The Phillips Curve - AP Macroeconomics

SECTION 1

Historical Context & Motivation

In the decades following the Great Depression and World War II, policymakers around the world grappled with a central question: could governments use fiscal and monetary policy to simultaneously achieve low unemployment and stable prices? Classical economists had generally assumed that markets would self-correct, but the Keynesian revolution of the 1930s and 1940s shifted attention toward active demand management. It was in this intellectual climate that A.W. Phillips, a New Zealand-born economist working at the London School of Economics, published a landmark empirical paper in 1958. Phillips documented an apparent inverse relationship between the rate of wage inflation and the unemployment rate in the United Kingdom over nearly a century of data, suggesting that low unemployment came at the cost of rising wages—and, by extension, rising prices.

1958 • Phillips's Original Study

A.W. Phillips published his study of UK wage data (1861–1957), revealing a stable inverse relationship between nominal wage growth and unemployment.

1960 • Samuelson & Solow Adapt the Curve

Paul Samuelson and Robert Solow reformulated the relationship using price inflation instead of wage inflation, giving U.S. policymakers an apparent "menu" of inflation–unemployment combinations.

1968 • Friedman & Phelps Challenge

Milton Friedman and Edmund Phelps independently argued that the tradeoff was temporary. In the long run, the economy returns to the natural rate of unemployment regardless of inflation—introducing the expectations-augmented Phillips Curve.

1970s • Stagflation Validates Critics

The oil shocks of 1973 and 1979 produced simultaneous high inflation and high unemployment (stagflation), undermining the simple Phillips Curve and lending empirical support to Friedman and Phelps.

1980s–Present • Modern Consensus

Macroeconomists now distinguish between the short-run Phillips Curve (SRPC), which shifts with inflation expectations, and the long-run Phillips Curve (LRPC), which is vertical at the natural rate of unemployment.

The story of the Phillips Curve is ultimately a story about expectations. The central question it forces us to address is: Can policymakers permanently reduce unemployment by tolerating higher inflation, or does the tradeoff erode once people adjust their expectations? Understanding why the answer differs in the short run versus the long run is essential for mastering AP Macroeconomics.

SECTION 2

Core Principles & Definitions

Before diving into the graphs and equations, it is important to establish the foundational concepts that underpin the Phillips Curve framework. The model rests on several interconnected ideas about labor markets, inflation, and expectations formation—each of which plays a distinct role in explaining why the inflation–unemployment tradeoff behaves differently across time horizons.

Short-Run Phillips Curve (SRPC)

A downward-sloping curve showing the inverse relationship between the inflation rate and the unemployment rate, holding inflation expectations constant. Movement along the SRPC reflects demand-side changes.

Long-Run Phillips Curve (LRPC)

A vertical line at the natural rate of unemployment (NRU). In the long run, there is no tradeoff: any rate of inflation is compatible with the NRU once expectations fully adjust.

Natural Rate of Unemployment (NRU)

The unemployment rate that prevails when the economy is at full employment—comprising only frictional and structural unemployment. Also called the non-accelerating inflation rate of unemployment (NAIRU).

Inflation Expectations

The rate of inflation that workers, firms, and consumers anticipate for the future. Changes in expected inflation shift the entire SRPC up (higher expectations) or down (lower expectations).

Supply Shocks

Unexpected changes in input costs (e.g., oil prices) that shift the SRPC. An adverse supply shock shifts the curve rightward/upward, producing stagflation—higher inflation at every unemployment rate.

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KEY TAKEAWAY

Think of the Phillips Curve like a thermostat analogy in reverse. In the short run, cranking up the heat (expansionary policy) lowers the "chill" (unemployment), but the room's occupants (workers and firms) eventually realize it is getting warmer and open windows (raise wage demands), neutralizing the effect. In the long run, you simply have a hotter room at the same temperature setting—higher inflation with unemployment back at the natural rate.

SECTION 3

Visual Explanation — The Short-Run Phillips Curve

The diagram below illustrates the fundamental short-run Phillips Curve. The horizontal axis measures the unemployment rate and the vertical axis measures the inflation rate. The downward slope captures the inverse relationship: as aggregate demand increases, firms hire more workers (lowering unemployment) while bidding up wages and prices (raising inflation). Notice that the LRPC is drawn as a vertical line at the natural rate of unemployment, emphasizing that no permanent tradeoff exists once expectations adjust.

Point A represents long-run equilibrium at the natural rate of unemployment (NRU) with actual inflation equal to expected inflation (πᵉ). Point B shows the short-run effect of expansionary policy (lower unemployment, higher inflation), while Point C shows contractionary policy (higher unemployment, lower inflation). The vertical LRPC at the NRU indicates no long-run tradeoff.

The key insight from this diagram is that movements along the SRPC represent demand-side fluctuations (corresponding to movements along the aggregate demand curve), whereas shifts of the entire SRPC occur when inflation expectations change or when supply shocks hit the economy. When policymakers pursue expansionary policy—say, increasing the money supply—the economy moves from Point A toward Point B in the short run, but as workers and firms revise their inflation expectations upward, the SRPC itself shifts upward, pulling the economy back to the NRU at a higher inflation rate.

SECTION 4

Mathematical Framework

The Phillips Curve can be expressed algebraically using the expectations-augmented Phillips Curve equation, which formalizes the relationship between actual inflation, expected inflation, the unemployment gap, and supply shocks. This equation is the workhorse model tested on the AP exam and connects directly to the AD-AS framework you have already studied.

EXPECTATIONS-AUGMENTED PHILLIPS CURVE

π = πᵉ − α(U − Uₙ) + ε

Where π = actual inflation rate, πᵉ = expected inflation rate, α = sensitivity of inflation to the unemployment gap (a positive constant), U = actual unemployment rate, Uₙ = natural rate of unemployment, and ε = supply shock term (positive for adverse shocks, zero when no shock).

This equation tells us several things simultaneously. First, when actual unemployment equals the natural rate (U = Uₙ), the unemployment gap term vanishes and actual inflation equals expected inflation plus any supply shock. Second, when unemployment falls below the natural rate, the term −α(U − Uₙ) becomes positive, pushing actual inflation above expected inflation—this corresponds to an economy operating beyond full employment with an inflationary gap. Third, the supply shock term ε captures events like oil price spikes that shift the SRPC.

LONG-RUN CONDITION

If π = πᵉ, then U = Uₙ (regardless of the level of π)

In the long run, actual inflation equals expected inflation because expectations fully adjust. This forces unemployment to equal the natural rate, producing the vertical LRPC. No sustained reduction in unemployment is achievable through demand-side inflation alone.

AD-AS CONNECTION

Expansionary AD shift → Y > Yf → U < Uₙ → π > πᵉ → SRPC shifts up → U returns to Uₙ

This chain links the Phillips Curve to the AD-AS model. An increase in aggregate demand raises real GDP above full-employment output (Yf), which means unemployment drops below the NRU. The resulting inflation exceeds expectations, and once expectations adjust upward, the SRPC shifts up and unemployment returns to the natural rate at a permanently higher inflation rate.

SECTION 5

Shifts of the SRPC & Supply Shocks

Understanding what shifts the SRPC is one of the most frequently tested concepts on the AP Macroeconomics exam. Two primary forces shift the curve: changes in inflation expectations and supply shocks. The diagram below shows how these shifts work, contrasting a demand-driven shift (via expectations) with a supply-shock-driven shift.

SRPC₁ is the original curve with expected inflation of 2%. When expected inflation rises to 5% (e.g., after sustained expansionary policy), the curve shifts up to SRPC₂. Point A and Point B both lie on the LRPC at the NRU—the economy is at long-run equilibrium in both cases, just at different inflation rates. SRPC₃ (red) represents an adverse supply shock, which shifts the curve rightward and upward, raising both inflation and unemployment simultaneously (stagflation).

Cause of Shift	Direction of SRPC Shift	Example
↑ Inflation expectations	Upward (rightward)	Workers expect 5% inflation and negotiate higher wages, shifting cost structures upward.
↓ Inflation expectations	Downward (leftward)	Central bank credibly commits to low inflation; expectations anchor at 2%, reducing wage pressures.
Adverse supply shock	Upward (rightward)	Oil embargo raises production costs across the economy (e.g., OPEC 1973).
Favorable supply shock	Downward (leftward)	Major technological breakthrough reduces production costs (e.g., the IT revolution of the 1990s).

Summary of factors that shift the SRPC

SECTION 6

Worked Example — From AD-AS to the Phillips Curve

This worked example walks through a complete policy scenario, tracing the effects of expansionary monetary policy through both the AD-AS model and the Phillips Curve framework. This type of dual-diagram analysis is commonly required on AP free-response questions.

Expansionary Monetary Policy: Short-Run and Long-Run Effects

1
Step 1 — Identify the Initial Equilibrium

The economy begins at long-run equilibrium. In the AD-AS model, the price level is stable at PL₁, and real GDP equals full-employment output (Yf). On the Phillips Curve diagram, the economy is at point A on the SRPC₁, where actual inflation (π = 2%) equals expected inflation (πᵉ = 2%) and unemployment equals the natural rate (Uₙ = 5%).

Initial: U = 5% = Uₙ, π = πᵉ = 2%
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Step 2 — Apply Expansionary Monetary Policy (Short Run)

The Federal Reserve increases the money supply, lowering interest rates and stimulating investment and consumption. AD shifts rightward from AD₁ to AD₂. Real GDP rises above Yf, and the price level increases to PL₂. On the Phillips Curve, this corresponds to a movement along SRPC₁ from point A to point B: unemployment falls below the NRU (say, to 3%) and actual inflation rises above expected inflation (say, to 5%).

Short run: U = 3% < Uₙ, π = 5% > πᵉ = 2%
3
Step 3 — Expectations Adjust (Long-Run Transition)

Workers and firms observe that actual inflation (5%) exceeds what they expected (2%). They renegotiate wages upward, raising production costs. In the AD-AS model, SRAS shifts leftward from SRAS₁ to SRAS₂. On the Phillips Curve diagram, expected inflation rises to 5%, shifting the entire SRPC upward from SRPC₁ to SRPC₂.

πᵉ adjusts from 2% → 5%; SRPC shifts up
4
Step 4 — New Long-Run Equilibrium

The economy reaches a new long-run equilibrium at point C on SRPC₂, back on the LRPC. Real GDP returns to Yf, and unemployment returns to Uₙ = 5%. However, both actual and expected inflation are now 5% instead of 2%. In the AD-AS model, the price level is permanently higher at PL₃. The policy achieved a temporary reduction in unemployment but resulted in a permanently higher inflation rate—illustrating the vertical LRPC.

Long run: U = 5% = Uₙ, π = πᵉ = 5% (higher than before)

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AP EXAM TIP

Free-response questions frequently ask you to draw both the AD-AS model and the Phillips Curve side by side. Always label: (1) the axes, (2) the initial and new equilibrium points, (3) the direction of curve shifts, and (4) the short-run versus long-run outcomes. Stating that "the SRPC shifts because inflation expectations change" earns you a rubric point that many students miss.

SECTION 7

Policy Tradeoffs & Limitations

The Phillips Curve framework has profound implications for stabilization policy. The distinction between the short-run tradeoff and the long-run vertical curve creates a fundamental tension for policymakers: demand-side tools can smooth cyclical fluctuations but cannot permanently alter the unemployment rate below its natural level. The table below compares key aspects of the short-run and long-run perspectives.

Feature	Short-Run Phillips Curve	Long-Run Phillips Curve
Shape	Downward-sloping	Vertical at the NRU
Inflation–Unemployment Tradeoff	Yes — lower U is achievable at the cost of higher π	No — any π is consistent with Uₙ
Expectations	Held constant (not yet adjusted)	Fully adjusted (π = πᵉ)
Policy Implication	Demand management can temporarily reduce unemployment	Only structural reforms (education, labor market) can lower Uₙ
AD-AS Parallel	Upward-sloping SRAS (output responds to price changes)	Vertical LRAS at Yf (output is supply-determined)

Short-run vs. long-run Phillips Curve characteristics

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KEY TAKEAWAY

The Phillips Curve teaches a lesson analogous to what engineers call a feedback loop. In control systems, you can temporarily force a variable away from its set point, but negative feedback eventually pulls it back. Similarly, expansionary policy pushes unemployment below the NRU, but the feedback mechanism of rising inflation expectations eventually restores unemployment to its natural rate. The only way to permanently lower the "set point" (NRU) is to change the system itself—through supply-side policies that reduce structural and frictional unemployment.

SECTION 8

Connection to Advanced Theory & Modern Debates

The expectations-augmented Phillips Curve studied on the AP exam is itself a simplification of a richer body of macroeconomic theory. Understanding where the AP model sits relative to more advanced frameworks will deepen your intuition and prepare you for college-level economics. The key development beyond the AP curriculum is the distinction between adaptive expectations (the Friedman-Phelps approach, which is what the AP exam tests) and rational expectations (the approach developed by Robert Lucas and Thomas Sargent in the 1970s).

Feature	AP Model (Adaptive Expectations)	Rational Expectations (Advanced)
How expectations form	People look backward: πᵉ is based on recent past inflation	People look forward: πᵉ incorporates all available information, including policy announcements
Short-run tradeoff	Yes — expectations lag behind actual inflation	Only if policy is unexpected; anticipated policy has no real effect even in the short run
Speed of adjustment	Gradual — takes time for workers and firms to update expectations	Immediate — expectations jump to the new equilibrium if the policy is credible
Policy implication	Stabilization policy works in the short run	Only surprise policy works; credibility and commitment are paramount

AP model vs. rational expectations theory

Modern central banking practice incorporates insights from both frameworks. The Federal Reserve's emphasis on forward guidance—clearly communicating its inflation targets and policy intentions—reflects the rational expectations insight that credible commitments can anchor inflation expectations and reduce the short-run costs of disinflation. Meanwhile, the observation that inflation expectations sometimes adjust sluggishly, especially among consumers and workers who do not closely follow Fed announcements, validates the adaptive expectations framework tested on the AP exam. The Phillips Curve remains a living area of macroeconomic research, with ongoing debates about whether the curve has "flattened" in recent decades as inflation expectations have become more firmly anchored around the Fed's 2% target.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

Which of the following best explains why the long-run Phillips Curve is vertical?

A. In the long run, the government cannot change the money supply.
B. In the long run, inflation expectations fully adjust to actual inflation, so unemployment returns to the natural rate regardless of the inflation level.
C. In the long run, aggregate supply is perfectly elastic, preventing any change in inflation.
D. In the long run, cyclical unemployment always falls to zero because recessions are temporary.

Show answer (B)

B is correct. The LRPC is vertical because, in the long run, inflation expectations fully adjust to match actual inflation (π = πᵉ). When this condition holds, the unemployment gap term in the Phillips Curve equation vanishes, and U = Uₙ at any inflation rate. A is incorrect because the government can and does change the money supply in the long run; the issue is that monetary expansion only raises prices without lowering unemployment once expectations adjust. C is incorrect because long-run aggregate supply is vertical (perfectly inelastic), not perfectly elastic. D is incorrect because the natural rate of unemployment includes frictional and structural unemployment, which are always positive; it is cyclical unemployment that falls to zero at full employment.

Question 2: BASIC CALCULATION

Suppose the expectations-augmented Phillips Curve is given by π = πᵉ − 0.5(U − Uₙ). If expected inflation is 3%, the natural rate of unemployment is 6%, and the actual unemployment rate is 4%, what is the actual inflation rate?

A. 2%
B. 3%
C. 4%
D. 5%

Show answer (C)

C is correct. Substituting into the equation: π = 3% − 0.5(4% − 6%) = 3% − 0.5(−2%) = 3% + 1% = 4%. Because actual unemployment (4%) is below the natural rate (6%), the economy has a negative unemployment gap, which pushes actual inflation above expected inflation. A (2%) results from incorrectly adding rather than subtracting in the gap term. B (3%) would only be correct if U = Uₙ. D (5%) results from using α = 1 instead of α = 0.5.

Question 3: INTERMEDIATE

An economy is initially at long-run equilibrium on the Phillips Curve. The central bank then unexpectedly increases the money supply. In the short run, which of the following changes will occur?

A. The SRPC shifts to the left, and the economy moves to a point with lower inflation and lower unemployment.
B. The economy moves along the existing SRPC to a point with higher inflation and lower unemployment.
C. The SRPC shifts upward, and the economy moves to a point with higher inflation and the same unemployment rate.
D. The economy moves along the existing SRPC to a point with lower inflation and higher unemployment.

Show answer (B)

B is correct. An unexpected increase in the money supply is a demand-side stimulus. In the short run, inflation expectations have not yet changed, so the SRPC does not shift. Instead, the economy moves along the existing SRPC—higher aggregate demand increases output, lowers unemployment below the NRU, and raises inflation above expected inflation. A is incorrect because expansionary policy does not shift the SRPC leftward—it is a demand-side change, not a change in expectations or supply. C is incorrect because the SRPC shifts only after expectations adjust, which is a long-run phenomenon. D is incorrect because it describes the effect of contractionary policy, not expansionary.

Question 4: APPLIED

3 pts

An economy is currently in a recession with an unemployment rate of 8% and an inflation rate of 1%. The natural rate of unemployment is 5%, and expected inflation is 1%. (a) On a correctly labeled Phillips Curve graph, show the current position of the economy and the long-run equilibrium. (b) If the government implements expansionary fiscal policy, explain the short-run effect on unemployment and inflation using the Phillips Curve. (c) Explain what happens to the SRPC in the long run as a result of this policy.

Show answer

Rubric (3 points): Part (a) — 1 point: The graph must include a correctly labeled vertical axis (inflation rate) and horizontal axis (unemployment rate), a downward-sloping SRPC, and a vertical LRPC at U = 5%. The current position of the economy is shown as a point on the SRPC to the right of the LRPC, at coordinates approximately (8%, 1%). One point is earned for a correctly drawn and labeled graph showing the economy's current position to the right of the NRU on the SRPC. Part (b) — 1 point: Expansionary fiscal policy increases aggregate demand, which moves the economy along the existing SRPC toward the upper left—unemployment falls (toward or below 5%) and inflation rises (above 1%). One point is earned for correctly stating that unemployment decreases and inflation increases in the short run, with reference to movement along the SRPC. Part (c) — 1 point: In the long run, if the expansionary policy pushes unemployment below the NRU, actual inflation exceeds expected inflation. Workers and firms revise their inflation expectations upward, which shifts the entire SRPC upward (to the right). The economy returns to the NRU at a higher inflation rate. One point is earned for explaining that the SRPC shifts upward due to rising inflation expectations and that unemployment returns to the natural rate.

Question 5: CRITICAL THINKING

5 pts

Country Z has a natural rate of unemployment of 5% and is initially at long-run equilibrium with an inflation rate of 2% and expected inflation of 2%. (a) Draw a correctly labeled graph of the Phillips Curve model showing the short-run Phillips Curve (SRPC₁), the long-run Phillips Curve (LRPC), and Country Z's initial equilibrium at point A. (b) Country Z experiences an adverse supply shock (e.g., a global oil price spike). On your graph, show the new short-run equilibrium at point B. Explain what happens to both the inflation rate and the unemployment rate. (c) Assume the central bank of Country Z responds to the supply shock by increasing the money supply. On your graph, show the effect of this policy on the short-run Phillips Curve. Label the new equilibrium point C. (d) Now assume instead that the central bank does nothing and the economy self-corrects. Explain the adjustment mechanism that returns the economy to long-run equilibrium, and show the final equilibrium point D on your graph. (e) Compare the long-run outcomes of the two policy choices in parts (c) and (d) in terms of the inflation rate and the unemployment rate.

Show answer

Rubric (5 points): Part (a) — 1 point: A correctly labeled graph with inflation rate on the vertical axis, unemployment rate on the horizontal axis, a downward-sloping SRPC₁, a vertical LRPC at 5%, and point A at the intersection of SRPC₁ and LRPC where π = 2%. Part (b) — 1 point: The adverse supply shock shifts the SRPC upward/rightward to SRPC₂. Point B is shown on SRPC₂ to the right of the LRPC, indicating both higher inflation (above 2%) and higher unemployment (above 5%). This is stagflation: the supply shock raises costs, increasing inflation while simultaneously reducing output and increasing unemployment. Part (c) — 1 point: If the central bank increases the money supply in response, aggregate demand increases, moving the economy along SRPC₂ toward lower unemployment. Point C is shown on SRPC₂ at or near the LRPC (U ≈ 5%) but at a significantly higher inflation rate. Critically, the accommodative policy validates the higher inflation expectations, and if they become embedded, the SRPC shifts up further. One point for correctly showing the movement along SRPC₂ and identifying that this policy reduces unemployment but at the cost of even higher inflation. Part (d) — 1 point: If the central bank does nothing, the economy self-corrects through the following mechanism: high unemployment puts downward pressure on wages, reducing production costs. Workers also lower their inflation expectations as the recession persists. Both effects shift the SRPC back downward toward its original position. Point D returns to the LRPC at U = 5% and π = 2% (or near it). One point for explaining the self-correction mechanism involving downward wage/expectations adjustment and showing the return to original long-run equilibrium. Part (e) — 1 point: In both scenarios, the economy eventually returns to the natural rate of unemployment (5%). However, the inflation outcomes differ dramatically. Under accommodative policy (part c), the long-run inflation rate is permanently higher because the central bank's response validated and embedded the higher inflation expectations. Under self-correction (part d), the inflation rate returns to 2% because no demand-side stimulus was added to reinforce the temporary price shock. One point for clearly comparing the two outcomes and identifying that the accommodative approach results in higher long-run inflation while self-correction preserves price stability, with both returning to the same unemployment rate.

SUMMARY

Summary — The Phillips Curve

Summary

The Phillips Curve captures the relationship between inflation and unemployment. The short-run Phillips Curve (SRPC) is downward-sloping, reflecting a temporary tradeoff: expansionary policy can lower unemployment at the cost of higher inflation, and contractionary policy can reduce inflation at the cost of higher unemployment. This tradeoff exists because inflation expectations are slow to adjust in the short run. The SRPC shifts when expectations change or when supply shocks hit the economy. The key equation is π = πᵉ − α(U − Uₙ) + ε, which links actual inflation to expected inflation, the unemployment gap, and supply shocks.

The long-run Phillips Curve (LRPC) is vertical at the natural rate of unemployment (NRU), demonstrating that there is no permanent tradeoff between inflation and unemployment. Once inflation expectations fully adjust so that π = πᵉ, the economy returns to the NRU regardless of the inflation rate. This parallels the vertical long-run aggregate supply (LRAS) curve in the AD-AS model. Permanently reducing the NRU requires supply-side policies—such as investments in education, job training, and labor market reforms—rather than demand-side stimulus alone.