Question

Consider the following model:

C=20+0.5(Y-T)

I=20-10r

T=0

G=50

QUESTIONS:

a) Obtain the equation of the IS curve. What is the slope of the curve? Calculate output if r=0.1

b) Suppose now that autonomous consumption increases to 30. What happens to the IS curve? Show your results in a graph.

c) Suppose now that there is a change in marginal propensity to consumption so that now c1=0.6. What happens to the IS curve? Show your results in a graph.

Answer 1

a) Equation of the IS curve:

Y = C+I+G

or, Y = 20+0.5(Y-0)+20-10r+50

or, 0.5Y = 90-10r

or, Y = 180-20r

Here, when Y=0, r=9 and when r=0,Y=180. Thus, vertical and horizontal intercept of the IS curve are 9 and 180 respectively.

Then, slope of the IS curve = -vertical intercept/horizontal intercept = -9/180 = -1/20 = -0.05

Now, if r=0.1, then, Output Y = 180-(20*0.1) = 178

b) If consumption increases to 30,

Equation of the new IS curve:

Y' = C+I+G

or, Y' = 30+0.5(Y'-0)+20-10r+50

or, 0.5Y' = 100-10r

or, Y' = 200-20r

Here, when Y'=0, r=10 and when r=0,Y'=200. Thus, vertical and horizontal intercept of the new IS curve are 10 and 200 respectively.

Then, slope of the new IS curve = -vertical intercept/horizontal intercept = -10/200 = -1/20 = -0.05 (Thus slope remains unchanged

Now, if r=0.1, then, Output Y' = 200-(20*0.1) = 198

We have shown the IS curves below:

c) If mpc = 0.6

Equation of the new IS curve:

Y'' = C+I+G

or, Y'' = 20+0.6(Y''-0)+20-10r+50

or, 0.4Y'' = 90-10r

or, Y'' = 225-25r

Here, when Y''=0, r=9 and when r=0,Y''=225. Thus, vertical and horizontal intercept of the new IS curve are 9 and 225 respectively.

Then, slope of the new IS curve = -vertical intercept/horizontal intercept = -9/225 = - 0.04

Now, if r=0.1, then, Output Y'' = 225-(25*0.1) = 222.5

We have shown all the IS curves below: