LM Model assignment help

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IS LM MODEL
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INVESTMENTS

• INVESTMENT IS NO LONGER AUTONOMOUS. IT IS NOW
  DEPENDENT ON INTEREST RATE.
• HIGHER THE INTEREST RATE, LOWER WILL BETHE
  INVESTMENT.
• I ? - b i
• b TELLS THE INTEREST RATE RESPONSIVENESS OF
  INVESTMENT

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AGGREGATE DEMAND

• AD ? - bi c( 1- t)Y
• Equilibrium in the goods market now requires AD
  Y
• Y ? - bi aG (?- bi) where aG 1-c(
  1-t)
• 1-c( 1-t)

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IS curve
It is the combination of all those points at
which the goods market is in equilibrium.
EQUATION OF IS CURVE i ? - Y b aG
b Reason why it is downward sloping It tells
as the interest rate falls, investment will
increase and thus output.
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Slope of the IS curve

• It depends on aG , b
• Higher the aG, flatter the IS curve, higher the
  change in output with a given change in interest
  rate.
• reason higher aG means higher MPC , higher
  MPC implies higher output.
• Higher b, flatter the IS curve, higher the change
  in output with a given change in interest rate.
• reason Higher b means that investment is
  highly sensitive to the interest rate, so small
  reduction can increase investment by a large
  amount and thus output.

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Disequilibrium points in IS curve

• E3 and E4 are disequilibrium points.
• At E3, interest rate is lower than the rate i1
  i.e. needed to attain equilibrium. At this point
  the investment will be higher. Thus, AD is higher
  than output.
• At E4, output is higher than the AD. Thus, excess
  supply of
• good

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Wealth constraint

• Wealth is stored either in form of money or in
  form of assets such as bonds.
• Money provide convenience for transactions. But
  it doesnt provide ay interest rate. Thus
  interest rate is the opportunity cost of holding
  money.
• Bonds provide interest rate but cant be used for
  transaction purposes.
• Real wealth real demand of money balances real
  demand of bonds.

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Real demand of money balances.

• L k Y hi
• Here k tells the income responsiveness to demand
  of real balances.
• h tells the interest rate responsiveness to
  demand of real balances.
• High income, allows individual to hold large
  amount of money. Thus, demand of real balances is
  positively related to income.
• Higher the interest rate, higher is the
  opportunity cost of holding money. Thus , demand
  of real balances is negatively related to income

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Real demand of money balances
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LM curve

• It is the combination of all those points at
  which money market is in equilibrium.
• With a given money supply, we can derive the LM
  curve from the demand of real balances curve.
• Reason why it is upward sloping
• as the interest rate increase, demand of bonds
  increase and thus demand of money falls. With the
  same level of money supply, inorder to achieve
  equilibrium income should increase.

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Derivation of LM curve
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LM curve
L money supply. kY hi m? / ?p kY m?
/ ?p hi i kY - m? / ?p h
h
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Slope of LM curve

• It depends on k and h
• Higher k, steeper the LM curve, smaller will the
  increase in the income due to given change in
  interest rate. Or large change in interest rate
  with a given change in income.
• reason if the income increase then the
  demand of money will rise by large amount. Thus,
  we require a huge increase in interest rate to
  bring the market into equilibrium.
• lower h, steeper the LM curve, smaller will the
  increase in the income due to given change in
  interest rate.
• Reason lower h means that if interest rates
  falls, the demand of money will rise by small
  amount. So, only small amount of increase in
  money ids required to bring the market into
  equilibrium.

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Points off the LM curve

• E1 is ESM
• Reason at higher interest rates, demand of bonds
  is high and thus there is excess supply of money.
• E3 is EDM
• Reason at same interest rate i1 income rise to
  Y2 . Thus, demand of money rise, causing excess
  demands of money.

E2
E1
i2
E3
E4
i1
Y1
Y2
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How the equilibrium output and interest rate are
determined

• They are determined by the intersection of two
  curves IS and LM.
• So that at equilibrium both the goods market and
  the asset market is in equilibrium.
• IS Y aG( ?- bi)
• LM i kY - m? / ?p
• h h
• Substituting the value of I from LM into Is will
  give

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What causes changes in equilibrium points

• Shifts in IS or LM curves , will bring changes in
  equilibrium points.
• Shift in LM due to changes in money supply
• Shift in IS due to change in autonomous spending.

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Suppose there is increase in autonomous spending

• This will shift IS curve rightwards.
• Change in Y is less than the aG
• Reason y L with the same
  money supply i I
• Y
• thus, both asset
• market and goods
• market clears

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