Answer to Question #230831 in Macroeconomics for Critical

Question

1. Given C=20+0.8YD, I=20+5i, G=500, X=400, and T=200.

a). Derive the IS equation

b). Find the value of the multiplier

c). Find the equilibrium consumption

2. Assuming Government spending increases by 50% and investment reduces by 10%, what happens to the IS equation

Answer 1

1. $C=20+0.8YD, I=20+5i, G=500, X=400, and T=200.$

a.

IS equation is given by$y = c + i + g + x + t$

$y = 20 + 0.8yd + 20 +5i + 500 + 400$

but disposable income is$yd = y-t$

$y = 20 + 0.8(y-200) +20 + 5i +500+400$

Removing the brackets and Making y the subject

$0.2y = 5i +740$

hence $y= 25i + 3700$

b.

the value of the multiplier is the coefficient of i in the IS equation

multiplier = 25

c.

equilibrium consumption is given by

$c= 20 + 0.8yd$

$c = 20 + 0.8(y-200)$

but y =25i + 3700

Therefore $c= 20+ 0.8(25i + 3700 -200)$

$c = 20i + 2820$

2.

The proportion in the increase in government spending is substantially huge as compared to a decrease in the interest rate. Therefore, the net effect is that IS equation will broaden thereby shift outwards to right hand right and upwards.