Inflation & the Return to Potential
Inflation does not move in the short run; over time it responds to the output gap. The Fed responds to inflation, so the economy is dragged back to Y = Y* and r back to r*. Every question here is answered in three stages.
The two facts that run the chapter
- Output gap
- Y − Y*. When it is negative, unemployment sits above its long-run level.
- Short run
- Inflation barely moves — nominal rigidity, or inflation inertia, from limited information, menu costs and long-term contracts.
- Over time
- Inflation responds to the output gap. Y > Y* ⇒ it gradually rises. Y < Y* ⇒ it gradually falls. Y = Y* ⇒ it holds steady.
- Inflation shock
- A sudden jump in a small set of prices, classically oil, unrelated to the output gap. It changes inflation immediately — 1973–74 is the textbook case.
The mechanism: with Y above Y*, firms are beyond comfortable capacity, so as contracts expire and menus wear out they raise prices by more than past inflation. Many firms doing that is rising inflation. At Y = Y*, firms simply keep up with expected inflation, and past inflation is a crucial determinant of expectations.
The reaction function
| π | Fed action | r | i = r + π | Output gap |
|---|---|---|---|---|
| 5% | Raise r a lot | 4.5% | 9.5% | Dips more negative |
| 3% | Raise r | 3.5% | 6.5% | Dips negative |
| 2% | Do nothing | 3.0% | 5.0% | Zero |
| 1% | Lower r | 2.5% | 3.5% | Dips positive |
How the economy self-corrects
Suppose Y₁ < Y*. Inflation starts to fall. Following its reaction function the Fed lowers r; lower r raises C and IP, so PAE shifts up and Y rises. As long as Y ≠ Y*, inflation keeps changing, so the Fed keeps moving r, so Y keeps moving — until Y = Y*. Long-run equilibrium is where the PAE line crosses the 45° line exactly at Y*.
Disinflation — the exam's favorite sequence
Start in long-run equilibrium with inflation steady but too high. The Fed shifts its reaction function up — tighter at every inflation rate.
| Stage | Inflation | r | PAE and Y |
|---|---|---|---|
| Short run | Unchanged — nominal rigidity | Jumps to r₂ | PAE shifts down; Y falls by more than the shift. A deliberately caused recession. |
| Adjustment | Starts falling, since Y < Y* | Fed lowers r along its new function | PAE shifts back up; Y rises |
| Long run | Ends permanently lower — it fell throughout and never rose | Back to r*, set by saving and investment | Y = Y* |
The slides put the inflation charts for 1976–79 and 2021–22 side by side for exactly this comparison — the late-1970s disinflation and the post-2021 tightening.
Rules that earn points
- Answer in three stages: short run, adjustment, long run. Never skip the middle.
- Short run: inflation fixed; r moves; PAE shifts; Y moves by the multiplier.
- Adjustment: inflation responds to the output gap; the Fed responds to inflation; PAE shifts back.
- Long run: Y = Y*, r = r*, and inflation is whatever the reaction function implies.
- Letting inflation move immediately. In the short run it does not — that is the whole mechanism.
- Saying the Fed permanently lowered the real rate. In the long run r returns to r*.
- Forgetting that disinflation costs a recession. That cost is the point of the question.
The Fed follows r − r̄ = 0.5(π − π̄) with π̄ = 2% and r̄ = 3%. Inflation comes in at 6%. The Fed sets:
- Ar = 5%, i = 11%
- Br = 7%, i = 13%
- Cr = 5%, i = 5%
- Dr = 3%, i = 9%
Answer
A — r = 5%, i = 11%.
r = 3 + 0.5(6 − 2) = 3 + 2 = 5%. Then i = r + π = 5 + 6 = 11%.
B is the trap: using a coefficient of 1 instead of 0.5, so r rises by the full 4 points. The 0.5 means r moves half as much as inflation. (C forgets to add π back to get the nominal rate.)
The Fed shifts its reaction function up to bring inflation down. Immediately afterwards, inflation:
- AFalls at once to the new target
- BFalls gradually, starting straight away
- CIs unchanged, while r jumps and output falls
- DRises, because higher rates raise firms' costs
Answer
C — inflation is unchanged; r jumps and Y falls.
Nominal rigidity means inflation cannot move in the short run. What moves is r, which cuts C, IP and NX, shifting PAE down. Y falls by more than the shift. Inflation only starts falling once Y sits below Y*.
B is the trap: it skips the recession. Inflation falls because the output gap opens first — no gap, no disinflation, and no cost to explain.
Once the disinflation is complete and output is back at Y*, the real interest rate:
- AIs permanently higher, which is what holds inflation down
- BHas returned to r*, set by saving and investment
- CEquals the new inflation target
- DIs permanently lower, since inflation is lower
Answer
B — back to r*.
r* is determined by saving and investment (Unit 24 adds net capital inflows), not by the central bank. What is permanently different is inflation and therefore the nominal rate i = r* + π.
A is the trap: it assumes the Fed can hold r above r* forever. It cannot — a persistent gap between r and r* keeps Y away from Y*, which keeps inflation drifting without limit.
The 1973–74 oil price jump differs from output-gap inflation chiefly in that it:
- ARaises inflation immediately, with no output gap required
- BRaises inflation only gradually, as contracts expire
- CLowers inflation, because it reduces output
- DHas no effect on inflation, since only a few prices move
Answer
A — immediately, with no gap required.
An inflation shock is a sudden jump in a small set of prices for reasons unrelated to how Y compares with Y*. Output-gap inflation is gradual, emerging only as contracts expire and prices reset; a shock skips that queue.
B is the trap: it describes the output-gap mechanism, which is the thing a shock is defined against. The policy problem is that the central bank now faces high inflation without the excess demand that normally comes with it, so fighting it means causing a recession that was not otherwise warranted.
The economy is in long-run equilibrium with inflation steady at 5%. The Fed decides that is too high and shifts its reaction function up. Walk through the short run, the adjustment and the long run, stating in each what happens to inflation, r, PAE and Y.
Model answer
Short run. Inflation does not change — nominal rigidity, from limited information, menu costs and long-term contracts. But the new function prescribes a higher r at the current 5% inflation, so r jumps to r₂. Higher r cuts C, IP and NX, so PAE shifts down and Y falls by more than the shift because of the multiplier. The Fed has deliberately caused a recession.
Adjustment. With Y < Y*, firms are operating below comfortable capacity, so as contracts expire and menus reset they raise prices by less than past inflation: inflation starts falling. Following its new reaction function, the Fed lowers r as inflation falls. That shifts PAE back up and raises Y. The loop repeats — gap moves inflation, inflation moves r, r moves Y — and only stops when Y = Y*.
Long run. Output is back at Y*. Inflation fell throughout the period Y was below Y* and never rose, so inflation is permanently lower. The real interest rate returns to r*, determined by saving and investment, not by the Fed. Long-run inflation settles where the new reaction function crosses r*.
On the diagram: PAE₁ shifts down in parallel to PAE₂, Y falls below Y*, then PAE drifts back up to cross the 45° line exactly at Y*.
- Inflation unchanged in the short run, with nominal rigidity named as the reason.
- Saying explicitly that the recession is deliberate and that Y falls by more than the PAE shift.
- The adjustment loop in the right order: gap → inflation → Fed → r → PAE → Y, repeating until Y = Y*.
- Using the new reaction function when the Fed cuts r during adjustment.
- Long run: inflation permanently lower, r back at r*, Y back at Y*.
Why can the Fed not hold the real interest rate below r* indefinitely? In answering, say what determines the long-run inflation rate.
Model answer
Holding r away from r* keeps Y away from Y*, and any persistent output gap keeps moving inflation. Hold r below r* and Y stays above Y*, so inflation rises without limit; hold r above r* and Y stays below Y*, so inflation falls without limit. Neither is sustainable.
A central bank following any sensible reaction function is then forced to respond to that drifting inflation, and responding pulls r back toward r*. In the long run r* is set by saving and investment — Unit 24 adds net capital inflows — not by the central bank.
What the Fed does choose is long-run inflation: the economy settles where the reaction function crosses r*, so shifting the whole function up — being tighter at every inflation rate — lowers long-run inflation.
- Linking r ≠ r* to a persistent output gap, not just to "the market".
- Working through both directions, with inflation drifting without limit in each.
- Naming saving and investment as what sets r*.
- The separation: the Fed picks long-run inflation, not the long-run real rate.
- Saying that lowering long-run inflation requires shifting the whole function, not a one-off rate hike.