Question

Suppose the IS curve for Fiji is Y = 2500-125i and the LM is Y = 1000+25i. Use Cramer’s rule to determine i* and Y*. Now suppose the Fijian Government increased spending by $100m. Determine the extent of crowding out of private investment and the increase in Ms required to dampen any crowding-out effect. You are given the following parameters: αG = 2.5, h = 65, k = 0.5, b = 50.

Answer 1

$1) Y = 1250 , i = 10$

$2) 233.5$

3) Increase in money supply = 100

Explanation:

The equation for IS:

$Y = 2500-125i ......(1)$

The equation for LM:

$Y = 1000+25i .......(2)$

Other given information are:

$αG = 2.5, h = 65, k = 0.5, b = 50.$

From equation;$(1): Y + 125i = 2500$

From equation;(2): Y - 25i = 1000

where:a1 = 1 , a2 = 1, b1 = 125 , b2 = -25 , c1 = 2500 , c2 = 1000

From Cramers rule 5:

$Y = | [2500(-25) - 1000(125)] / [1(-25) - 1(125)] |$

$= | (-62500 - 125000) / (-25 - 125) |$

$= 187500/150$

$= 1250$

By substituting the value of Y in equation (2):

$i = 10$

2)

change in Y = government spending multiplier * change in G

$= αG *100$

$= 2.5 * 100$

$= 250$

It implies that due to an increase in G by $100m , the increase in Y should be 250.

But due to the crowd out of private investment, the increase in Y is less. The real increase in Y can be calculated as follows:

New equation of IS:

$Y = 2500 - 125i + 100$

$Y = 2600 - 125i$

The equation of LM is same as before:

$Y = 1000+25i$

By solving these two equations:

$Y = 1266.5 and i = 10.66$

The real change in Y = 1266.5 - 1250 = 16.5 

Crowd out $= 250 - 16.5 = 233.5$

3)

The equation of Lm explains the money market equilibrium:

Money supply = money demand 

$MS = kY - hi$

Suppose with the increase in money supply to offset the crowd out effect, the new money supply is MS'.

$MS' =kY - hi$

$MS' = 0.5Y - 65i$

At the new equilibrium, we want an increase in Y of 250 and i $= 10$

$MS' = 0.5*(1250 + 250) - 65*(10)$

$MS' = 0.5(1500) - 650$

$MS' = 750 - 650$

$MS' = 100$

Thus, an increase in money supply should be 100.