Question

In the Keynesian cross model, assume that the consumption function is given by C=$105+0.7(Y−T) Planned investment is $150; government purchases and taxes are both $150.

c. If government purchases increase to $165, what is the new equilibrium income? What is the multiplier for government purchases?

new Y = $

multiplier:

Answer 1

Before the change Y is

Y=C+I+G

Y=105+0.7*(Y-150) +150+150

Y=405+0.7Y-105

Y-0.7Y=300

0.3Y=300

Y=1000

c)

Y=105+0.7*(Y-150) +150+165

0.3Y=315

Y=1050

Multiplier =change in Y/change in G

=50/15

=3.33

Also by second method

The consumption function is the form of

C=autonomous consumption +MPC*YD

YD=Y-T=disposable income and MPC=0.7=marginal propensity to consume

Multiplier =1/ (1-MPC)

=1/ (1-0.7)

= 3.3333333333333333333

Change in equilibrium income =change in government purchase * multiplier

= (165 - 150)*3.3333333333333333333

= 50

New Y=old Y+change in Y=1000+50 = $1050