Question

We suppose that:

C = 70 + 0.70YD, I = 90, G = 100, T = 0.10Y

(i) Find the equilibrium income.

(ii) What are the tax revenues at equilibrium income? Does the government have a balanced budget?

Answer 1

(i) $C=7+0.70YD$

I = 90

G = 100

T = 0.10 Y

Y = C + I + G

$=70+0.70YD+90+100$

$=70+0.70YD+190$

$=70+0.70(Y-T)+190$

$=70+0.70Y-0.70\times 0.10Y+190$

$=70+0.70Y-0.07Y+190$

$=70+0.63Y+190$

$=260+0.63Y$

$Y-0.63Y=260$

$0.37Y=260$

$Y=\frac{260}{0.37}$

$=702.7$

(ii) T = 0.10Y

$=0.10\times 702.7$

$=70.27$

Government expenditure = 100

Tax revenue = 70.27

Government has a deficit budget, not a balanced budget because government expenditure exceeds the tax revenue. (G > T)