Lesson M17.L03: IS-LM-PC Dynamics: Supply Shocks and Stagflation

Module: From Short to Medium Run: The IS-LM-PC Model Level: intermediate Duration: 30 minutes Learning Objective: Analyse the policy dilemma created by an adverse supply shock in the IS-LM-PC model. Data as of: 2024 Provenance: RBA Statement on Monetary Policy | ABS Consumer Price Index

Explanation

A supply shock shifts the Phillips Curve directly, independently of the output gap. In the IS-LM-PC framework, the PC is:

π = πᵉ + β × (Y − Yₙ)/Yₙ + ε

Notation: - ε = supply shock (ε > 0 = adverse/cost-push shock, e.g., oil price spike, supply-chain disruption, drought) - All other variables as in M17.L01

Supply shock mechanics: When ε > 0, the PC shifts upward. At any level of Y — including Y = Yₙ (zero output gap) — inflation is higher than expected. This is not driven by excess demand; it reflects rising costs of production passed through to consumer prices.

The policy dilemma — three options:

Option A — Accommodate: The central bank keeps Y = Yₙ by not tightening. The output gap stays at zero, unemployment does not rise. But: π > πᵉ for each period ε persists. With adaptive expectations, πᵉ ratchets upward each period → further PC shift → inflation spiral. Acceptable only if the shock is believed to be genuinely temporary.

Option B — Fight (disinflation): The central bank tightens monetary policy (raises i, shifts LM left), pushing Y below Yₙ. The negative output gap counteracts the supply shock: π = πᵉ + β × (negative gap) + ε. To hold π = π, the CB must create: β × |gap| = ε. This is stagflation: high inflation and* high unemployment simultaneously. The economy suffers a real output loss (sacrifice ratio).

Option C — Supply-side / incomes policy: Structural reforms or wage/price controls shift the PC back down (reduce ε). This is the ideal solution but difficult to implement quickly. Examples: energy subsidies, supply-chain diversification, productivity reform.

Australia 2021–2023: Global supply-chain disruptions and the Russia–Ukraine conflict (energy prices) produced ε > 0. CPI peaked at 7.8% in Q4 2022. The RBA chose Option B — raising the cash rate 13 times from May 2022 to November 2023 (0.10% → 4.35%), accepting below-potential growth to prevent inflation expectations from de-anchoring.

Worked Example

Setup: - Yₙ = 100, Y = 100 (no demand shock, gap = 0) - πᵉ = 2.5% (anchored at target), π* = 2.5% - Supply shock: ε = 3% (adverse, e.g., energy price spike) - β = 0.5

Step 1 — Inflation with accommodation (Option A):

CB keeps Y = Yₙ = 100, gap = 0.

π = πᵉ + β × 0 + ε
π = 2.5% + 0 + 3% = 5.5%

Inflation rises to 5.5% despite no output gap. In next period, πᵉ → 5.5%, PC shifts further up.

Step 2 — Required output gap to hold π = π* = 2.5% (Option B):

The CB wants π = 2.5%.

2.5% = 2.5% + 0.5 × gap + 3%
0 = 0.5 × gap + 3%
0.5 × gap = −3%
gap = −6%

To offset the supply shock, the CB must push the output gap to −6%, meaning Y must fall to 94 (i.e., 6% below potential). This would raise unemployment substantially. The real cost of fighting the shock is large.

Step 3 — Calculating the sacrifice:

With Yₙ = 100 and required Y = 94:

Output lost = Yₙ − Y = 100 − 94 = 6 units
Output gap = −6/100 = −6%

Using Okun's Law (λ = 0.5): rise in unemployment above uₙ = λ × |gap| = 0.5 × 6% = 3 pp.

If uₙ = 4%, then u rises to 7% — a severe recession — just to hold inflation at target in the face of a 3% supply shock.

Step 4 — Intermediate option (partial fight):

Suppose the CB accepts π = 4% (above target but below 5.5%). Required gap:

4% = 2.5% + 0.5 × gap + 3%
0.5 × gap = 4% − 2.5% − 3% = −1.5%
gap = −3%

Output gap of −3% → Y = 97, unemployment rises 1.5 pp above uₙ. A softer recession, but inflation stays above target until ε dissipates.

Common Misconception

Misconception: "An adverse supply shock is the same as a demand shock — the central bank should always tighten to fix it."

Correction: Demand shocks raise Y above Yₙ (positive output gap). The correct response is tightening to close the gap without incurring unnecessary output loss. An adverse supply shock raises inflation even at Y = Yₙ. Tightening to fully offset a supply shock requires deliberately creating a recession — pushing Y below potential. The optimal policy response depends on whether the shock is permanent or temporary, whether expectations are anchored, and what sacrifice ratio the community accepts. Blanket tightening for supply shocks can produce deep recessions unnecessarily.

Practice Prompts

1. Conceptual: Explain why a positive supply shock (ε < 0, e.g., a technology improvement reducing costs) creates a policy opportunity rather than a dilemma. → Answer: A negative ε shifts the PC downward. For any given output gap, inflation is lower than expected. The CB can accommodate this by cutting interest rates — stimulating demand, raising Y above Yₙ — without generating inflation. This is the rare case where the central bank can achieve both higher output and lower inflation simultaneously. The RBA might cut rates to boost growth while inflation remains within target. The policy dilemma disappears; the CB faces a policy gift.

2. Numerical: Suppose πᵉ = 3%, β = 0.6, Yₙ = 200, ε = 2%. The CB wants to hold inflation at π = 3%. What level of Y must the central bank engineer? → Answer:
   Set π = π = 3%:
   3% = 3% + 0.6 × (Y − 200)/200 + 2%
   0 = 0.6 × (Y − 200)/200 + 2%
   0.6 × (Y − 200)/200 = −2%
   (Y − 200)/200 = −2%/0.6 = −0.0333...
   Y − 200 = −0.0333 × 200 = −6.67
   Y = 193.3
   The CB must push output 3.3% below potential, creating a recession, to fully offset the 2% supply shock.

3. Application: Using the IS-LM-PC model, evaluate the RBA's decision to raise the cash rate sharply in 2022–23 given that inflation was driven partly by supply shocks (global energy, supply chains). What were the costs and benefits? → Answer: Benefits: Tightening helped close any positive output gap component, prevented πᵉ from de-anchoring (long-run inflation expectations stayed near 2.5–3%), and sent a credibility signal. Costs: Pushing Y toward or below Yₙ created unnecessary unemployment for the portion of inflation that was purely supply-driven (ε component). A supply shock cannot be fully eliminated by monetary tightening — it just shifts the distribution of costs from inflation to unemployment. The RBA acknowledged this trade-off, opting for gradual tightening ("less rapid" compared to US Fed), accepting that inflation would return to target over a longer horizon to limit the output sacrifice.

Further Resources

• 📺 How Does Stagflation Challenge The Traditional Phillips Curve? — Learn About Economics (8 min)
• 📺 Ch15 — Supply Shocks and Phillips Curve — Macro Lecture Series (14 min)
• 📚 ABS CPI Data — Australian CPI quarterly series for tracking the 2021–23 supply shock episode