4/2/12

What is the IS LM model? A brief introduction with equations and graphs



The IS LM model is a model used in macroeconomics to help explain the possible relationships between the interest rate and real GDP.  While not very accurate for real world analysis, it gives an interesting look at possible outcomes of various policy tools for a classroom setting.

The IS (Investment and savings equilibrium) equation:

Y = C(Y-T(Y))+I(r)+G+NX(Y)

Where
Y = national income or real GDP
C(Y-T(Y)) = consumption or consumer spending which is a function of disposable income
(Y-T(Y)) = disposable income which is equal to national income minus tax (which is a function of income)
I(r) = Investment which is a function of the real interest rate
G = Government spending/expenditures
NX(Y) = Net exports, where imports depend on income (Y)

The IS/LM model showing possible shifts in the IS curve
The IS curve is downward sloping in the graph because a lower real interest rate motivates higher investment (look at the above equation) which translates to a higher Y.  Note that Y is endogenous, and responds to changes in r, and the IS curve shows this relationship.  Remember that the IS curve shows every possible point with respect to the interest rate and real GDP where investment is equal to savings.  For example, if the interest rate falls savings must fall (because people don’t like the lower return) which means that real GDP must rise so that people can save more.  The increase in Y will be caused by an increase in investment which must be matched by an increase in savings either from the private, public (government), or foreign sector.

 
The LM (Liquidity preference and money supply equilibrium) equation:

M/P = L(i,Y)

Where
M/P = the real money supple where M is the actual amount of money in the economy and P is the overall price level
L(i,Y) = the real demand for money which is a function of the interest rate (i) and national income (Y)


The same IS/LM graph showing possible shifts in the IS curve
The LM curve is upward sloping because it shows the possible interest rate and real GDP values that allow for equilibrium to exist in the money market.  You can see in the LM equation that i and Y both enter on the right hand side in the real demand for money function.  Since people demand less money when the interest rate is high, L has a negative relationship with i.  But people demand more money when their income rises so L has a positive relationship with Y.  This means that if i goes up, Y go up as well so that L doesn’t change.  And if i goes down, Y must fall as well so L doesn’t change.  This means that they have a positive relationship hence the upward slope.

Equilibrium level of national income in the IS-LM model is considered to be aggregate demand.  And any change in the price level (P) will result in a shift in the LM curve and its new equilibrium with respect to IS will show the new point on the AD (aggregate demand curve). 


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