Mathematical Model for Deriving Equilbrium Income and Interest Rate

In this article we are going to explain the mathematics behind deriving Aggregate Demand from IS - LM Model (where goods and capital market are both in equilbrium simultaneously).

The intersection of IS and LM schedules determines the equilbrium income and the equilbrium interest rate. We will use the equationg derived for IS and LM schedules

IS schedule : Y = α  ( Â – b i )

LM schedule :  i = (1/h ) ( kY - M / P )

Solving the two schedules we will derive the equilbrium income

Equilbrium Income       Y = γ Â + γ ( b / h) ( M / P)

We can calculate equilbrium interest rate by substituting  eqilbrium income in Lm schedule.

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