# The m and the LM curve is defined

The Poole model extends the IS-LM
model to include uncertainty or shocks. If there were no shocks either setting
i, interest rates, or M, money supply, would achieve the target Y, GDP, there
is no problem over the choice of monetary instrument. But, setting M requires
additional knowledge of money demand, whereas i only requires knowledge of the
IS curve. The aim of Monetary Authority is to minimize output volatility, the
difference in output volatility between the two regimes generally depends on
certain characteristics of the economy. The Central Bank can either choose to
set the stock of money and let the interest rate be decided by the interaction
of money demand and supply, or it can set the interest rate and let the supply
of money be determined by the demand for money.

The IS curve is defined as Y
= a0 + a1r + m and the LM curve is defined as M = b0 + b1 Y + b2r + n. M and Y are defined as the logarithms of money supply and
output. b0,
b1, b2, a0 and a1 are parameters and r is the interest rate. There are three
standard assumptions which apply: b1 > 0, b2 < 0 and a1 < 0. The IS and LM equations are expanded with unpredictable shock terms m and n. These unpredictable shock terms have the five following properties: E m = 0, E n = 0, E m2 = s2m, E n2 = s2n  and E mn = smn = rsmsv. The first and second assumptions state that the mean of the shocks is zero, however this does not mean that shocks are not expected and the third states that their variances are constant. m is a shock to the IS curve, for example an increase in investor confidence, more positive values of the coefficient relate to higher levels of investor confidence, this leads to increased spending and so equilibrium GDP increases all else equal and vice versa for negative values. n is a shock to the LM curve and money demand in particular. However, in this case more positive values correspond to economic bad time, this is due to money demand being part of the IS-LM model liquidity preference. In bad times liquid assets are preferred, so money demand is higher as individuals have less confidence in a bond being paid back due to the possibility of the company or government defaulting.

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