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
.