The Phillips Curve and the Natural Rate of Unemployment — AP Macroeconomics Study Guide

For: AP Macroeconomics candidates sitting AP Macroeconomics.

Covers: This chapter explains the Short-run Phillips Curve (SRPC), Long-run Phillips Curve (LRPC), natural rate of unemployment (NRU), NAIRU, expected inflation, SRPC/LRPC shift factors, and the link between Phillips curves and the AD-AS model.

You should already know: How the AD-AS model determines equilibrium output and price levels; The three types of unemployment (frictional, structural, cyclical); How expansionary and contractionary stabilization policies shift aggregate demand.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Macroeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is The Phillips Curve and the Natural Rate of Unemployment?

The Phillips Curve is a core macroeconomic model that describes the relationship between inflation and unemployment, adapted from early empirical observation to account for long-run expectation adjustments. Per the AP Macroeconomics CED, this topic makes up 10-15% of Unit 5, appearing in both MCQ (2-4 questions per exam) and FRQ (typically one multi-part question section) on nearly all exam administrations.

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

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 intuition for this inverse relationship comes from short-run wage and price stickiness: when aggregate demand increases unexpectedly, firms raise output to meet demand, hire more workers, and reduce unemployment. Higher demand also pushes up overall prices, leading to higher inflation. Conversely, a negative AD shock reduces inflation but increases cyclical unemployment.

The relationship is formalized by the standard SRPC formula: $$\pi ={\pi }^e-\alpha (u-u_n)$$ where $\pi$ = actual inflation, ${\pi }^e$ = expected inflation, $\alpha$ = 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, and vice versa, which matches the downward slope of the SRPC.

Worked Example

Suppose expected inflation is 3%, the natural rate of unemployment is 4.5%, and $\alpha =1.5$. 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: ${\pi }^e=3\%$, $\alpha =1.5$, $u=3\%$, $u_n=4.5\%$
3. Calculate: $\pi =3-1.5(3-4.5)=3+2.25=5.25\%$. Unemployment 1.5 percentage points below NRU leads to inflation 2.25 percentage points above expected inflation.
4. Plug in values for the second case: $\pi =3-1.5(6-4.5)=3-2.25=0.75\%$. Unemployment 1.5 percentage points above NRU leads to inflation 2.25 percentage points below expected inflation.

This result confirms the inverse short-run relationship between inflation and unemployment.

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. The Long-Run Phillips Curve (LRPC) and the Natural Rate of Unemployment

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. For example, if expansionary monetary 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 their wage expectations to reflect higher inflation, SRAS shifts left in the AD-AS model, output returns to potential, unemployment returns to $u_n$, and inflation is permanently higher. This 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 $\alpha =1$ for simplicity).

1. Short run: Expected inflation has not adjusted yet, so ${\pi }^e=2\%$, $\pi =5\%$, $u_n=4\%$.
2. Solve for $u$ using the SRPC formula: $5=2-1(u-4)\to 3=-u+4\to u=1\%$. Unemployment falls well below NRU in the short run, as expected.
3. Long run: Workers adjust their inflation expectations to match the new 5% actual inflation, so ${\pi }^e=5\%$.
4. At long-run equilibrium, actual inflation equals expected inflation, so $5=5-1(u-4)\to 0=-(u-4)\to u=4\%=u_n$.

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 Short-Run and Long-Run Phillips Curves

Students often confuse movements along a curve with shifts of the entire curve, so it is critical to distinguish the triggers for each. 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: if people expect higher inflation, SRPC shifts upward/rightward (inflation is higher at every unemployment rate), and shifts downward/leftward if expected inflation falls. (2) Aggregate supply shocks: a negative supply shock (e.g., rising oil prices) increases inflation at every unemployment rate, shifting SRPC up/right, while a positive supply shock (e.g., falling energy costs) shifts SRPC 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 ${\pi }_1$.
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 ${\pi }_2>{\pi }_1$ 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.

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.

Common Pitfalls (and how to avoid them)

• 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.

Practice Questions (AP Macroeconomics Style)

Question 1 (Multiple Choice)

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 $\pi ={\pi }^e-2(u-u_n)$? A) 3% B) 4% C) 5% D) 6%

Worked Solution: In the short run after an unexpected policy change, expected inflation has not adjusted, so ${\pi }^e=4\%$ (the original equilibrium inflation rate). The natural rate of unemployment $u_n=5\%$, since initial equilibrium is long-run. Plugging into the formula: $6=4-2(u-5)$. Rearranging gives $2=-2u+10$, so $-8=-2u$, so $u=4\%$. This matches the inverse short-run relationship: higher inflation leads to lower unemployment. The correct answer is B.

Question 2 (Free Response)

An economy has a natural rate of unemployment of 5%, initial expected inflation of 3%, and is currently in long-run macroeconomic equilibrium. (a) Draw a correctly labeled Phillips curve graph of this economy, labeling the initial equilibrium point A. (b) The government passes a large permanent increase in the minimum wage. On your graph from (a), show how this change affects SRPC and LRPC, and label the new long-run equilibrium point B. (c) Suppose instead policymakers run an expansionary fiscal policy to reduce unemployment in the short run. What happens to inflation and unemployment in the long run, relative to the initial equilibrium?

Worked Solution: (a) Correct graph: Y-axis labeled "Inflation Rate", X-axis labeled "Unemployment Rate". Draw a vertical LRPC at 5% unemployment, labeled LRPC. Draw a downward-sloping SRPC that intersects LRPC at 3% inflation, labeled SRPC. Point A is at $(u=5\%,\pi =3\%)$, the initial long-run equilibrium. (b) A permanent increase in the minimum wage raises structural unemployment, so the natural rate of unemployment increases to $u_n^{\prime }>5\%$. LRPC shifts rightward to the new higher NRU, labeled LRPC₂. The SRPC also shifts right to intersect the new LRPC at the original 3% expected inflation. The new long-run equilibrium point B is at $(u=u_n^{\prime },\pi =3\%)$. (c) In the short run, expansionary fiscal policy increases AD, moving the economy up along the original SRPC: unemployment falls below 5% and inflation rises above 3%. In the long run, workers adjust their inflation expectations to the new higher actual inflation, so SRPC shifts upward. Unemployment returns to the original 5% natural rate, and inflation is permanently higher than the initial 3% level. There is no long-run change in unemployment, only higher inflation.

Question 3 (Application / Real-World Style)

In 2010, following a deep recession, the U.S. unemployment rate was 10%, while actual inflation was 1.6%. At the time, the natural rate of unemployment was estimated at 5.2%, and expected inflation was 2%. Use the SRPC formula $\pi ={\pi }^e-0.8(u-u_n)$ to calculate the model's predicted inflation, and interpret what the difference between predicted and actual inflation tells us.

Worked Solution:

1. Plug in the given values: ${\pi }^e=2\%$, $u=10\%$, $u_n=5.2\%$, $\alpha =0.8$.
2. Calculate: $\pi =2-0.8(10-5.2)=2-0.8(4.8)=2-3.84=-1.84\%$.
3. The model predicts deflation of ~1.8%, but actual inflation was 1.6%, 3.44 percentage points higher than predicted.
4. This gap implies the SRPC shifted rightward after the recession: sectoral shifts in the labor market after the crisis increased frictional and structural unemployment, raising the natural rate of unemployment and leading to higher inflation at the 10% actual unemployment rate than the original model predicted.

Quick Reference Cheatsheet

What's Next

This chapter provides the core framework for analyzing the long-run consequences of stabilization policy, the central theme of Unit 5. Next, you will apply this model to analyze inflation targeting, central bank credibility, and the long-run effects of government deficit spending, all of which build directly on your understanding of SRPC shifts, expectation adjustment, and the natural rate of unemployment. Without mastering the difference between short-run and long-run Phillips curve outcomes, you will not be able to correctly answer FRQ questions about the costs of expansionary policy and the role of expectations in macroeconomic policy. The follow-on topics that connect directly to this chapter are: Inflation targeting Fiscal policy and crowding out Monetary policy and long-run growth