Question

2. Suppose,

• C=0.8(1-t)Y

• t=0.25

• I = 900 –50i

• G=800

a)     What is the equation for IS curve

b) What is the effect of increase in govt. expenditure by 100 on the IS equation & IS curve? Show the effect using graphs

c)What will happen to the slope of IS curve if Investment becomes more sensitive to interest, say I = 900 – 60i ?

Answer 1

(a). To find the equation for the IS-curve let use the following equilibrium condition

$Y=C+I+G\\Where,\\C=0.8(1−0.25)Y\\Y=0.8(1−0.25)Y+900−50i+800\\Y=1700+0.6Y−50i\\Y−0.6Y=1700−50i\\0.4Y=1700−50i\\Y=\frac{1700−50i}{0.4}\\Y=4250−125i (equation of IS curve)$

(b). If government expenditure increases by 100 then the G= 800 + 100 = 900

$Y=0.8(1−0.25)Y+900−50i+900\\Y=1800+0.6Y−50i\\Y−0.6Y=1800−5oi\\0.4Y=1800−5oi\\Y=\frac{1800−5oi}{0.4}\\Y=4500−125i (new IS equation)$

Graphical presentation:

According to the above figure the x-axis measures the output and the y-axis measures the interest rate. IS1 is the old IS curve and IS2 is the new IS curve. After the increase in government expenditure the IS curve shifts up by 2 at each income level.

$(c). I= 900 - 60i\\ So,\\ Y=0.8(1−0.25)Y+900−60i+800\\Y=1700+0.6Y−60iY−0.6\\Y=1700−60i0.4\\Y=1700−60i\\Y=\frac{1700−60i}{0.4}\\Y=4250−150i$

If the investment becomes more sensitive to the interest rate then the IS-curve will become flattered. It means the slope will decrease.