The IS Curve

There are several more or less equivalent ways to arrive at an IS Curve.

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EconModel (Loanable Funds) Graphical

The EconModel presentation for the IS/LM Model constructs an IS Curve graphically from equilibrium movements in the supply and demand for loanable funds. The IS Curve shows those points that are consistent with equilibrium in the supply and demand for loanable funds.

Physical Investment

An alternative,
more common view is that the IS Curve shows those points that are consistent
with **C + I + G = C + S + T**. These two views are operationally
equivalent if you take the supply of loanable funds to be **S** and the
demand to be **I + G - T**. That, is real capital investment is
financed by borrowing.

General Algebraic

An algebraic approach is to let savings be a function
**S(Y)** of income and let investment be a function **I(R)** of the
interest rate. An increase in income **Y** causes more savings.
This forces down the interest rate R so that investment increases and the
identity **I(R) +G - T = S(Y)** is maintained. The IS Curve is thus downward sloping. The increase in
income **Y** causes increased savings, which drives down the interest rate
and increases investment.

Simple Keynesian Model

The EconModel presentation for the Simple Keynesian Model derives an IS Curve under the simplifying assumptions of that model.

IS/MP Version

References

Link: Keynesian Models