The IS curve shows all the combinations of interest rates i and outputs Y for which the goods market is in equilibrium.

To derive the IS curve, we equate the aggregate income with the aggregate expenditure:

Aggregate Income = Aggregate Expenditure

C + S + T = C + I + G + (X – M)

This can be simplified as follows:

(S – I) = (G – T) + (X – M)

This means that the excess savings minus investments goes towards funding government deficit and it also helps in supporting a trade surplus. This equation can be used to derive the IS Curve.

We will work with two graphs. 

The first graph plots Income (Y) with (S – I). When income (Y) increases, savings (S) also increase. Investments (I) also increase, however, the increase in investments is less than the increase in savings. This means that S – I goes up. This will result in an upward sloping (S - I) curve.