The Phillips Curve and the Natural Rate of Unemployment

AP Macroeconomics· AP Macroeconomics CED — Long-Run Consequences of Stabilization Policies· 14 min read

1. Core Concepts: The Phillips Curve and Natural Rate of Unemployment★★☆☆☆⏱ 3 min

The Phillips Curve is a core macroeconomic model describing the relationship between inflation and unemployment, updated from early empirical work to account for long-run inflation expectation adjustments. This topic makes up 10-15% of AP Macroeconomics Unit 5, appearing in both MCQ and FRQ sections on nearly every exam.

📘 Definition

Natural Rate of Unemployment (NRU)

The unemployment rate that prevails when the economy is at potential output, with no cyclical unemployment—only frictional and structural unemployment. Also called the non-accelerating inflation rate of unemployment (NAIRU).

Example:

A typical developed economy has an NRU between 3-5%.

The central insight of the modern Phillips Curve model is that a trade-off between inflation and unemployment exists only in the short run; no permanent trade-off exists in the long run, as inflation expectations adjust to actual inflation, shifting the short-run curve back to align with the long-run vertical curve at NRU.

2. The Short-Run Phillips Curve (SRPC)★★★☆☆⏱ 4 min

The Short-Run Phillips Curve (SRPC) is a downward-sloping curve that shows the inverse relationship between inflation and unemployment when expected inflation and the natural rate of unemployment are held constant. The inverse relationship comes from short-run wage and price stickiness: unexpected increases in aggregate demand lead firms to raise output, hire more workers (lower unemployment), and push up prices (higher inflation).

pi = pi^e - alpha(u - u_n)

Where: $π$ = actual inflation, $π^{e}$ = expected inflation, $α$ = a positive constant measuring how responsive inflation is to cyclical unemployment, $u$ = actual unemployment, and $u_{n}$ = the natural rate of unemployment. When actual unemployment falls below $u_{n}$ , actual inflation rises above expected inflation, giving the SRPC its downward slope.

📐 Worked Example

Suppose expected inflation is 3%, the natural rate of unemployment is 4.5%, and $α = 1.5$ . Calculate the actual inflation rate when actual unemployment is 3%, then when actual unemployment is 6%.

1
Start with the standard SRPC formula:
$pi = pi^e - alpha(u - u_n)$
2
Plug in values for the first case: $π^{e} = 3%$ , $α = 1.5$ , $u = 3%$ , $u_{n} = 4.5%$
3
Calculate the result:
$pi = 3 - 1.5(3 - 4.5) = 3 + 2.25 = 5.25\%$
4
Unemployment 1.5 percentage points below NRU leads to inflation 2.25 percentage points above expected inflation.
5
Plug in values for the second case:
$pi = 3 - 1.5(6 - 4.5) = 3 - 2.25 = 0.75\%$
6
Unemployment 1.5 percentage points above NRU leads to inflation 2.25 percentage points below expected inflation. This confirms the inverse short-run relationship.

Exam tip:

On AP FRQs, always label SRPC with a negative slope, axes (Y: Inflation Rate, X: Unemployment Rate), and remember that changes in AD cause movement along the SRPC, not a shift of the curve itself.

3. Long-Run Phillips Curve (LRPC) and Long-Run Equilibrium★★★☆☆⏱ 4 min

In the long run, wages and prices are fully flexible, and workers adjust their inflation expectations to match actual inflation. Any attempt to keep unemployment below the natural rate via expansionary policy will only lead to permanently higher inflation, not sustained lower unemployment. This means the Long-Run Phillips Curve (LRPC) is a vertical line drawn exactly at the natural rate of unemployment $u_{n}$ , with no trade-off between inflation and unemployment in the long run.

There is a direct 1:1 mapping between the LRPC and the long-run aggregate supply (LRAS) curve in the AD-AS model: LRAS is vertical at potential output, which corresponds to an unemployment rate exactly equal to the natural rate. If expansionary policy shifts AD right, output rises above potential, unemployment falls below $u_{n}$ , and inflation rises in the short run. In the long run, workers adjust wage expectations, SRAS shifts left, output returns to potential, unemployment returns to $u_{n}$ , and inflation is permanently higher, which corresponds to the SRPC shifting upward to intersect LRPC at the new higher inflation rate.

📐 Worked Example

An economy starts at long-run equilibrium with 2% expected inflation and a 4% natural rate of unemployment. The central bank engages in expansionary policy that pushes actual inflation to 5%. Calculate the short-run unemployment rate and the new long-run equilibrium (assume $α = 1$ for simplicity).

1
Short run: Expected inflation has not adjusted yet, so $π^{e} = 2%$ , $π = 5%$ , $u_{n} = 4%$ .
2
Solve for $u$ using the SRPC formula:
$5 = 2 - 1(u - 4) \rightarrow 3 = -u + 4 \rightarrow u = 1\%$
3
Unemployment falls well below NRU in the short run, as expected.
4
Long run: Workers adjust their inflation expectations to match the new 5% actual inflation, so $π^{e} = 5%$ .
5
At long-run equilibrium, actual inflation equals expected inflation, so:
$5 = 5 - 1(u - 4) \rightarrow 0 = -(u - 4) \rightarrow u = 4\% = u_n$
6
The new long-run equilibrium has unemployment back at the natural rate, but inflation is permanently higher, confirming no long-run trade-off.

Exam tip:

If a question asks how a change in frictional unemployment affects the Phillips curve, remember it shifts both LRPC and SRPC, since SRPC always intersects LRPC at the new NRU.

4. Shifts of the SRPC and LRPC★★★★☆⏱ 3 min

It is critical to distinguish between movements along a curve and shifts of the entire curve, a common source of error on AP exams. Movements along the SRPC are only caused by changes in aggregate demand that change actual inflation and unemployment. Shifts of the SRPC are caused by two factors: (1) Changes in expected inflation: higher expected inflation shifts SRPC upward/rightward (higher inflation at every unemployment rate), lower expected inflation shifts it downward/leftward. (2) Aggregate supply shocks: a negative supply shock (e.g., rising oil prices) shifts SRPC up/right, a positive supply shock shifts it down/left.

Shifts of the LRPC are only caused by changes in the natural rate of unemployment, which stem from changes to labor market structure, frictional unemployment, or structural unemployment. For example, increased job training reduces structural unemployment, so NRU falls and LRPC shifts left. A permanent increase in the minimum wage raises structural unemployment, so NRU rises and LRPC shifts right.

📐 Worked Example

An economy starts at long-run equilibrium. A sudden global supply chain disruption causes a permanent negative supply shock that pushes up input prices. Trace the effect on the Phillips curve model.

1
Initial equilibrium: SRPC₁ intersects vertical LRPC at $u_{n}$ and initial inflation $π_{1}$ .
2
The negative supply shock increases inflation at any given unemployment rate, so the entire SRPC shifts upward/rightward to SRPC₂. The new short-run equilibrium has higher inflation $π_{2} > π_{1}$ and higher unemployment $u_{2} > u_{n}$ , a condition called stagflation.
3
If the supply shock is permanent, it may also increase the natural rate of unemployment, shifting LRPC rightward to LRPC₂. If the shock is temporary, LRPC remains unchanged.
4
If policymakers do nothing, over time inflation expectations adjust, SRPC shifts back to its original position, and unemployment returns to the original $u_{n}$ . If policymakers expand AD to lower unemployment, inflation becomes permanently higher.

✓ Quick check

Test your understanding of SRPC calculations:

An economy initially is in long-run equilibrium with an inflation rate of 4% and an unemployment rate of 5%. The central bank unexpectedly increases the money supply growth rate, pushing actual inflation to 6%. In the short run, what is the new unemployment rate, assuming no change in the natural rate of unemployment and the SRPC formula $π = π^{e} - 2 (u - u_{n})$ ?
- A) 3%
- B) 4%
- C) 5%
- D) 6%
Reveal answer
B) 4% —
In the short run, expected inflation remains at 4% (the original long-run equilibrium value). Plugging in the values gives $6 = 4 - 2 (u - 5) \to u = 4%$ , which matches the inverse relationship between inflation and unemployment.

Exam tip:

On AP MCQs, if you are asked to identify the effect of a supply shock, always eliminate options that show a shift of LRPC unless the question explicitly states the shock changed the natural rate of unemployment.

5. Common Pitfalls

Wrong move:

Drawing a downward-sloping LRPC instead of a vertical LRPC at the natural rate of unemployment.

Why:

Students confuse the short-run inverse relationship with the long-run relationship, memorizing the wrong slope.

Correct move:

When drawing any Phillips curve graph, draw and label the vertical LRPC first at your given NRU, then draw the downward-sloping SRPC crossing it to avoid mixing up slopes.

Wrong move:

Calling a movement along the SRPC caused by an AD shift a 'shift of the SRPC'.

Why:

Students confuse the causes of movement vs shift, mixing up AD changes with expected inflation/supply shock changes.

Correct move:

Before answering any shift question, ask: does this change actual inflation, or expected inflation/supply conditions? If only actual, it is a movement along; if it changes expectations or supply, it is a shift.

Wrong move:

Claiming the natural rate of unemployment is zero.

Why:

Students confuse 'no cyclical unemployment' with 'no unemployment' altogether.

Correct move:

Always remember NRU equals frictional unemployment plus structural unemployment, so it is always positive, never zero.

Wrong move:

Stating that an increase in expected inflation shifts the SRPC downward.

Why:

Students mix up direction of shift, incorrectly associating lower unemployment with lower inflation.

Correct move:

Recall that higher expected inflation means higher actual inflation at every unemployment rate, which is an upward (rightward) shift of the SRPC.

Wrong move:

Failing to connect the Phillips curve to the AD-AS model on FRQs when asked.

Why:

Students treat the two models as separate, not linked.

Correct move:

Whenever you describe a Phillips curve change, explicitly link it to AD-AS: e.g., 'expansionary AD shifts right along SRAS, which corresponds to a movement up along the SRPC'.

Wrong move:

Arguing that there is a permanent long-run trade-off between inflation and unemployment.

Why:

Students confuse short-run gains from expansionary policy with long-run outcomes.

Correct move:

On any long-run FRQ question, always state that no permanent trade-off exists, because expectations adjust and unemployment returns to NRU.

6. Quick Reference Cheatsheet

Category	Formula / Property	Notes
Short-Run Phillips Curve Relationship	$π = π^{e} - α (u - u_{n})$	Holds expected inflation and NRU constant; $α > 0$ , inverse relationship
SRPC Slope	Downward-sloping	Y-axis = Inflation, X-axis = Unemployment
LRPC Slope	Vertical at $u = u_{n}$	No long-run trade-off between inflation and unemployment
Natural Rate of Unemployment	$u_{n} = u_{f r i c t i o na l} + u_{s t r u c t u r a l}$	No cyclical unemployment; corresponds to potential output
Movement along SRPC	N/A	Caused by changes in aggregate demand that change actual inflation/unemployment
SRPC Shift	N/A	Caused by changes in expected inflation or supply shocks; up/right for higher expected inflation/negative shocks
LRPC Shift	N/A	Caused only by changes in the natural rate of unemployment from labor market changes
AD-AS / Phillips Curve Mapping	N/A	Vertical LRAS at potential output = vertical LRPC at NRU; sticky SRAS = downward-sloping SRPC

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · AP Macroeconomics
FRQ section on LRPC shifts
2022 · AP Macroeconomics
MCQ on SRPC shift factors

What's Next

This guide provides the core framework for analyzing the long-run consequences of stabilization policy, the central theme of AP Macroeconomics Unit 5. The Phillips curve model is foundational for understanding how policymakers balance inflation and unemployment goals, and how expectations shape macroeconomic outcomes. Mastery of this topic is critical for earning a high score on the AP exam, as it regularly appears in multi-part free response questions that connect to AD-AS and monetary policy. Next, you will build on this framework to analyze advanced topics that rely on the SRPC/LRPC relationship you learned here.