Question

Aggregate Demand I — Work It Out Question 1 In the Keynesian cross model, assume that the consumption function is given by C = $70 +0.7(Y – T) Planned investment is $200; government purchases and taxes are both $100. c. If government purchases increase to $115, what is the new equilibrium income? What is the multiplier for government purchases? new Y=$ multiplier:

Answer 1

Answer

Before the change Y is

Y=C+I+G

Y=70+0.7*(Y-100) +200+100

Y=370+0.7Y-70

Y-0.7Y=300

0.3Y=300

Y=1000

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After change

It is

Y=70+0.7*(Y-100) +200+115

0.3Y=315

Y=1050

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Multiplier =change in Y/change in G

=50/15

=3.33

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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

= (115-100)*3.3333333333333333333

=50

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