.

Misconception check. Students often treat the approximation as exact, or decide that one school has won. Both moves are tempting, because a single tidy answer is easier to remember. But the approximation holds only when velocity is stable, and both schools accept the vertical long-run curve. A strong answer names the agreed ground first, then states each side's best case, then labels which parts are positive and which are normative.

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

(a) Write the strongest one-sentence case for bringing inflation down gradually, then the strongest one-sentence case for bringing it down fast, and label the normative part of each.
(b) Name one piece of evidence that would move you toward one side, and say whether that evidence is positive or normative.

Memory hook: money growth minus output growth, if velocity holds still.

Key terms

short-run Phillips curve — A downward-sloping curve with the unemployment rate on the horizontal axis and the inflation rate on the vertical axis, showing that in the short run lower unemployment tends to come with higher inflation for a given level of expected inflation. (first used: 1. Read the short-run Phillips curve: jobs and prices on one diagram)
inflation–unemployment trade-off — The short-run pattern in which pushing unemployment lower tends to bring higher inflation, and accepting higher unemployment tends to bring lower inflation; it holds along one short-run Phillips curve and fades once expected inflation adjusts. (first used: 2. Read the trade-off forwards: a slide along the curve)
natural rate of unemployment — The unemployment rate that remains when the economy produces at potential output, made up of frictional plus structural unemployment with no cyclical unemployment; it is written u*. (first used: 3. Find the natural rate and the vertical long-run curve)
long-run Phillips curve — A vertical line at the natural rate of unemployment, showing that once expected inflation has caught up, unemployment returns to the natural rate whatever the inflation rate, so there is no lasting trade-off. (first used: 3. Find the natural rate and the vertical long-run curve)
natural-rate argument — The case, associated with Milton Friedman and Edmund Phelps, that policy can hold unemployment below the natural rate only until people come to expect the higher inflation it brings, after which unemployment returns to the natural rate at a higher inflation rate. (first used: 3. Find the natural rate and the vertical long-run curve)
quantity equation — The identity M × V = P × Q, which says the money supply times the number of times each dollar is spent equals the price level times real output, the nominal value of what the economy produces. (first used: 5. Write the quantity equation: money, velocity, prices, output)
velocity of money — The number of times an average dollar is spent on final goods and services in a year, found as nominal output divided by the money supply and written V. (first used: 5. Write the quantity equation: money, velocity, prices, output)
long-run neutrality of money — The result that, in the long run, a change in the money supply changes the price level and other nominal values but leaves real output and unemployment unchanged. (first used: 6. Test long-run neutrality: more money, same real output)
quantity theory of money — The use of the quantity equation with velocity and real output held steady, which predicts that the price level changes in proportion to the money supply. (first used: 6. Test long-run neutrality: more money, same real output)
money growth rate — The percentage change in the money supply over a year; when velocity is stable, the inflation rate is approximately the money growth rate minus the growth rate of real output. (first used: 7. Approximate inflation from money growth, and weigh how fast to bring it down)

Summary

The short-run Phillips curve slopes down: lower unemployment comes with higher inflation.
A slide between two points is a movement along the curve.
On the course's curve, each point less unemployment costs two points more inflation.
The natural rate is frictional plus structural unemployment, 5% in the course's economy.
The long-run Phillips curve is vertical at the natural rate; it has no slope.
Higher expected inflation shifts the short-run curve up, so the trade-off does not last.
The quantity equation says money times velocity equals the price level times real output.
With velocity and real output fixed, a 10% rise in money is a 10% rise in prices.
Inflation is about money growth minus output growth, when velocity is stable.
How fast to bring inflation down is a live debate; label each claim positive or normative.

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.

In an illustrative coastal economy (not real data), one short-run Phillips curve passes through (u = 3%, π = 7%) and (u = 7%, π = 1%), and the natural rate is 5%. Find the slope of the short-run curve and say it in words. Then say where the economy ends up in the long run if policy holds unemployment at 3% and people come to expect the inflation that comes with it.
In an illustrative island economy (not real data), the money supply is 800 dollars, velocity is 5, and real output is 1,600 units. Find the price level. Then raise the money supply 20% with velocity and real output fixed, and find the new price level and the percentage rise in prices.
In an illustrative mountain town (not real data), the nominal value of a year's output is 9,000 dollars and the money supply is 1,500 dollars. Find velocity and say what it means.
In an illustrative economy (not real data), money grows 6% a year and real output grows 2% a year. Estimate inflation. Then a classmate says, "Velocity fell sharply this year, but that changes nothing." Explain what a fall in velocity does to the estimate.

Answers (worked reasoning — read after attempting)

The slope is (1 − 7) ÷ (7 − 3) = −6 ÷ 4 = −1.5, so each one-point fall in unemployment comes with a rise of one and a half points in inflation along this curve. Holding unemployment at 3% means inflation of 7% on this curve in the short run. Once people expect 7%, the curve shifts up, and unemployment drifts back to the natural rate of 5% with inflation at 7%. The trade-off was short-run only.
Spending is 800 × 5 = 4,000, so the price level is 4,000 ÷ 1,600 = 2.5. A 20% rise makes the money supply 800 × 1.20 = 960, spending 960 × 5 = 4,800, and the price level 4,800 ÷ 1,600 = 3. Prices rise (3 − 2.5) ÷ 2.5 × 100 = 20%, the same 20% as money, with real output unchanged. That is long-run neutrality.
Velocity is 9,000 ÷ 1,500 = 6. An average dollar in that town is spent on final goods and services 6 times a year. Velocity is measured from the data, not invented to make the equation balance.
With stable velocity, inflation ≈ 6% − 2% ≈ 4%. The classmate is wrong: the shortcut holds only when velocity is stable. If velocity falls, each dollar is spent less often, so the same money growth produces less spending and less inflation than 4%.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the comparative advantage model asks why any country gains from trade.

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