Macro Analytics · Interactive model

IS–MP–PC–Okun Simulator

Explore how goods demand, monetary policy, unemployment, and inflation interact in a four-equation economy.

Section 3 · Four-equation system

Preset shocks · each is isolated relative to the stored baseline

Exogenous variables and model parameters — adjust sliders or enter exact values

Default calibration. Choose a shock above or adjust any parameter.

Baseline (0)Scenario (1)

Red curves indicate changed relationships. A new point on an unchanged curve is a movement along that curve.

IS curve

Goods market · real rate versus output

Higher output is associated with a lower real rate along IS.

MP curve

Monetary policy · real rate versus inflation

The real rate responds to inflation and the MP shock.

Phillips curve

Inflation versus unemployment

Lower unemployment raises inflation, holding expectations fixed.

Okun's Law

Unemployment versus real output

Higher output is associated with lower unemployment.

Derived AD–AS equilibrium

IS + MP produce AD; Phillips curve + Okun's Law produce AS

This is an inflation–output diagram; the vertical axis is inflation π, not the price level.

Show scenario curves and equilibrium

Equilibrium comparison

Endogenous variable	Baseline (0)	Scenario (1)	Change (1 − 0)

Output is measured in real-output units; unemployment (UR), inflation (π), and the real interest rate (r) are expressed in percent. Accordingly, differences in UR, π, and r are percentage-point changes. Expectations are held fixed unless changed explicitly.

Model equations and analytical solution

Four structural equations

IS:  y = y* − α(r − r*) + εIS
MP:  r = r* + β(π − π*) + εMP
PC:  π = E[πt+1] − δ(UR − UR*) + εPC
OL:  UR = UR* − γ(y − y*) + εOL

Derived schedules

AD: π = π* + [y* + εIS − αεMP − y]/(αβ)
AS: π = E[πt+1] + δγ(y − y*) − δεOL + εPC

These are short-run, static comparative-statics relationships. The equilibrium is obtained from the intersection of AD and AS and then substituted into the four equations. The app requires α>0, β>0 to express AD as a function of inflation.

Closed-form equilibria

D = 1 + αβδγ

q = αβ(π* − E[πt+1]) + εIS − αεMP
    − αβεPC + αβδεOL

y_eq  = y* + q / D
UR_eq = UR* − γ(y_eq − y*) + εOL
π_eq  = E[πt+1] − δ(UR_eq − UR*) + εPC
r_eq  = r* + β(π_eq − π*) + εMP

Partial derivatives: exogenous shocks

∂y/∂εIS =  1 / D
∂y/∂εMP = −α / D
∂y/∂εPC = −αβ / D
∂y/∂εOL =  αβδ / D
∂UR/∂εOL = 1 / D

The direct unemployment shock raises unemployment even though the output response partly offsets it. The equilibrium computations use the source PDF's equations (47), (55)–(63) exactly.