Graphical Derivation of the LM curve

Graphical Derivation of the LM curve

The nominal quantity of money is assumed to be an exogenous variable determined by the central bank. Mathematically, this means that the supply of real money balance is a vertical line as it is independent of interest rates.

At income level Yo, the demand for real money balance is indicated by Lo (Yo). Equilibrium in the money market therefore occurs at A at interest rate ro. When income increases to Y1, the
demand for real money balance likewise increases to L1(Y1).

At this higher level of income, equilibrium in the money market occurs at a higher interest rate, r1. This relationship between income and interest rate gives us the LM curve. The LM curve is
positively sloped because when income increases, a higher interest rate is needed to bring about equilibrium in the money market.