§4 The IS-LM Model

The IS Relation

• Rather than assuming a constant investment $\bar I$, we replace it for a more realistic investment function

  $$I = I(Y,i);\quad I_Y>0,I_i < 0$$

• With this modification, equilibrium in the goods markets becomes:

  $$Y = C(Y - T)+I(Y,i)+G$$

• This is the IS relation, and captures all the combinations of $Y$ and $i$ that are consistent with equilibrium in the goods market.

The LM Relation

• Recall equilibrium in the financial markets requires

  $$M=\$YL(i)$$

• Dividing both sides by $P$, yields

  $$\frac{M}{P}=YL(i)$$

  which is the LM relation.

• In equilibrium, real money supply equals real money demand, which depends on real income $Y$ and the interest rate $i$.

• In practice, central banks set $i$ and chose the $M$ they need to make that $i$ consistent with equilibrium in financial markets.

• That is, the LM relation captures all the combinations of $Y$ and $i$ that are consistent with equilibrium in the financial markets.

— Apr 12, 2025

§4 The IS-LM Model by Lu Meng is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Permissions beyond the scope of this license may be available at About.