菲利普斯曲线与自然失业率

AP 宏观经济学· AP Macroeconomics CED — Long-Run Consequences of Stabilization Policies· 14 分钟阅读

1. 核心概念：菲利普斯曲线与自然失业率★★☆☆☆⏱ 3 min

菲利普斯曲线是描述通货膨胀与失业之间关系的核心宏观经济学模型，从早期实证研究发展而来，修正后纳入了长期通货膨胀预期调整。本主题占AP宏观经济学第5单元分值的10-15%，几乎每次考试都会出现在MCQ和FRQ部分。

📘 定义

自然失业率（NRU）

经济处于潜在产出水平时存在的失业率，此时只有摩擦性失业和结构性失业，不存在周期性失业。也被称为非加速通货膨胀失业率（NAIRU）。

例:

典型发达经济体的自然失业率在3%-5%之间。

现代菲利普斯曲线模型的核心结论是：通货膨胀与失业之间的权衡取舍仅存在于短期；长期中不存在永久权衡取舍，因为通货膨胀预期会调整至实际通货膨胀水平，推动短期曲线回移，与自然失业率处的长期垂直曲线对齐。

2. 短期菲利普斯曲线（SRPC）★★★☆☆⏱ 4 min

短期菲利普斯曲线（SRPC）是一条向下倾斜的曲线，显示当预期通货膨胀和自然失业率保持不变时，通货膨胀与失业之间的反向关系。反向关系来自短期工资和价格粘性：总需求的意外增加会促使企业提高产出、雇佣更多工人（失业率降低），推高价格（通货膨胀升高）。

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

Where: $π$ = 实际通货膨胀, $π^{e}$ = 预期通货膨胀, $α$ = a positive constant measuring how responsive inflation is to cyclical unemployment, $u$ = 实际失业率, and $u_{n}$ = 自然失业率. When actual unemployment falls below $u_{n}$ , actual inflation rises above expected inflation, giving the SRPC its downward slope.

📐 例题

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:

在AP FRQ题目中，务必给SRPC标注负斜率、坐标轴（Y轴：通货膨胀率，X轴：失业率），记住总需求的变化只会导致沿SRPC移动，不会移动曲线本身。

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.

📐 例题

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.

📐 例题

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.

✓ 快速检测

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%
显示答案
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. 常见陷阱

错误做法:

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

原因:

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

正确做法:

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.

错误做法:

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

原因:

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

正确做法:

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.

错误做法:

Claiming the natural rate of unemployment is zero.

原因:

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

正确做法:

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

错误做法:

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

原因:

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

正确做法:

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

错误做法:

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

原因:

Students treat the two models as separate, not linked.

正确做法:

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'.

错误做法:

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

原因:

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

正确做法:

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

6. 速查表

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

真题中的出现

AI 根据考纲规律估算的考点位置,请对照官方真题核实准确性。仅作复习重点参考。

2023 · AP Macroeconomics
关于LRPC移动的FRQ题目
2022 · AP Macroeconomics
关于SRPC移动因素的MCQ题目

下一步

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.