National Income Determination

Example 1
Given that
G=20
I=35
C=0.9Yd + 70
T=0.2Y + 25
Calculate the equilibrium level of national income

Y=C+I+G
Yd=Y-T

Solution
Y=C+I+G
G=20 I=35 C=0.9Yd + 70 T=0.2Y + 25
Y=C+35+20=C+55
Yd=Y-T = Y – 0.2Y -25=0.8Y-25 C =0.9 * (0.8Y -25) +70
So,
Y=C+55=0.9*(0.8Y-25)+70+55
0.9*(0.8Y-25)+70+55=Y 0.72Y-22.5+125=Y
Y=102.5/0.28=366

Example 2
Consider an economy described by the following equations: Y =C+I+G; Y= 5,000; G= 1,000; T= 1,000; С = 250 + 0.75(Y- T); I = 1,000-50r.
In this economy, compute private saving, public saving, and national saving.
Find the equilibrium interest rate.
Now suppose that G rises to 1,250. Compute private saving, public saving, and national saving.
Find the new equilibrium interest rate.

private saving = (Y – T ) – C
public saving = T – G
national saving, S
= private saving + public saving
= (Y –T ) – C + T – G
= Y – C – G

Example 3
Assume that a technology of production is shown by the production function Q=√(KL). The firm’s cost is 36 cur.units in wage rate w=4cur.units and rent rate r=6 cur.units. Find optimum production volume.