Supply and demand by bwzPATb

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									The IS-LM model



                  1
The model

   The IS-LM model was developed in
    1937 by John R. Hicks in an attempt
    to authentically interpret the “General
    Theory of Employment, Interest and
    Money”, the famous book published
    by John Maynard Keynes in 1936.


                                              2
The model

   The model tries to explain the movement of
    output and interest rate in the short run.
   To this end, it uses two curves: the IS (short
    for Investment and Saving) and the LM (short
    for Liquidity and Money).
   The IS curve represents equilibrium in the
    goods market.
   The LM curve represents equilibrium in the
    financial markets.
                                                 3
The IS curve

   We will try to use the goods market to
    establish a relationship between the interest
    rate and output.
   We already know [from introductory macro…]
    that output in a closed economy is the sum of
    consumption (C), investment (I) and
    government expenditures (G).


Y    =C+I+G
                                                4
The IS curve (the Keynesian cross)

   We also know that output (Y) is by definition equal
    to income and that it represents the amount of
    spending undertaken by households, firms and the
    government.
   But, how much do we want to spend? In other
    words, what is our demand for goods and services?
   If we denote demand with Z, then:
    Z=C+I+G
   So, demand (like output) is simply equal to the sum
    of consumption, investment and government
    expenditures.

                                                          5
The IS curve (the Keynesian cross)

   If we try to elaborate a bit more on the form
    of consumption, we can say that consumption
    must depend on our disposable income.
   Our disposable income must be equal to total
    income (Y) minus the taxes that we pay to
    the government (T).
   So, consumption is a function of our
    disposable income C(Y-T).


                                                6
The IS curve (the Keynesian cross)
   What if we want to be more specific about the functional form of the
    consumption function.
   Let’s assume that we must cosume something anyway in order to
    survive, like food. We call this amount autonomous consumption
    and let’s denote it by c0.
   The rest of our consumption depends on our disposable income (Y-
    T). It is reasonable to assume that we consume a percentage of our
    disposable income and that we save the rest of it. We call this
    percentage marginal propensity to consume (MPC) and let’s denote
    it by c1. Since we consume less than our disposable income, c1
    must be a number between 0 and 1. So, the non autonomous part of
    consumption must look like that: c1(Y-T).
   Therefore, consumption in general must be equal to:
    C = c0 + c1(Y-T)


                                                                       7
The IS curve (the Keynesian cross)
   If this is the form of consumption, then demand in total must be equal
    to:
    Z = C + I + G =>
    Z = c0 + c1(Y-T) + I + G =>
    Z = (c0 - c1T + I + G) + c1Y
   This last equation tells us that demand is equal to a sum of some
    variables that are exogenously given, namely:
    c0 : the amount of autonomous consumption,
    c1T: the amount of taxes times MPC,
    I: investment, which for now we can assume that it is constant, and
    G: government expenditures.
    We will call this whole expression (c0 - c1T + I + G), autonomous
    spending.
   It also tells us that demand is a positive function of income (Y) and,
    moreover, that the slope of this positive function is c1, which is less than
    one. So the slope of the demand is flatter than the 45o line (the slope of
    which is 1).

                                                                               8
The IS curve (the Keynesian cross)

   Now we have the first building block of the
    Keynesian cross. We are going to graph the
    demand as a function of income. We already
    proved earlier that the demand is a positive
    function of income and this is what we are
    going to graph now.




                                                   9
The IS curve (the Keynesian cross)

Z
                                                This is a picture of the demand
                                                as a function of income. The
                                      ZZ
                                                vertical intercept of the line ZZ
                                                which represents the demand, is
                               Slope: MPC       the autonomous spending and
                          1$
                                                its slope is the marginal
                                                propensity to consume.

    Vertical intercept:
    autonomous
    spending


                                            Y



                                                                               10
The IS curve (the Keynesian cross)

   Our economy is in equilibrium when actual
    production is equal to the demand, i.e. Y = Z.
   The only place that generally satisfies this
    equilibrium condition is the 45o line in our
    previous graph. So, our equilibrium must be
    on that line.




                                                 11
The IS curve (the Keynesian cross)

   If we assume further, that there is no
    inventory investment, then output (= income)
    must always be equal to the demand.
   So, in that case, not only are we always on
    the 45o line, but also always on the
    intersection of the demand function with the
    45o line, which is our equilibrium point.



                                                   12
The IS curve (the Keynesian cross)

           Actual
Z          Production        This is a picture of the
           Y=Z
                             Keynesian cross. We observe
                    ZZ
                             that in equilibrium, demand is
                             equal to income and production
Y*                           along the 45o line. In our model,
                             since there are no inventories,
                             we are always in equilibrium.




     45o

           Y*            Y



                                                             13
The IS curve (the multiplier)

   If we combine the equilibrium condition Y = Z,
    with the expression for the demand that we
    derived earlier, Z = c0 + c1(Y-T) + I + G, we get:
    Y = c0 + c1(Y-T) + I + G =>
    Y = c0 + c1Y - c1T + I + G =>
    Y - c1Y = c0 - c1T + I + G =>
    Y(1 - c1) = c0 - c1T + I + G =>
    Y = [1/(1 - c1)] (c0 - c1T + I + G)


                                                         14
The IS curve (the multiplier)

   We have already called the (c0 - c1T + I + G)
    part of the above equation, autonomous
    spending.
   Now, we will give a name to the 1/(1 - c1) part
    and we will call it the multiplier. The reason
    for that name is that this fraction is greater
    than one (remember that 0<c1<1).



                                                  15
The IS curve (the multiplier)

   Therefore, whatever the change is in any of the
    parts of autonomous spending, the change in
    output is a multiple of that change.
   So, if the government, e.g., decides to increase
    G by an amount x, this will result in an increase
    of Y by x times the multiplier.
   Graphically, the demand will shift up by as much
    as the change in autonomous spending (the
    vertical intercept) but output will increase by
    more than that.

                                                    16
The IS curve (the multiplier)

   The size of the multiplier obviously depends on c1,
    the marginal propensity to consume. The larger the
    MPC, the smaller the denominator and the larger the
    multiplier.
   Graphically, a large MPC corresponds to a steeply
    sloped demand curve. Shifts of a steep demand
    curve have large effects on income.
   A small MPC corresponds to a relatively flatter
    demand curve. Shifts of a flatter demand curve have
    relatively milder effects on income.
   We will now graph those two cases.

                                                      17
     The IS curve (the multiplier)
      The Keynesian cross                            The Keynesian cross
      with a steep demand                            with a flat demand
      (large MPC). The shift                         (small MPC). The shift
      in demand has a large    Actual                in demand has a          Actual
      effect on output.        Production            milder effect on         Production
Z                                               Z    output.
                               Y=Z        ZZ2                                 Y=Z
Y2
                                         ZZ1


                                                                                            ZZ2

Y1                                              Y2
                                                                                            ZZ1

                                                Y1

         45o                                         45o

                  Y1               Y2      Y            Y1       Y2                        Y


                                                                                           18
Deriving the IS curve

   The Keynesian cross is an important building
    block toward the IS curve but our mission is not
    accomplished yet.
   However, from this point the derivation of the IS
    curve is straightforward. It relies on the
    relaxation of an assumption that we made
    earlier, namely that the level of investment is
    constant.



                                                        19
Deriving the IS curve
   Constant investment is a clear simplification of the Keynesian cross
    model. We already know that investment is not constant but rather a
    negative function of the interest rate.
   At this point we also add that investment is also positively related
    with output. The line of reasoning is that as firms see their volume of
    sales going up, they will undertake more investment to
    accommodate this increase. But the level of sales is just proportional
    to output, since if output is increasing, more goods are going to be
    sold and if output is decreasing less goods are going to be sold. So,
    the bottom line is that we observe a positive relationship between
    the level of investment and the level of output.
   Therefore, investment is a negative function of the interest rate and
    a positive function of output. In symbols we write:
    I = I(Y,i)


                                                                         20
Deriving the IS curve

   Focusing on the interest rate, we can say that
    if the interest rate increases, this reduces the
    level of investment, shifts down the demand
    and consequently, through the multiplier,
    reduces the level of income.
   On the other hand, if the interest rate
    decreases, the level of investment increases,
    the demand shifts up and the level of income
    increases.

                                                   21
Deriving the IS curve

   We have therefore shown that there exists a
    negative relationship between the interest rate and
    income.
   This negative relationship is what is known as the IS
    curve.
   The mathematical form of the IS curve is called the IS
    relation and it is simply:
    Y = C(Y-T) + I(Y,i) + G
   A more specific form of this equation is the already
    familiar to us equation:
    Y = [1/(1 - c1)] (c0 - c1T + I + G)
   This is the graphical derivation of the IS curve.

                                                             22
  Deriving the IS curve
                                        Z               Actual
   A decrease in the interest rate                      Production
                                                        Y=Z
   increases the level of investment                                  ZZ2
   (Panel A), which shifts up the       Y2
   demand and increases income                                              Panel B
                                                                      ZZ1
   (Panel B). The IS curve sums up
   these movements in the goods         Y1
   market (Panel C).
                                             45o

                                                   Y1   Y2        Y
          i                             i

          i1
                                        i1
Panel A                                                                     Panel C
          i2
                                        i2                   IS
                                I

                I1         I2       I          Y1       Y2        Y

                                                                               23
Shifts of the IS curve

 As always in economics, here too we
  are interested in curve shifts.
 So, we are going to mix things up a
  bit, shift the curves around and see
  what happens.



                                         24
Shifts of the IS curve

   So, what could possibly move the IS curve?
   First, let’s recall the IS relation, Y = C(Y-T) + I(Y,i) + G, the
    general equation that describes the IS curve.
   Which part of this equation could move the IS curve?
   Maybe, it’s better if we start by what could by no means
    move the IS curve: income (Y) and the interest rate (i).
   Why? Because, these are the endogenous variables of our
    model. These are the variable that we are trying to explain.
    They are the variables on the two axes of our graph (like
    price and quantity in a supply and demand diagram). So, if
    these two variables move, we move along the curve. We
    don’t shift it.


                                                                    25
Shifts of the IS curve

    So, what could move the IS curve is any of the other
     variables that are exogenous, i.e. they are taken as given
     outside the model, namely:
a)   G, government expenditures (variable controlled by the
     government),
b)   T, taxes (variable controlled by the government),
c)   C, consumption patterns that are independent of disposable
     income, if for example, the households decide to consume
     more because an asteroid is going to hit the earth (variable
     controlled by household preferences), and
d)   I, investment patterns that are independent of the interest
     rate and income, if for example firms go into an unexplained
     investing spree (variable controlled by the animal spirits of
     the investors).
                                                                     26
Shifts of the IS curve

   Out of those four parameters, we are mostly
    interested in the first two (G and T), because it is
    only those that policy makers can control. The other
    two cannot be affected directly by government
    policies.
   So, our analysis will be primarily focused on
    government expenditures and taxes.
   However, just bear in mind that changes in
    consumption and investment patterns affect the IS
    curve in exactly the same way as changes in
    government expenditures.

                                                       27
What happens if the government decides to increase
government expenditures (G↑)?

   We will use the Keynesian cross to explore the
    effects of such a move.
   First, let’s recall the equation for the demand that we
    derived earlier:
    Z = (c0 - c1T + I + G) + c1Y
   If, ceteris paribus, the government decides to
    increase G (by ΔG), then it is obvious that the
    demand curve would shift up by an amount equal to
    ΔG. The vertical intercept would move up by ΔG but
    the slope would remain the same.

                                                          28
What happens if the government decides to increase
government expenditures (G↑)?

   But would happen to income after this shift of the
    demand curve?
   Now, we have to recall the IS relation in the specific
    form that we also mentioned earlier:
    Y = [1/(1 - c1)] (c0 - c1T + I + G)
   If G↑, then Y would go up by as much as ΔG times the
    multiplier 1/(1 - c1), so by more than ΔG.
   So, it looks like it’s a good deal for the government to
    increase G, since with an initial amount of increase, it
    can get income to increase more through the
    multiplier.
                                                           29
What happens if the government decides to increase
government expenditures (G↑)?

   But, what does this mean for the IS curve?
   It means that the increase in government
    expenditures caused an increase in income
    for a given level of interest rate. Remember
    that the interest rate did not move at all.
   This corresponds to a shift of the IS curve to
    the right. For a given level of interest rate
    now we have more income.
   Let’s look at this effect graphically.
                                                     30
  The effects of G↑
          Z                  Actual
                             Production
                             Y=Z
                                                ZZ2
          Y2
Panel A                                ΔG               An initial increase in G shifts up
                                                ZZ1
                                                        the demand by ΔG, which
          Y1                                            increases income by ΔG/(1 - c1)
                                    ΔY=ΔG[1/(1 - c1)]   in Panel A. This means that for a
                    o
                   45
                                                        given level of interest rate, the
                        Y1      Y2          Y           IS curve in Panel B must shift to
          i
                                                        the right by ΔG/(1 - c1).
                                    ΔY=ΔG[1/(1 - c1)]

Panel B       i*



                                      IS1       IS2

                        Y1     Y2           Y

                                                                                        31
What happens if the government decides to decrease
government expenditures (G↓)?

   The process that we follow must be clear by
    now.
   Again we use the demand equation:
    Z = (c0 - c1T + I + G) + c1Y
   If, ceteris paribus, the government decides to
    decrease G (by ΔG), then it is obvious that
    the demand curve would shift down by an
    amount equal to ΔG. The vertical intercept
    would move down by ΔG but the slope would
    remain the same.
                                                     32
What happens if the government decides to decrease
government expenditures (G↓)?

   Then we use the IS relation to see what happens to
    income:
    Y = [1/(1 - c1)] (c0 - c1T + I + G)
   If G↓, then Y would go down by as much as ΔG times
    the multiplier 1/(1 - c1), so by more than ΔG.
   This means that the decrease in government
    expenditures caused a decrease in income for a given
    level of interest rate.
   This corresponds to a shift of the IS curve to the left.
    For a given level of interest rate now we have less
    income.
                                                           33
  The effects of G↓
          Z                  Actual
                             Production
                             Y=Z
                                                ZZ1
          Y1
Panel A                                ΔG               An initial decrease in G shifts
                                                ZZ2
                                                        down the demand by ΔG, which
          Y2                                            decreases income by ΔG/(1 - c1)
                                    ΔY=ΔG[1/(1 - c1)]   in Panel A. This means that for a
                    o
                   45
                                                        given level of interest rate, the
                        Y2      Y1          Y           IS curve in Panel B must shift to
          i
                                                        the left by ΔG/(1 - c1).
                                    ΔY=ΔG[1/(1 - c1)]

Panel B       i*



                                      IS2       IS1

                        Y2     Y1           Y

                                                                                       34
What happens if the government decides to decrease
taxes (T↓)?

   Again we use the demand equation:
    Z = (c0 - c1T + I + G) + c1Y
   If, ceteris paribus, the government decides to
    decrease T by ΔT (so ΔT is negative), then it
    is obvious that the demand curve would shift
    up by an amount equal to -c1ΔT. The vertical
    intercept would move up by -c1ΔT but the
    slope would remain the same.


                                                     35
What happens if the government decides to decrease
taxes (T↓)?

   Then we use the IS relation to see what happens to
    income:
    Y = [1/(1 - c1)] (c0 - c1T + I + G)
   If T↓, then Y would go up by as much as ΔT times [- c1/(1 -
    c1)].
   The expression [- c1/(1 - c1)] is the version of the multiplier
    when taxes are changed by the government.
   We observe that in the numerator of this expression there
    is c1, which corresponds to a number that is less than one.
    Therefore, if we compare this version of the multiplier with
    the general version [1/(1 - c1)], we conclude that the
    general version is larger. This means that expansionary
    fiscal policy is normally more effective if conducted through
    increases in government expenditures rather than
    decreases in taxation.
                                                                  36
What happens if the government decides to decrease
taxes (T↓)?

   So, in effect the decrease in taxes caused
    an increase in income for a given level of
    interest rate.
   This corresponds to a shift of the IS curve
    to the right. For a given level of interest
    rate now we have more income.




                                                     37
  The effects of T↓
          Z                  Actual
                             Production
                             Y=Z
                                                ZZ2
          Y2                                               An initial decrease in T shifts up
Panel A                               -c1ΔT
                                                ZZ1        the demand by -c1ΔT, which
                                                           increases income by
          Y1                                               ΔT[- c1/(1 - c1)] in Panel A. This
                                    ΔY=ΔT[- c1/(1 - c1)]
                    o
                   45                                      means that for a given level of
                        Y1      Y2          Y              interest rate, the IS curve in
          i
                                                           Panel B must shift to the right by
                                                           ΔT[- c1/(1 - c1)].
                                    ΔY=ΔT[- c1/(1 - c1)]

Panel B       i*



                                      IS1       IS2

                        Y1     Y2           Y

                                                                                           38
What happens if the government decides to increase
taxes (T↑)?

   Again we use the demand equation:
    Z = (c0 - c1T + I + G) + c1Y
   If, ceteris paribus, the government decides to
    increase T by ΔT (now ΔT is positive), then it
    is obvious that the demand curve would shift
    down by an amount equal to -c1ΔT. The
    vertical intercept would move down by -c1ΔT
    but the slope would remain the same.


                                                     39
What happens if the government decides to increase
taxes (T↑)?

   Then we use the IS relation to see what happens to
    income:
    Y = [1/(1 - c1)] (c0 - c1T + I + G)
   If T↑, then Y would go down by as much as ΔT times
    [- c1/(1 - c1)].
   So, in effect the increase in taxes caused a
    decrease in income for a given level of interest rate.
   This corresponds to a shift of the IS curve to the left.
    For a given level of interest rate now we have less
    income.

                                                          40
  The effects of T↑
          Z                  Actual
                             Production
                             Y=Z
                                                ZZ1
          Y1
Panel A                                -c1ΔT               An initial increase in T shifts
                                                ZZ2        down the demand by -c1ΔT,
                                                           which decreases income by
          Y2
                                    ΔY=ΔT[- c1/(1 - c1)]   ΔT[- c1/(1 - c1)] in Panel A. This
                    o
                   45
                                                           means that for a given level of
          i
                        Y2      Y1          Y              interest rate, the IS curve in
                                                           Panel B must shift to the left by
                                                           ΔT[- c1/(1 - c1)].
                                    ΔY=ΔT[- c1/(1 - c1)]

Panel B       i*



                                      IS2       IS1

                        Y2     Y1           Y

                                                                                                41
To sum up IS shifts…
           Initial
                     Shift of IS
          Change
            G↑         Right

            G↓          Left

            T↓         Right

            T↑          Left



                                   42
The LM curve

   To get to the LM curve, we have to use financial
    markets and go through the theory of liquidity
    preference. We have to understand why people
    decide to hold money in their pockets or in non-
    interest bearing bank accounts (checking
    accounts). In other words why we choose to
    forgo the interest rate that the banks offer us
    when we hold illiquid bank products (e.g. CDs,
    etc.).


                                                       43
The LM curve

   The answer is very simple: convenience and
    security.
   It is true that having highly liquid assets, such as
    cash or immediately available, through an ATM,
    checking accounts makes our life easier.
   Imagine if we had to go to the bank to liquidate
    part of our investments every time we needed to
    go to the grocery store. Also having liquid assets
    provide us with a sense of security, that we will,
    no matter what, have some money immediately
    available in case an emergency (or a new
    financial opportunity) occurs.

                                                       44
The LM curve

   Since we have answered why, now we have
    to answer how much money we hold.
   To answer this question, first we have to
    define what is money.
   Generally, for our purposes money is cash
    and checking (non interest bearing) bank
    accounts. This is known as M1.
   There are also other measures of money but
    we are not really interested in them.
                                                 45
The LM curve

   Then we have to come up with a measure of
    money. We call the measure of money with
    the interesting name: real money balances or
    real money stock (M/P).
   To determine how much money we hold, as
    always in economics, we will look for an
    equilibrium.
   The equilibrium between the supply of real
    money balances and the demand for real
    money balances.
                                               46
The LM curve (Money supply)

   The supply of real money balances is easy
    because it is exogenously given. It is
    controlled by the central bank through the
    ways that we learned in introductory macro
    (open market operations, discount rate,
    required reserves ratio). So the supply is just
    a number decided by the central bank and we
    do not need to worry about it.


                                                  47
The LM curve (Money supply)

  i
                    Since money supply (Ms) is
           Ms       independent of the interest rate,
                    it can be represented by a
                    vertical line. The amount of
                    money supplied only depends
                    on the decision of the central
                    bank and nothing else.




                  M/P


                                                    48
The LM curve (Money demand)
   The demand for real money balances is more complicated. The
    amount of real money balances that we demand, depends on
    what?
   Well, first it depends on income (Y). The more income in an
    economy, the more transactions will occur and the more money
    we will demand to effect these transactions. So, there is a
    positive relationship between demand for real money balances
    and income.
   But also, it depends on the interest rate. The higher the interest
    rate on illiquid financial products (e.g. CDs), the less money we
    will demand, since money pays no interest whereas these illiquid
    products do. Because we do not want to lose a lot of interest, as
    interest rates go up, we will hold less and less real money
    balances. So, there is a negative relationship between demand
    for real money balances and interest rate.

                                                                     49
The LM curve (Money demand)

   If we wanted to write down in symbols what we
    just said in words, we would write this
    expression for money demand:
    (M/P)d = L(i,Y)
   Demand for real money balances is a function
    L of the interest rate and income.
   Or, if we want to assume that money demand
    is exactly proportional to the level of income in
    an economy, we can even more simply write:
    (M/P)d = YL(i)
                                                    50
The LM curve (Money demand)

  i
                       So, if we want to graph the
                       relationship between money
                       demand (Md) and the interest
                       rate, it must be represented by a
                       downward sloping curve. As we
                       just said, money demand
                       depends negatively on the
                       interest rate.

                Md = YL(i)



                    M/P


                                                      51
The LM curve (Money supply and money
demand in equilibrium)
   So, now that we have all the pieces, we can equate money
    demand and money supply and find the equilibrium in the money
    market, i.e. the equilibrium amount of real money balances in our
    economy and the equilibrium level of interest rate.
   Mathematically:
    Ms = Md =>
    (M/P)s = (M/P)d =>
    (M/P)s = YL(i)
   This expression is what is called the LM relation. It is the
    mathematical representation of the LM curve.
   Note that for the purposes of these notes, the symbols Ms and Md
    refer to real money supply and real money demand, unless
    otherwise specified.


                                                                    52
The LM curve (Money supply and money
demand in equilibrium)
   i
                                 Therefore in equilibrium if we
                     s
                 M               equate money supply and
                                 money demand, we get the
                                 equilibrium level of real money
                                 balances and the equilibrium
                                 level of interest rate.
       i*



                         Md = YL(i)


            (M/P)*
                              M/P


                                                                   53
Deriving the LM curve

   From here the crucial step in order to derive the LM
    curve is to bring income (Y) into play.
   We have already said that money demand depends
    positively on income.
   This means that for a given level of interest rate, a
    higher income would result to a shift of the money
    demand to the right. If income increases, for a given
    level of interest rate, I engage in more transactions
    and I demand more real money balances.
   The picture is as follows:

                                                        54
Deriving the LM curve

   i
                                  So, we notice that a higher level
                     s
                 M                of income (Y2 >Y1), by shifting
                                  the money demand to the right,
       i2
                                  is associated with a higher level
                                  of interest rate.

       i1
                         Md = Y2L(i)


                         Md = Y1L(i)


            (M/P)*
                            M/P


                                                                  55
Deriving the LM curve

   Therefore we have proved that, through the
    channel of financial markets and the liquidity
    preference theory, there is a positive
    relationship between the interest rate and
    output.
   This positive relationship between interest
    rate and output is represented by the LM
    curve.


                                                     56
         Deriving the LM curve

            Panel A                          Panel B
                                                                In Panel A, a higher level of
i                                   i                           income (Y2 >Y1) shifts the
                Ms
                                                       LM       money demand to the right
    i2                                                          and results in a higher level
                                        i2
                                                                of interest rate. In Panel B,
                      Md = Y2L(i)                               the LM curve sums up this
    i1                                                          positive relationship between
                                        i1
                                                                income and interest rate.
                      Md = Y1L(i)

             (M/P)*                             Y1     Y2
                       M/P                                  Y




                                                                                        57
Shifts of the LM curve

   Now we will explore what shifts the LM curve.
   To this end, we have to recall the LM relation,
    (M/P)s = YL(i), the equation that describes the LM
    curve.
   Starting again by what could by no means
    move the LM curve, it is now very easy to say:
    income (Y) and the interest rate (i). Exactly like
    in the IS case, if these two variables move, we
    move along the curve. We don’t shift it.

                                                         58
Shifts of the LM curve
    So, what could move the LM curve is any of the other variables that are
     exogenous, i.e. they are taken as given outside the model, namely:
a)   Ms, the money supply controlled by the central bank (note that the central
     bank controls the nominal money supply, but given that we can assume
     constant prices, effectively the central bank can control the real money
     supply),
b)   P, the level of prices, and
c)   Md, the demand for real money balances, BUT only to the extent that this is
     affected by factors other than the interest rate and income. So, if just like
     that, for some weird reason, we start demanding more or less money for a
     given level of interest rate and income. E.g. because an asteroid is going to
     hit the earth and we want to engage in more transactions in the last days of
     our earthly existence, we increase our demand for money.
    Since, out of those factors, the policy maker can directly control only the
     money supply (case (a)) through monetary policy, we are mostly interested
     in changes in this first factor. However, for reasons of completeness, we will
     examine here the other two factors as well (cases (b) and (c)).



                                                                                  59
What happens if the central bank decides to increase the
money supply (Ms↑)?

   If the central bank decides to increase the
    money supply, this would certainly mean that
    the interest rate would decrease.
   So, for a given level of income, now we would
    have a lower level of interest rate.
   This necessarily means that the LM curve
    must shift down.



                                                       60
         The effects of Ms↑


            Panel A                                 Panel B
                                                                            In Panel A, the increase in
i               s
             (M )1        s
                       (M )2               i                                money supply shifts the
                                                                            money supply to the right
                                                            LM1   LM2       and results in a lower level
                                                                            of interest rate. In Panel B,
    i1                                         i1
                                                                            the LM curve shifts down
                                                                            since, for the same level of
    i2                                                                      income, now we have a
                                               i2
                              Md = YL(i)                                    lower level of interest rate.

           (M/P)1    (M/P)2                            Y*
                               M/P                                      Y




                                                                                                    61
What happens if the central bank decides to decrease
the money supply (Ms↓)?

   If the central bank decides to decrease the
    money supply, this would certainly mean that
    the interest rate would increase.
   So, for a given level of income, now we would
    have a higher level of interest rate.
   This necessarily means that the LM curve
    must shift up.



                                                       62
         The effects of Ms↓


            Panel A                                 Panel B
                                                                        In Panel A, the decrease in
i               s
             (M )2        s
                       (M )1               i                            money supply shifts the
                                                            LM2
                                                                        money supply to the left and
                                                                  LM1   results in a higher level of
                                                                        interest rate. In Panel B, the
    i2                                         i2
                                                                        LM curve shifts up since, for
                                                                        the same level of income,
    i1                                                                  now we have a higher level
                                               i1
                              Md = YL(i)                                of interest rate.

           (M/P)2    (M/P)1                            Y*
                               M/P                                  Y




                                                                                                  63
What happens if the level of prices goes down (P↓)?


   Since we are interested in real money balances, a
    decrease in the level of prices effectively means that
    the supply of real money (M/P)s increases. The
    supply of real money balances increases without the
    intervention of the central bank but only due the
    price change.
   Therefore, because of the increase in money
    supply, the interest rate decreases.
   So, for a given level of income, now we would have
    a lower level of interest rate.
   This necessarily means that the LM curve must shift
    down.


                                                         64
         The effects of P↓

                                                                           In Panel A, the decrease in
            Panel A                                Panel B
                                                                           prices (P2< P1) causes the
i            (M/P1) s (M/P2) s            i                                money supply to increase
                                                                           and shift to the right. This
                                                           LM1   LM2       results in a lower level of
                                                                           interest rate. In Panel B, the
    i1                                                                     LM curve shifts down since,
                                              i1
                                                                           for the same level of income,
    i2                                                                     now we have a lower level of
                                              i2                           interest rate.
                             Md = YL(i)

           (M/P)1   (M/P)2                            Y*
                              M/P                                      Y




                                                                                                    65
What happens if the level of prices goes up (P↑)?


   An increase in the level of prices effectively means
    that the supply of real money (M/P)s decreases. The
    supply of real money balances decreases without
    the intervention of the central bank but only due the
    price change.
   Therefore, because of the decrease in money
    supply, the interest rate increases.
   So, for a given level of income, now we would have
    a higher level of interest rate.
   This necessarily means that the LM curve must shift
    up.

                                                        66
         The effects of P↑

                                                                           In Panel A, the increase in
            Panel A                                Panel B
                                                                           prices (P2>P1) causes the
i            (M/P2) s (M/P1) s            i                                money supply to decrease
                                                                           and shift to the left. This
                                                           LM2   LM1       results in a higher level of
                                                                           interest rate. In Panel B, the
    i2                                                                     LM curve shifts up since, for
                                              i2
                                                                           the same level of income,
    i1                                                                     now we have a higher level
                                              i1                           of interest rate.
                             Md = YL(i)

           (M/P)2   (M/P)1                            Y*
                              M/P                                      Y




                                                                                                     67
What happens if money demand decreases (Md↓)?


   If money demand decreases for a given level
    of income and interest rate (i.e. the asteroid
    case), then the money demand curve shifts to
    the left. This results in a lower interest rate.
   So, for a given level of income, now we would
    have a lower level of interest rate.
   This necessarily means that the LM curve
    must shift down.


                                                   68
         Effects of Md↓


            Panel A                     Panel B
                                                  LM1       In Panel A, a decrease in the
i                              i                            demand for money shifts the
                Ms                                LM2
                                                            money demand to the left
    i1                                                      and results in a lower level
                                   i1
                                                            of interest rate. In Panel B,
                       (Md)1
                                                            the LM curve shifts down
    i2                             i2                       since, for the same level of
                                                            income, now we have a
                      (Md)2                                 lower level of interest rate.

             (M/P)*                        Y*
                       M/P                              Y




                                                                                    69
What happens if money demand increases (Md↑)?


   If money demand increases for a given level
    of income and interest rate (again the
    asteroid case), then the money demand shifts
    to the right. This results in a higher interest
    rate.
   So, for a given level of income, now we would
    have a higher level of interest rate.
   This necessarily means that the LM curve
    must shift up.
                                                  70
         Effects of Md↑


            Panel A                     Panel B
                                                  LM2       In Panel A, an increase in
i                              i                            the demand for money shifts
                Ms                                LM1
                                                            the money demand to the
    i2                                                      right and results in a higher
                                   i2
                                                            level of interest rate. In
                       (Md)2
                                                            Panel B, the LM curve shifts
    i1                                                      up since, for the same level
                                   i1
                                                            of income, now we have a
                      (Md)1                                 higher level of interest rate.

             (M/P)*                        Y*
                       M/P                              Y




                                                                                     71
To sum up LM shifts…
       Initial change   Shift of LM
            M s↑          Down
            Ms↓             Up
            P↓            Down
            P↑              Up
           Md↓            Down
           Md↑              Up



                                      72
The IS-LM model in all its glory…

   i
                  LM            If we put the IS and the LM curves
                                together in a diagram we are able
                                to determine the equilibrium level
                                of output and interest rate in a
   i*                           closed economy.



                       IS




             Y*             Y


                                                             73
So, what happens if we shift the curves in
the full scale model?
   Now it’s time to use our model to see what
    happens when we use fiscal or monetary
    policy in order to affect different macro
    variables.
   We will examine in turn fiscal expansion and
    contraction and monetary expansion and
    contraction.



                                                   74
Fiscal expansion

   As we already know, a fiscal expansion is a
    situation where the government increases
    government expenditures (G) or reduces
    taxes (T).
   As we have mentioned, this corresponds to a
    shift of the IS curve to the right.
   The result is a higher a level of output and a
    higher level of interest rate.


                                                 75
     Fiscal expansion

i

                               LM              If the government engages in a
                                               fiscal expansion, the IS curve
                                               shifts to the right. The LM stays
    i2                     B                   still. The equilibrium moves from A
                                               to B indicating a higher level of
    i1
                                               output and a higher level of
                  A
                                               interest rate.

                               IS1       IS2




             Y1       Y2
                                     Y


                                                                                     76
Fiscal expansion elaborated…
   Now, let’s ask ourselves why did this happen?
   The first move was made by the government that chose to
    embark on a fiscal expansion (by raising G or cutting T).
    What’s the result?
   Either way (G↑ or T↓), the demand (Z) increases and
    therefore output (= income) increases (remember the
    Keynesian cross). What’s next?
   The increase in income, through the LM relation, increases
    the demand for money leading to a higher interest rate
    (remember the money supply and demand graph). What’s
    next?
   The higher interest rate, by reducing private investment,
    reduces demand and output but not enough to offset the
    positive effect of the fiscal expansion on them.


                                                                 77
Fiscal expansion elaborated…
    So now, we have a clear picture of how all our variables moved:
a)   C: consumption is positively affected either the fiscal expansion
     was effected by an increase in G or through a reduction in T
     (disposable income increases in both cases).
b)   I: the movement of investment is ambiguous because on the one
     hand output went up and we know that this boosts I, but on the
     other hand the interest rate increased and we also know that this
     shrinks investment. So the net effect is ambiguous.
c)   G: government expenditures went up if the fiscal expansion was
     effected by an increase in G or were unaffected if the fiscal
     expansion was effected by a decrease in T.
d)   T: taxes went down if the fiscal expansion was effected by a
     decrease in T or were unaffected if the fiscal expansion was
     effected by an increase in G.


                                                                         78
Aggregate effects of a fiscal expansion
conducted by G↑

      Y     i     C     I     G     T

      ↑     ↑     ↑     ?     ↑     0




                                          79
Aggregate effects of a fiscal expansion
conducted by T↓

      Y     i     C     I     G     T

      ↑     ↑     ↑     ?     0     ↓




                                          80
Fiscal contraction

   As we already know, a fiscal contraction is a
    situation where the government decreases
    government expenditures (G) or increases
    taxes (T).
   This corresponds to a shift of the IS curve to
    the left.
   The result is a lower level of output and a
    lower level of interest rate.


                                                     81
     Fiscal contraction

i

                            LM              If the government engages in a
                                            fiscal contraction, the IS curve
                                            shifts to the left. The LM stays
    i1                      A               still. The equilibrium moves from A
                                            to B indicating a lower level of
    i2             B                        output and a lower level of
                                            interest rate.

                                      IS1
                            IS2



              Y2       Y1
                                  Y


                                                                                  82
Fiscal contraction elaborated…
   Now, let’s ask again ourselves why did this happen?
   The first move was made by the government that chose to
    embark on a fiscal contraction (by reducing G or increasing
    T). What’s the result?
   Either way (G↓ or T↑), the demand (Z) decreases and
    therefore output (= income) decreases (remember the
    Keynesian cross). What’s next?
   The decrease in income, through the LM relation, decreases
    the demand for money leading to a lower interest rate
    (remember the money supply and demand graph). What’s
    next?
   The lower interest rate, by increasing private investment,
    increases demand and output but not enough to offset the
    negative effect of the fiscal expansion on them.


                                                                  83
Fiscal contraction elaborated…
    So now, we have a clear picture of how all the variables moved:
a)   C: consumption is negatively affected either the fiscal contraction
     was effected by a decrease in G or through an increase in T
     (disposable income decreases in both cases).
b)   I: the movement of investment is ambiguous because on the one
     hand output went down and this decreases I, but on the other
     hand the interest rate decreased and this boosts investment. So
     the net effect is ambiguous.
c)   G: government expenditures went down if the fiscal contraction
     was effected by a decrease in G or were unaffected if the fiscal
     contraction was effected by an increase in T.
d)   T: taxes went up if the fiscal expansion was effected by an
     increase in T or were unaffected if the fiscal expansion was
     effected by a decrease in G.


                                                                           84
Aggregate effects of a fiscal contraction
conducted by G↓

      Y     i     C      I    G     T

      ↓     ↓     ↓     ?     ↓     0




                                            85
Aggregate effects of a fiscal contraction
conducted by T↑

      Y     i     C      I    G     T

      ↓     ↓     ↓     ?     0     ↑




                                            86
Monetary expansion

   We already know that a monetary expansion
    is a situation where the central bank
    increases the money supply.
   We also know that this shifts the LM curve
    down.
   The result is a higher a level of output and a
    lower level of interest rate.



                                                     87
     Monetary expansion

i
               LM1           LM2       If the central bank engages in a
                                       monetary expansion, the LM
                                       curve shifts down. The IS stays
          A                            still. The equilibrium moves from A
    i1
                                       to B indicating a higher level of
    i2              B                  output and a lower level of
                                       interest rate.
                        IS




          Y1   Y2                  Y


                                                                             88
Monetary expansion elaborated…

   Now we have to tell the story again.
   The first move was made by the central bank that
    chose to expand the money supply. What’s the
    result?
   By remembering the money supply and money
    demand graph, we conclude that this leads to a
    lower interest rate. What’s next?
   The lower interest rate in turn leads to higher
    investment and thus, higher demand and output
    (remember the Keynesian cross).
                                                       89
Monetary expansion elaborated…
    So now, we have a clear picture of how all our
     variables moved:
a)   C: consumption increases since income went up and
     so our disposable income (Y-T) went up.
b)   I: investment unambiguously increased because we
     saw that the interest rate went down (this increases
     investment) and also income went up (this also
     increases investment). So a monetary expansion
     gives a twofold boost to investment (compare that to
     the fiscal expansion which had an ambiguous effect
     on investment).
c)   G: government expenditures are unchanged.
d)   T: taxes are unchanged.

                                                        90
Aggregate effects of a monetary expansion



     Y      i    C     I    G     T

      ↑    ↓     ↑    ↑     0     0




                                        91
Monetary contraction

   We already know that a monetary contraction
    is a situation where the central bank
    decreases the money supply.
   We also know that this shifts the LM curve
    up.
   The result is a lower level of output and a
    higher level of interest rate.



                                              92
     Monetary contraction

i
                 LM2
                              LM1       If the central bank engages in a
                                        monetary contraction, the LM
                                        curve shifts up. The IS stays still.
           B                            The equilibrium moves from A to
    i2
                                        B indicating a lower level of output
    i1               A                  and a higher level of interest rate.

                         IS




           Y2   Y1                  Y


                                                                               93
Monetary contraction elaborated…

   Let’s tell the story for one last time.
   The first move was made by the central bank that
    chose to contract the money supply. What’s the
    result?
   By remembering the money supply and money
    demand graph, we conclude that this leads to a
    higher interest rate. What’s next?
   The higher interest rate in turn leads to lower
    investment and thus, lower demand and output
    (remember the Keynesian cross).
                                                       94
Monetary contraction elaborated…

    So now, we have a clear picture of how all our
     variables moved:
a)   C: consumption decreases since income went down
     and so our disposable income (Y-T) went down.
b)   I: investment unambiguously decreased because we
     saw that the interest rate went up (this decreases
     investment) and also income went down (this also
     decreases investment). So a monetary contraction
     gives a twofold blow to investment.
c)   G: government expenditures are unchanged.
d)   T: taxes are unchanged.


                                                      95
Aggregate effects of a monetary
contraction

      Y     i    C     I    G     T

      ↓    ↑     ↓     ↓    0     0




                                      96

								
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