Derivation of the IS:LM curves PDF

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Derivation of the IS/LM curves

The derivation of the is curve for a closed economy

a

b

d

c

• An increase in income leads to an increase in leakages in figure (a) this needs to be matched by an increase in injections (J) in figure (b).

• An increase in injections can occur if there is a fall in the rate of interest from r1 to r2 in figure (c) which increases investment.

• Figures (d) shows that rate of interest at and level of national income for which leakages and injections are equal or aggregate demand equal aggregate supply.

steepness of the is curve The steepness of the IS curve is dependent on: 1. The interest elasticity of the demand for investment. The less sensitive the level of ! investment is to changes in the rate of interest the steeper the ! IS curve 2. The rate of taxation the higher the rate of taxation the steeper the curve 3. The marginal propensity to save, the higher the marginal propensity to save the steeper the curve

• The IS curve shows different combinations of the rate of interest and level of national income for which the goods market is in equilibrium.

• A rise in the national income will require a lower rate of interest to raise aggregate demand sufficiently to absorb the increase aggregate supply (or national income)

!

!

Factors which shift the is curve Factors which can shift the IS curve: 1. A decreases autonomous savings (i.e. increase in autonomous consumption) which will require a higher level of income for a given rate of interest so as to raise leakages 2. An increase in government expenditure G, which will require a higher level of income for a given rate of interest so as to raise leakages 3. An increase in investment expenditure I, which will require a higher level of income for a given rate of interest so as to raise leakages

The derivation of the LM curve for a closed economy

!

!

• An increase in income leads to an increase in the transactions demand for money figure (a).

• The money supply in figure (b) is given by the distance OM on both the horizontal and vertical axis.

• An increase in the transaction demand from Mt1 to Mt2 when the money stock is fixed has to be met by a decrease in the speculative demand for money.

• In figure (c) we can see that in order to reduce the speculative demand for money from Msp1 to Msp2 we require the interest rate to rise from r1 to r2.

• Hence a rise in income from Y1 to Y2 requires a rise in the rate of interest to maintain money demand equal to money supply.

steepness of the LM curve The steepness of the LM curve is dependent on: 1. The interest elasticity of the demand for money. The less sensitive the level of money demand (the more interest inelastic money demand) is to changes in the rate of interest, the steeper the LM curve

• The LM curve shows different combinations of the rate of interest and level of national income for which the money market is in equilibrium.

• A rise in the national income will require a higher rate of interest since the increase in the transactions demand for money needs to be met by a similar fall in the speculative demand for money for a given money supply, to ensure money demand remains equal to money supply

Factors which shift the LM curve Factors which can shift the LM curve: 1. An increase in the money supply will shift the LM curve to the right. Since it will require a higher level of income for a given rate of interest so as to raise the transactions demand for money to match the increase in the money supply 2. A fall in the price level which will shift the LM curve to the right. Since it will reduce the transactions demand for money. Hence it will require a higher level of income for a given rate of interest so as to raise money demand back to its original level and so maintain equilibrium in the money

Equilibrium in the closed economy using the is-lm model The IS-LM model shows how the level of national income and the interest rate are determined simultaneously by equilibrium in both the goods market and the money market equilibrium.

Note: while we have equilibrium in the goods and money market at interest r1 and income Y1, there is no reason why the two curves necessarily intersect at the full employment level of output YF. This was the point made by Keynes we can have equilibrium in the goods market without necessarily having full employment....