In: Economics
What is an LM curve? How is it derived from the money supply and money demand equilibriam points?
The LM curve is the relation between interest rate and GDP/ouput, both of which clears the money market.
The money market consists of the money demand function, which is , and money supply in the nominal terms will be . The equilibrium will be where the real money demand will be equal to the real money supply, ie will be equal to the . Note that P is termed as price level, L is the real demand for money function, Y is the real output and i is the nominal intertest rate, and L increases as Y increases and/or i decreases.
The equilibrium will be at , ie . The LM curve will be derived by taking P, Ms as constant, and changind Y or i. The demand for money is downward sloping as the interest rate and money demand are negatively correlated. The graph is as below.
Suppose economy's output is at . At that output, the money demand is for variable i. The money demand curve intersects the vertical money supply curve at interest suppose . Now, suppose further that output has increased to . At that output, the money demand is , and the money demand curve intersects the money supply curve at interest . As output further increases to , the constant money supply intersects with the new money demand curve at . The LM curve depicts these equilibrium points which clears the money market, having coordinates , and . Joining many such coordinates, the whole LM curve can be derived graphically.
Mathematically, the derivation will be as, for , the interest rates that clears the money market for a constant money supply will be as , such that , where Ms, P and L as a function, would be constant/same, and . The respective LM curve would be the (function satisfying) set of coordinates , for .