The LM curve is derived from the money market equilibrium. It shows the range of values of interest rates, i, which when combined with the outputs, Y, give an equilibrium money market. The interest rate, i, can be interpreted as the opportunity cost of money i.e., payment for liquidity preference.
The money market equilibrium can be expressed as: M/P = L (i, Y) = L (r, Y), where M is the money in circulation as supplied by the central bank (the Fed), while P is the price level. Based on the Keynesian model, the Fed influences the price level and interest rates by determining the amount of money in circulation; thus, at money market equilibrium, the interest rates (i.e. the nominal rate, r and the real interest rate, i) can be assumed as being equal. The money market equilibrium is reached when the real money demand, L, is equal to the real money supply, M/P. Thus, at a particular output, Y, the interest rate, i, changes so that the liquidity function, L (demand) is at equilibrium with the exogenous supply. Thus, by simplifying the liquidity function, it is possible to determine the demand for real money. Two motives influence demand for real money balances; the transaction/precautionary motive, which is a function of the output L1 (Y), and the speculative motive L2 (i), which depends on interest rate speculations. This can be represented graphically as shown in the LM curves below.
Given that the money supply, M determined exogenously, to achieve money market equilibrium, the sum of its supply must be equal to the sum of its demand. Thus:
(M/P) = L1 (Y) + L2 (I).
Any change in one or more of these variables causes the LM curve to shift. The demand for real money balances (speculative motive, L2) decreases as a function of interest, i. At a low-interest level, the demand for money is infinite as there is less money in circulation.