Question

In: Economics

What is an LM curve? How is it derived from the money supply and money demand...

What is an LM curve? How is it derived from the money supply and money demand equilibriam points?

Solutions

Expert Solution

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 .


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