Module 09 · Chapters 9

IS-LM-PC: Short to Medium Run

The full three-equation model: IS sets Y, LM sets i, PC drives π → adjustment over time.

“Where short-run comparative statics meet long-run discipline.”

~45 min· 4 sub-skills·5 exercisesExam frequency · high0% mastered

The full Bocconi macro engine: IS (goods market), LM (CB rate-setting), PC (price-setting). Together they tell you (1) where Y is now, (2) what i achieves it, and (3) how π evolves. With adaptive expectations, the system always converges to u = u_N in the medium run — but the path matters.
Definition·The three equations
IS: Y = f(G, T, i, c₀, I₀) — demand-determined output.

LM (modern): i = i^T(π, Y) — central bank's interest-rate rule (e.g., Taylor).

PC: π = π^e − α(u − u_N) — inflation responds to the unemployment gap.

Close with Okun: u − u_N ≈ −β(Y − Y_N).
Figure · IS-LM-PC equilibrium and adjustment
IS-LM
Phillips
Top: IS-LM in (Y, i) — short-run equilibrium. Bottom: PC in (Y, π) — medium-run anchor. CB moves i to bring Y to Y_N.
Taylor rule (central-bank reaction function)
$i_t \;=\; \bar i + \phi_\pi(\pi_t - \pi^*) + \phi_y(Y_t - Y_N)/Y_N$
$\bar i$
long-run nominal rate (= r* + π*)
$\phi_\pi$
weight on inflation gap, typically > 1 (Taylor principle)
$\phi_y$
weight on output gap
Taylor principle: φ_π > 1 ensures rate hikes raise the *real* rate when inflation rises.
Tip·Medium-run adjustment loop
Suppose a positive demand shock pushes Y > Y_N. Sequence:
1. PC: π rises (gap closes only when u = u_N).
2. CB: raises i to lean against π.
3. IS: higher i pulls Y back down.
4. Convergence: Y → Y_N, π → π* (target). Speed depends on α, φ_π, φ_y.
Common misconception
A permanent fiscal expansion permanently raises Y.
Actually**Only short-run.** In the medium run, Y returns to Y_N. The composition shifts (more G, less I via higher i), but the level is anchored by labour-market structure.
Exercise · multiple choice · +8 XP
Identify the three equations
Which equation determines inflation in the IS-LM-PC model?
Exercise · predict shift · +12 XP
Demand boom, short run
ΔG > 0. Predict the *short-run* response (before PC adjusts).
Scenario: Fiscal expansion. Wages and π still anchored at π^e_t = π_{t-1}.
Exercise · true false · +10 XP
Convergence to u_N
Following a fiscal expansion, in the medium run u returns to u_N regardless of whether the CB targets π or i.
"Following a fiscal expansion, in the medium run u returns to u_N regardless of whether the CB targets π or i."
Exercise · multiple choice · +12 XP
Composition in medium run
After a permanent ΔG > 0, in the medium run, what changes vs. the original equilibrium?
Exercise · numerical · +14 XP
Taylor rule numerical
Taylor rule with bar i = 4%, π* = 2%, output gap = 0, π_t = 4%, φ_π = 1.5, φ_y = 0.5. What is i_t?
Your answer (% per year)

Mastery check

5 questions · pass with 80%

Answer all five to confirm you've internalised the module. A passing run unlocks the next module.

Q1
Which trio describes IS-LM-PC?
Q2
"The Taylor principle requires φ_π > 1."
Q3
"A permanent fiscal expansion permanently raises Y above Y_N."
Q4
Following ΔG > 0 in the short run:
Q5
bar i=3%, π*=2%, π_t=2.5%, gap=−1%, φ_π=1.5, φ_y=0.5. i_t?

0 / 5 answered

Exam pitfalls

Treating short-run results as medium-run. IS-LM-PC's short run = IS-LM only; medium run = full three-equation system converging to u = u_N.
Forgetting Taylor principle (φ_π > 1) — without it, indeterminacy.
Saying fiscal stimulus permanently raises Y. It only changes the *composition* in the medium run.
Mixing levels and gaps in the Taylor rule. The output gap is normalized: (Y − Y_N) / Y_N.