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					                                        The IS-LM Model

       During the current period of a cyclical slowdown in economic activity, economists
debate on effectiveness of macroeconomic policies.
       We studied goals and instruments of fiscal policy and their impact on macroeconomic
variables in the real sector. On the other hand, we studied goals and instruments of monetary
policy and their effectiveness in the regulation of the financial sector. In real life these two
sectors are not isolated. Now we have to analyze the impact of both fiscal and monetary
policy on macroeconomic activity.
       Since the central economic problems at the moment are related rather to income and
unemployment than to the price level, we will concentrate on changes in macroeconomic
equilibrium under the assumption of constant prices.
       The analytical tool widely used in this analysis is the IS-LM model, developed by the
British economist Sir John Hicks and the American economist Alvin Hansen.
       The IS-LM model brings together the impact of fiscal and monetary policies on both
the real sector and the financial sector.
       In addition to the assumption of
              constant price level
       we will assume
              only two types of financial assets: money and bonds (interest bearing assets),
               and
              a closed economy (we will ignore foreign exchange fluctuations and
               international capital movements)


       Later we will relax some of these assumptions.


       1. The LM curve
       a) the equilibrium in the money market as a function of income and definition of the
           LM curve


           In order to put together the monetary and the real sector, we have to define the
       equilibrium in the monetary sector as a function of a income, which is a real sector
       variable.
       The equilibrium in the monetary sector is set when MS = MD. Under a given level of
       income (Y1) money supply and money demand determine the equilibrium interest rate
       (i1), presented on the graph below (Fig. 1).




            i                    MS




                 i1                       MD




                                                          M/P




Fig. 1. Equilibrium in the money market.

       The increase in income from Y1 to Y2 raised the demand for real money balances and
the money demand curve shifts to the right, as shown on Fig. 2 (left panel). Thus, if income
rises, the equilibrium interest rate increases, other things held constant. We can build a
relationship between income and the equilibrium interest rate, as shown on Fig. 2 (right panel).
The point of macroeconomic equilibrium E1 under income Y1 is presented on the right panel
as a function of income. It shows what the interest rate should be, in order to have equilibrium
in the money market. When income rises to Y2 the equilibrium in the money market at point
E2 is achieved at a higher interest rate i2 .On the left panel this equilibrium point shows what
the interest rate should be under income Y2 in order to have equilibrium in the money market.
When we put together the equilibrium points on the money market we derive the LM curve.
It presents the relationship between the level of income and the equilibrium interest rate, as
shown on Fig. 2 (left panel).
          i         MD1
                          MD2 MS                i

                                                                          LM
                               E2
              i2                                i2
                                                                          E2
           i1
                          E1                     i1            E1




                                          M/P             Y1         Y2         Y



      Fig. 2. Deriving the LM curve


      The LM curve shows what the interest rate should be at every level of income, so that
we have equilibrium in the money market.
      b) analyzing the LM curve
          The first point of the analysis of the LM curve is its slope. When is the LM curve
      shallow and when is it steep?
                   If money demand is highly elastic as regard income, a relatively small increase
      in income in percentage terms, would lead to a relatively large increase in the money
      demand in percentage terms. The equilibrium interest rate will increase significantly
      and as a result the LM curve will be very steep, as shown on Fig. 3.
                   If money demand is inelastic as regard income, a relatively large increase in
      income in percentage terms, would lead to a relatively small increase in the money
      demand in percentage terms. The equilibrium interest rate will increase just a little and
      as a result the LM curve will be very shallow, as shown on Fig. 4.
   i
                       MS                 i                    LM
                                                     E2

                       E2
       i2                                 i2

                              MD2               E1
    i1
                  E1                       i1

                            MD1




                                    M/P          Y1 Y                         Y
                                                     2




Fig. 3. Highly elastic money demand as regard income and a steep LM curve.




   i        MD1
                  MD2 MS                  i


                       E2
       i2                                 i2                             LM


    i1                                                                   E2
                  E1                       i1             E1




                                    M/P          Y1                 Y2        Y



Fig. 4. Highly inelastic money demand as regard income and a shallow LM curve


The second factor determining the slope of LM depends on the slope of the MD curve.
If the money demand is elastic as regard interest rate, the money demand curve is very
shallow and this will contribute to a greater slope of the LM curve. If money demand
is inelastic as regard interest rate, the MD curve is steep and this will contribute to a
steeper LM curve.
Thus, the slope of the LM curve depends on
      the elasticity of money demand as regard income and
      the elasticity of money demand as regard interest rate.


       If the money demand is elastic as regard income and inelastic as regard interest
rate, the LM curve is steep.
       If money demand is inelastic as regard income and elastic as regard interest
rate, the LM curve is shallow. Such an LM curve is usually observed during recessions.


       If the money market is in disequilibrium, at a given level of income the interest
rate is either lower, or greater than the equilibrium interest rate. Let’s take the case
when the level of the interest rate is below the equilibrium, as shown on Fig. 5. At
point A at a lower interest rate the opportunity cost of holding money is lower. The
public will prefer more liquidity. MD > MS. How can the public have more liquidity?
They will start selling their interest bearing assets (bonds). The excess supply of bonds
will drive their price down and the interest rate will increase until it gets to its
equilibrium point A’ on the LM curve.




               i
                                           A’


          i1        LM                          A



                                                    Y
                                      y1




       Fig. 5. MD>MS and a move to equilibrium interest rate.
       If the LM curve is very steep, the achievement of the equilibrium interest rate
assumes a significant reduction in the prices of financial assets and a respective
significant increase in the interest rate. If the LM curve is shallow, small activities in
the bonds market lead to equilibrium in the money market.
       The second point of the analysis of the LM curve is its location. Thus, we have
to analyze factors, determining the shifts in the LM curve.
                 Changes in money supply
       If MS increases at the same level of income, the equilibrium interest rate falls.
The equilibrium in the money market shifts from E1 to E2, as shown on Fig. 6 (left
panel). Respectively, point E1 shifts to point E2, at the same level of income (right
panel). The LM curve shifts to the right.




                                                                       LM1
                           MS1   MS2           i
          i
                                                                             LM2



                          E1                              E1
                                                   i1
         i1                      MD
                                               i2
         i2                                                    E2
                                 E2

                                       M/P                                   Y
                                                          Y




       Fig. 6. Increase in money supply and a shift in the LM curve to the right


       If MS falls, the LM curve shifts leftwards.


       Autonomous changes in money demand
       Autonomous increase in money demand means that it rises not because of the
increase in income, in the interest rate or in the price level, but because of a change in
an exogenous variable. For example, if holding bonds becomes more risky, the public
prefers liquidity as a less risky asset and money demand rises. At the same level of
income the equilibrium interest rate increases (Fig. 7 left panel) and respectively, the
LM curve shifts leftwards (Fig. 7 right panel).




              i
                          MS                      i                  LM2
                                                                           LM1


                                                           E2
                          E2
              i2

                                 MD2
                                                      i1
         i1
                                                  i2            E1
                    E1
                          MD1


                                    M/P                                          Y
                                                            Y




        Fig. 7. An increase in autonomous money demand and a leftward shift in LM
        If autonomous money demand falls, LM shifts rightwards.


2. The IS curve
    a) the equilibrium in the real sector as a function of the interest rate and the IS
curve


    In the analysis of the LM curve we studied the impact of income as a real sector
variable on the equilibrium in the monetary sector. Now we will shift our attention to
the impact of the interest rate as a monetary sector variable on the equilibrium in the
real sector.
        Under the assumption of a constant price level the equilibrium in the real sector
is best presented on the AE-Y diagram. On Fig. 8. AE1 = Y1 under a given price level.
                                     AE




                                                                   AE


                                      AE1




                                                450

                                            0            Y1             Y




                                    Fig. 8 AE – Y diagram


        AE = C + I + G + X – M. Investment spending depends on the interest rate. If
the interest rate falls, investment spending rises. Since investment spending is a
component of AE, aggregate expenditures increase with the reduction in the interest
rate. As a result, the equilibrium income rises from Y1 to Y2, as shown on the upper
panel of Fig. 9. Thus, we found a relationship between the interest rate and the
equilibrium income. We can develop in on a graphical model as shown on the lower
panel of Fig. 8. At the higher interest rate i1 the equilibrium income (AE + Y) is Y 1.
At a lower interest rate i2, the equilibrium income rises to Y2 . When we put together
all equilibrium points E as a function of the interest rate we derive the IS curve, as
shown on Fig. 8.
        The IS curve shows what should be the equilibrium income at every level of
the interest rate.
                                                   AE2
                                    E2
                                                     AE1
             AE


                               E1



                                     Y2                  Y
                          Y1
         i           IS

                               E1
             i1
                                              E2
             i2

                                                             Y
                          Y1             Y2



        Fig. 8. Deriving the IS curve
c) analyzing the IS curve
    The slope of the IS curve depends on the elasticity of investment demand as regard
the interest rate.
    If the investment demand is highly elastic as regard the interest rate, small changes
in the interest rate in percentage terms cause large changes in investment in percentage
terms. Respectively, AE changes significantly and the IS curve is shallow, as shown
on Fig. 9.
    If the investment demand is highly inelastic as regard the interest rate, significant
changes in the interest rate in percentage terms cause small changes in investment
demand in percentage terms and respectively in the AE. As a result, the IS curve is
steep, as shown on Fig. 10.
                                                  E2
                                                                        AE2
    AE



                                                                      AE1

                              E1



                                                  Y2                          Y
                         Y1
i                  IS
                                                                       E2
                              E1
    i1
    i2


                                                                              Y
                         Y1                            Y2



         Fig. 9. Elastic investment demand as a shallow IS curve




              AE
                                                                       AE2

                                        E2
                                                                      AE1

                                    E1



                                                            Y2                    Y
                               Y1
          i         IS

                                    E1
              i1
              i2
                                             E2


                                                                                  Y
                                   Y1                            Y2



         Fig. 10. Inelastic investment demand and a steep IS
               The economy is in disequilibrium when AE are larger or smaller than income
       for a given interest rate. If, for instance income is at a lower level for a given interest
       rate (at point A on Fig. 11), investment demand is motivated by this the low interest
       rate and AE > Y. As you remember, in this case inventories fall, production rises,
       unemployment falls and income increases. This process of increase in income will
       take place until it grows to its equilibrium point A’.




                   i
                            IS




                           A
                                            A’




                                                       Y


               Fig. 11. AE > Y and a move to equilibrium income


               If the economy is at a disequilibrium above the IS curve, AE < Y. Inventories
       increase, production falls, unemployment rises and income falls until it achieves its
       equilibrium point on the IS curve.
               Thus, the IS curve shows what should be the level of income at every level of
       the interest rate so that AE = Y.
               Factors, determining the location of the IS curve:
                      Injections
               Injections are assumed to be autonomous, which means that they do not depend
on the interest rate, or income. These could be government spending, autonomous investment
and exports.
          If for instance government spending rises at the same level of the interest rate, AE
increases and the equilibrium income increases. The equilibrium point A shifts to point A’. As
a result, the IS curve shifts to the right as shown on Fig. 12.




AE
                              A’             AE2
                                               AE1



                      A


                               Y2                  Y
                 Y1
 i          IS

                  A
     i1                                 A’


     i2

                                                       Y
                 Y1                Y2

Fig. 12. An increase in injections and a shift in the IS curve to the right.


          If injections fall the IS curve shifts leftwards.
                              leakages
          Leakages are assumed to be autonomous as regard interest rate. These are autonomous
savings, taxes and imports. If leakages increase, equilibrium income falls and the IS curve
shifts to the left.
          If leakages fall the IS curve shifts rightwards.
          3. Macroeconomic equilibrium in the real sector and in the monetary sector
              The LM curve shows what should be the equilibrium interest rate at every level of
          income. In other words, it shows the equilibrium in the monetary sector as a function
          of income.
                  The IS curve shows what should be the equilibrium income at every level of
          the interest rate. In other words, it shows the equilibrium in the real sector as a
          function of the interest rate.
       Macroeconomic equilibrium is achieved when there is an equilibrium in the monetary
       sector and at the same interest rate there is an equilibrium in the real sector.
       Graphically it is presented by the intersection of the IS and the LM curve. Fig. 13




                i
                                 LM
                    IS


                         Е
           ie




                          Ye           Y




       Fig. 13. Macroeconomic equilibrium in the real and in the monetary sector – the IS-
       LM equilibrium


The IS-LM equilibrium could be easily destroyed by any changes in the real or in the
monetary sector.
                        Changes in the real sector and macroeconomic equilibrium


       Let’s assume that exports increase. This injection will increase equilibrium income
and shift the IS curve to the right. The equilibrium in the real sector will be presented by IS2.
(Fig. 14) Point E1 shifts to point R. This destroys the equilibrium in the monetary sector. At
the higher income level Y2 i1 is lower than the equilibrium i. MD > MS. The public starts
selling bonds, because they prefer more liquidity. PV of bonds falls and the interest rate rises.
However, the increase in the interest rate affects the real sector, as well. At the higher interest
rate investment falls and as a result income falls. This is why the move is along the new IS
curve instead of being straight upwards to point K. The new equilibrium is achieved at E2.
       Thus, the increase of injections raises the equilibrium income, but it raises the
equilibrium interest rate as well.
        i
              IS1   IS2            LM

                              Е2
                                    K
                    Е1
   i1                               R




                     Y1        Y2       Y




Fig. 14. The impact of an increase in injections on the IS-LM equilibrium


            We can draw a conclusion that expansionary fiscal policy leads to an increase in
equilibrium income but to a rise in the equilibrium interest rate, as well.
            Restrictive fiscal policy (a leftward shift in the IS curve) would reduce both
equilibrium income and equilibrium interest rate.


                              Changes in the monetary sector and macroeconomic equilibrium


            Let’s assume that money supply rises at the same income. As a result, the equilibrium
interest rate falls and the LM curve shifts rightwards, as shown on Fig. 15. The equilibrium
point E1 shifts to point T. There is an equilibrium in the monetary sector, but in the real sector
the new low interest rate raises investment and AE > Y. Inventories fall and income rises.
However, the increase in income affects money demand and it increase as well. This is why
the move is along the new LM curve instead of being straight rightwards to point P. The new
equilibrium is achieved at E2.
            Thus, the increase in money supply reduces the equilibrium interest rate and raises the
equilibrium income.
    i
                       LM1
         IS

                             LM2
              E1



                       Е2

                   T         P


              Y1                   Y




Fig. 15. The impact of the increase in money supply on the IS-LM equilibrium


                   Expansionary monetary policy reduces the interest rate and at the same time
        raises the equilibrium income.
                   Monetary restriction ( a leftward shift in the LM curve) raises the equilibrium
        interest rate and reduces the equilibrium income.

				
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posted:4/17/2012
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