Q. 20

# Consider an economy described by the following functions: C = 20 + 0.80Y, I = 30, G = 50, TR = 100 (a) Find the equilibrium level of income and the autonomous expenditure multiplier in the model. (b) If government expenditure increases by 30, what is the impact on equilibrium income? (c) If a lump-sum tax of 30 is added to pay for the increase in government purchases, how will equilibrium income change?

Equilibrium level of income

Y = 1/1-c (Auto. C.-cT+I+G)

= 1/1-0.80 (20+0.80*100+30+50)

=1/0.20 * 180

=180/20 * 100

=900

EXpenditure multiplier

1/1-c

= 1/1-0.80

=1/0.20

=100/20

=5

Increase in government expenditure

1/1-c (Auto. C+cT+I+G+Change in G)

= 1/1-0.80(20+0.80*100+30+50+30)

= 1/0.20 * 210

=210/20 * 100

=1050

Tax multiplier = -c/1-c

Change in Y/Change in Taxes = -c/1-c

Change in Y = -c/1-c * Change in tax

= - 0.80/1-0.80 * 30

= -80/20 * 30

= -120

New equilibrium level of income = Y +Change in Y

= 900+ (-120)

= 780

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