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Resources › Inflation and the Phillips curve › 7. Expectations
Inflation and the Phillips curve · Lesson 7 of 12

Expectations: Friedman, Phelps and the vertical long run

Lesson 5 left a question: if a policymaker holds unemployment at 3% year after year, does inflation stay at 4%? Workers who watch prices rise will not keep accepting wages calculated for stable prices. Put what they expect into the curve and the trade-off becomes a short-run one, and in the long run it disappears. This is the most examined idea in the module.

← Inflation and the Phillips curve moduleLesson 7 of 12 · about 50 minutes
1Measuring inflation2Measuring unemployment3Causes4Costs5The original curve6Okun's law7Expectations8The natural rate9Stagflation10Disinflation11In the data12Delhi School
A question to hold on to
Suppose expected inflation is πet = (1 − θ)π̄ + θπt−1, where π̄ is constant inflation, πt−1 is last year’s inflation, and 0 ≤ θ ≤ 1. Which of the following is NOT correct? (A) If θ = 0, the individual assumes a constant inflation rate. (B) If θ ≈ 1 and π̄ < πt−1, the individual expects this year’s inflation similar to last year’s. (C) The original Phillips curve is derived under the assumption of θ ≈ 1. (D) A modified Phillips curve is derived under the assumption of θ = 1.
IIT JAM 2024Solved at the end ↓
In this guide
Lesson · about 50 minutes
  1. Why expectations matter
  2. How expectations form
  3. Try it: hold unemployment below the natural rate
  4. The vertical long run
  5. Along or shift
  6. Traps
  7. Worked questions
  8. The lesson on one screen
  9. Check yourself
  10. Past papers, by level
01
The missing variable

Why expectations matter

Workers care about what their wages will buy. If everyone expects prices to rise 5% this year, a wage rise of 5% is no rise at all, so wage claims are built on expected inflation, and firms pass the wage bill into prices. Whatever inflation people expect therefore sets the starting point: when unemployment is at its natural rate, actual inflation comes out equal to expected inflation. Unemployment below the natural rate pushes inflation above it; unemployment above pulls inflation below.

The expectations-augmented Phillips curve
π=πe−β(u−un​)
The curve passes through (uₙ, πᵉ). Raise πᵉ and the whole curve moves up (and to the right). Raise uₙ and it moves right.

Read it as the exam does. If actual unemployment equals the natural rate, unanticipated inflation, π − πᵉ, is zero (IIT JAM 2021). If unemployment is above the natural rate, inflation is below expected inflation, not above it, which is the common sign slip in the options. If unemployment is below the natural rate, inflation rises (Hyderabad 2018, 2020). An increase in expected inflation shifts the curve up and to the right, and an increase in the natural rate shifts it to the right, not to the left (IIT JAM 2021).

Who, when and why it mattered
  1. 1967
    Edmund Phelps published “Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time” (Economica, vol. 34, no. 135, pp. 254–281), whose subject, as the title says, is the Phillips curve with expectations of inflation in it.
  2. 1968
    Milton Friedman in his presidential address to the American Economic Association, “The Role of Monetary Policy”, published in the American Economic Review in March 1968, argued that there is no trade-off between inflation and unemployment in the long run (as the Hyderabad question puts it, dating the statement to 1967), and popularised the term “natural rate”.

Sources: the bibliographic details in Federal Reserve Board working paper “Seven Fallacies Concerning Milton Friedman’s ‘The Role of Monetary Policy’’” (2018) and a university reading list citing Phelps; read on 25 October 2026.

02
Where πᵉ comes from

How expectations form

The simplest story is adaptive expectations: people expect next year’s inflation to look like what they have just seen. The puzzle mixes that with a constant anchor:

Adaptive expectations with a weight
πte​=(1−θ)πˉ+θπt−1​
θ = 0: expectations never move (the original curve, a stable trade-off). θ = 1: expected inflation is last year's inflation (the accelerationist curve). In between, a mixture.

That settles the opening question. With θ = 0 the individual assumes a constant rate (A is correct), and this is the case in which the original Phillips curve holds, a fixed trade-off, so (C), which says the original curve needs θ close to 1, is the statement that is not correct. The modified curve of Friedman and Phelps, in which expected inflation is last year’s, is the θ = 1 case (D).

Pause and predict
With θ = 1, β = 1 and the natural rate 5%, unemployment is held at 3% each year. Each year inflation rises by
03
Interactive

Try it: hold unemployment below the natural rate

The Dial of Lesson 5 again, now with θ. Start with “Hold below the natural rate”: expectations are last year’s inflation and the curve climbs every year. Then press “Original curve” to see the menu of Lesson 5 (θ = 0) and “Expectations half adjust” for the case in between.

One economy: natural rate 5%, inflation anchor 2%, and the response of inflation to the unemployment gap, β. You hold unemployment at the target you set, for ten years. Each year, expected inflation is a mix of last year's inflation (weight θ) and the 2% anchor.

24685101520unemployment, %inflation, %
Phillips curve (darker is later)The curve with expectations at the 2% anchorNatural rate, 5%
2468105101520yearinflation, %
Inflation each year2% anchor
Year one

Unemployment 3% is 2 points below the natural rate. Inflation is 4% = 2 − 1 × (3 − 5).

After 10 years

Inflation is 22%. With θ = 1 it moves by 2 points every year and never settles.

What to notice

Expected inflation is last year's inflation (θ = 1). Holding unemployment 2 points below the natural rate makes inflation rise by 2 points every year: the curve keeps shifting up.

Where it settles (θ below 1)
π∗=πˉ+1−θβ(un​−u)​
At θ = 0.5, π̄ = 2, β = 1 and u = 3 this gives 2 + 1 × 2/0.5 = 6%. At θ = 1 there is no settling point, which is the accelerationist result.
04
The long run

The vertical long run

In the long run people stop being surprised: expected inflation catches up with actual inflation, πᵉ = π, and the curve says u = uₙ whatever the rate of inflation. The long-run Phillips curve is vertical at the natural rate, which is the monetarist view (JNU 2015). In the Keynesian view the short-run and the long-run curves both slope down (JNU 2015). Friedman’s claim was that there is no trade-off between inflation and unemployment in the long run, and what would refute it is a long-run curve that is steeper than first thought but not vertical (Hyderabad 2010).

Three things follow. First, the natural rate is the unemployment rate at which inflation is stable, which is the idea of the NAIRU, developed in Lesson 8. Second, unemployment returns to the natural rate when the real wage is back at its long-run level (CUET 2022). Third, an economy held below its natural rate has rising inflation (Hyderabad 2018, 2020) and one held above has falling inflation: the cost of bringing inflation down, which Lesson 10 prices.

The one-line version

The trade-off is a short-run one. Hold unemployment below the natural rate and inflation keeps rising; give it long enough and unemployment returns to the natural rate, at a higher rate of inflation.

Pause and predict
In the monetarist view the long-run Phillips curve is
05
The standard questions

Along or shift

  • Expected inflation unchanged, actual inflation rises: a move along the short-run curve, not a shift (Hyderabad 2018). With expected inflation of 8% and unemployment of 3%, a rise in actual inflation to 10% with expected inflation unchanged is exactly this.
  • Expected inflation rises: the curve shifts up and to the right.
  • The natural rate rises: the curve shifts to the right; the natural rate does not move with a change in actual inflation.
  • Inflation increases when unemployment is below the natural rate, the NAIRU (Hyderabad 2020). Short-run curve negatively sloped, long-run steeper, and inflation expectations central to wage negotiations: the three true statements of CUET 2026.
  • A number. Expected inflation 5%, natural rate 4%, response 0.5, actual unemployment 5%: π = 5 − 0.5 × (5 − 4) = 4.5% (IIT JAM 2026).
  • The supply side. The curve relating unanticipated inflation and the output gap, with Okun’s law, is the expectations-augmented Phillips curve, and it represents the supply side of the economy (GATE 2026).
06
Traps

What examiners are fishing for

Watch out for

The mistakes examiners are fishing for

  • Above the natural rate means below expected inflation. The option that says the opposite is the trap.
  • θ = 0 is the original curve, θ = 1 the accelerationist. The puzzle’s option C swaps them.
  • Along against shift. Only a change in expected inflation or in the natural rate shifts the curve.
  • Rate against level. Holding unemployment below the natural rate makes the rate of inflation keep rising (θ = 1), not the level jump once.
  • Vertical means no long-run trade-off, not that unemployment never moves in the short run.
07
Worked questions

Worked questions

IIT JAM 2024 · standard (the opening question)
Expected inflation is πᵉ = (1 − θ)π̄ + θπ₋₁. Which statement is NOT correct?
  1. 1
    θ = 0.
    πᵉ = π̄, a constant: statement A is correct.
  2. 2
    θ close to 1.
    πᵉ is last year’s inflation, so with π̄ below last year’s the individual expects this year to be like last year: B is correct. This case gives the modified (accelerationist) curve: D is correct.
  3. 3
    The original curve.
    It holds expected inflation fixed, which is θ = 0, not θ close to 1: C is the incorrect statement.
Answer
(C): the original Phillips curve is derived under θ near 0, not near 1.
IIT JAM 2026 · standard
In an expectations-augmented Phillips curve, expected inflation is 5% and the natural rate 4%. The responsiveness of inflation to the unemployment gap is 0.5. Actual unemployment is 5%. What is actual inflation?
  1. 1
    The gap.
    5 − 4 = 1 point above the natural rate.
  2. 2
    Apply the curve.
    π = 5 − 0.5 × 1 = 4.5%.
Answer
4.5% (the key accepts 4.0 to 5.0).
Hyderabad 2018 · standard
Expected inflation is 8% and unemployment is 3%. If the inflation rate rises to 10% and expected inflation does not change, then?
  1. 1
    What shifts the curve.
    Only a change in expected inflation or the natural rate.
  2. 2
    What changed.
    Actual inflation, with expectations fixed: a movement along the curve.
Answer
There will be a movement along the short-run Phillips curve.
JNU 2015 · foundation
In the monetarist view, the long-run Phillips curve is?
  1. 1
    Expectations fully adjusted.
    Unemployment is at the natural rate at every inflation rate.
Answer
Vertical.
08
Revise

The lesson on one screen

The lesson on one screen
The curve
π = πᵉ − β(u − uₙ). It passes through (uₙ, πᵉ).
At the natural rate
π = πᵉ: no unanticipated inflation.
Shifts
A rise in πᵉ shifts it up and right; a rise in uₙ shifts it right. A change in actual inflation with fixed expectations is a move along.
Expectations
πᵉ = (1 − θ)π̄ + θπ₋₁. θ = 0: the original curve. θ = 1: accelerationist.
Accelerationist result
Hold u below uₙ and inflation rises every year by β(uₙ − u); above it, falls.
Long run
πᵉ = π, so u = uₙ: a vertical curve (monetarist); both curves slope down in the Keynesian view.
Natural rate
The unemployment rate at which inflation is stable (NAIRU).
09
Practice

Check yourself

0 of 9 correct so far

Quick questions

1Unemployment is above the natural rate. Actual inflation is
2Expected inflation rises and nothing else changes. The short-run curve
3The long-run Phillips curve in the monetarist view is
4Unemployment is held below the natural rate with θ = 1. Inflation
5The natural rate of unemployment is the rate at which

Numerical problems

Apply the curve
Expected inflation is 6%, the natural rate is 5%, β = 0.4 and actual unemployment is 4%. What is inflation, in percent?
The accelerationist path
θ = 1, β = 1, the natural rate is 5% and inflation starts at 2%. Unemployment is held at 3.5% from year 1. What is inflation in year 3, in percent?
Where it settles
θ = 0.5, π̄ = 2%, β = 1, the natural rate is 5% and unemployment is held at 4%. At what inflation rate does inflation settle, in percent?
Bringing inflation down
θ = 1 and β = 1.5; the natural rate is 5%. To lower inflation by 3 points in one year, what unemployment rate must be held that year, in percent?
10
Real questions

Past papers, by level

Foundation

Definitions, formulas and one-step problems. Most CUET, UGC NET and Hyderabad questions on this topic sit here.

2 questionsPractise →

Standard

Statements to judge, matching lists and calculations with several steps, up to the hardest JNU, JAM and GATE questions.

10 questionsPractise →

Delhi School level

This topic’s hardest questions, from the DSE entrance, are worked through in Lesson 12: The NAIRU, productivity growth and the accelerationist path.

4 questionsLesson 12 →
All 12 past-paper questions for this lesson, easiest first: practise the full set →

✦These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.

← Lesson 6Okun's law and the output gapLesson 8 →Where the natural rate comes from: wage-setting and price-setting

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