Question

The fundamental equations in an economy are given as:

Consumption function C =200+0.8yd

Investment function. I=300

Tax. T=120

Government expenditure. G=200

Exports. X=100

Imports M=0.05y

Find the following.

1.The equilibrium level of income.

2.The net exports.

Answer 1

The consumption function is given

$C=200+0.8yd$

$C=200+0.8(Y-T)$

$C=200+0.8(Y-120)$

The equilibrium is

$Y=C+I+G+X-M$

$=200+0.8(Y-120)+300+200(100-0.05Y)$

$200+0.8Y-96+600-0.05Y$

$Y-0.8Y+0.05Y=704$

$0.25Y=704$

$Y=\frac{704}{0.25}=2,816$

The equilibrium level of income is 2,816

Equilibrium in a four sector model, leakages is equal to injections

so, $C+I+G+X=C+S+T+M$

The consumption function is $C = 200 + 0.8Y$

$C=200+0.8(2,816-120)$

$C=200+2,156.8$

$C=2,356.8$

The saving function is

$S=Yd-C$

$=(Y-120)-2,356.8$

$=2,816-2476.8$

$S=339.2$

Thus,

$I + G + X = S + T + M$

$300 + 200 + 100 = 339.2 + 120 + 0.05Y$

$600 = 459.2 + 0.05 Y$

$600 = 459.2 + 0.05 (2,816)$

$600 = 600$

Imports      

$M = 0.05Y = 0.05 (2,816)$

$=140.8$

Net Exports:

$X – M = 100 – 140.8$

$X - M = - 40.8$

there is deficit in the balance of trade.