From Short to Medium Run (IS-LM-PC)

Short-Run to Medium-Run Adjustment

coreExam · high

The economy adjusts from short-run to medium-run equilibrium via the Phillips curve and CB response. If Y > Yn: ↑π → CB tightens → ↑r → ↓Y back to Yn. If Y < Yn: ↓π → CB eases → ↓r → ↑Y. In the medium run: Y = Yn, Δπ = 0, r = rn. A demand shock changes rn — the CB must deliver the new natural rate.

Derivation

Step 1 / 7

1Press Space or click Reveal next
(hidden)
2Press Space or click Reveal next
(hidden)
3Press Space or click Reveal next
(hidden)
4Press Space or click Reveal next
(hidden)
5Press Space or click Reveal next
(hidden)
6Press Space or click Reveal next
(hidden)
7Press Space or click Reveal next
(hidden)

Short Run vs Medium Run

| State | Conditions | |-------|------------| | Short run | $Y$ at intersection of IS and flat LM; can be above, below, or at $Y_n$ | | Medium run | $Y = Y_n$ , $\Delta\pi = 0$ , $r = r_n$ |

Adjustment Dynamics

The Phillips curve is the engine: any output gap triggers inflation drift, which triggers CB response, which closes the gap. Output returns to $Y_n$ ; inflation stabilises at whatever level the CB tolerates.

Y > Y_n \to \uparrow \pi \to \uparrow i^T \to \uparrow r \to \downarrow Y \to Y_n

The Natural Real Rate

The medium-run real rate $r_n$ is pinned down by the IS curve at $Y = Y_n$ :

Y_n = C(Y_n - T) + I(Y_n, r_n + x) + G

Solve this for $r_n$ . A demand shock (↑ $c_0$ , ↑ $G$ , ↑ $I_0$ ) shifts IS right, raising $r_n$ . A negative shock lowers $r_n$ — possibly into ZLB territory.

Medium-Run Policy

i^T_{MR} = r_n + \pi^e

The CB delivers the natural real rate at the stable inflation expectation. This is the "neutral rate" discussion in monetary-policy commentary.

Mock-Exam Pattern

Start from old medium run, compute $r_n$ .
Apply shock → new $r_n$ .
Determine new $i^T$ .
If $i^T < 0$ (ZLB), gap doesn't close via conventional tools.

Worked Example

Yn = 900. Original IS: Y = 1000 − 2000r. πe = 2%. Autonomous demand falls: new IS = 900 − 2000r.

Original medium-run: 900 = 1000 − 2000rn → rn = 5%. iᵀ = 5% + 2% = 7%.
After shock: new rn = (900 − 900)/2000 = 0%. iᵀ = 0% + 2% = 2%.
Short-run transition: CB sees Y < Yn → ↓iᵀ → ↓r → Y recovers to 900.
If shock is permanent, CB settles at new iᵀ = 2% in medium run.

Old rn = 5%, new rn = 0%. Medium-run iᵀ falls from 7% to 2%. Demand shock lowered the natural real rate — CB must follow it down.

Common Mistakes

—Conflating short-run Y (determined by IS given CB's iᵀ) with medium-run Y (always Yn).
—Assuming the CB can keep Y ≠ Yn indefinitely — Phillips dynamics force adjustment.
—Forgetting that rn is endogenous to IS — a demand shock changes rn.
—Treating πe as exogenous in the medium run — it's pinned down by CB credibility and target.

Exam Cues

→Medium run: Y = Yn, Δπ = 0, r = rn. Know this triple.
→Adjustment via Phillips: Y > Yn → ↑π → CB tightens → Y falls back.
→Demand shock changes rn. CB must deliver new rn via new iᵀ = rn + πe.
→ZLB complication: if new rn < −πe, CB cannot achieve Y = Yn.