Question

Consider an economy described by the following function: C = 20 + 0.80Y, I = 30, G = 50, TR = 100.

(i) Find the equilibrium level of income and the autonomous expenditure multiplier in the model.

(ii) If government expenditure increases by 30, what is the impact on equilibrium income?

(iii) If a lump sum tax of 30 is added to pay for the increase in government purchases, how will equilibrium income change?

Answer 1

I = 30

$\Delta G$ = 30

G = 50

TR = 100

c = 0.80

C = 20 + 0.80Y

(i) Equilibrium level of income

$Y=\frac{1}{1-c}[\overline{C}+cTR+I+G]$

$=\frac{1}{1-0.80}[20+0.80\times 100+30+50]$

$=\frac{1}{0.20}\left[180\right]$

$=\frac{180}{20}\times 100$

$=900$

Expenditure mulitplier

$\frac{1}{1-c}=\frac{1}{1-0.80}$

$=\frac{1}{0.20}$

$=\frac{100}{20}=5$

(ii) Increase in government expenditure =

$\frac{1}{1-c}[\overline{C}+cT+I+G+\Delta G]$

$=\frac{1}{1-0.80}[20+0.80\times 100+30+50+30]$

$=\frac{1}{0.20}\left[210\right]=\frac{210}{20}\times 100=1050$

(iii) Tax multiplier $=\frac{-c}{1-c}$

$\frac{\Delta Y}{\Delta T}=\frac{-c}{1-c}$

$\Delta Y=\frac{-c}{1-c}\times \Delta T$

$=\frac{-0.80}{1-0.80}\times 30$

$=\frac{-80}{20}\times 30$

$=-120$

New equilibrium level of income = $-Y+\Delta Y$

= $900+(-120)$

$=780$