Answer to Question #185445 in Microeconomics for Edward Kamutuva

Question

Suppose an economy is described by the following equations: Y = C + I + G + X – M C = 14 + 0.60Yd I = 20 G = 20 X = 15 M = 5 +0.1Y T = 20 + 0.4Y Where Y is domestic income Yd is private disposable income C is aggregate consumption spending T is government tax revenue I is investment spending G is government spending E represents exports M represents imports of goods and services.Page 14 of 15 (a) Find out the equilibrium value of income. (4) (b) What is the value of export multiplier? (2) (c) If the equilibrium national income is less than the full-employment level of income by N$100, what should be the increase in government spending or in exports to attain the full-employment level of income? (6) (d) With a help of a diagram explain and discuss life cycle hypothesis.

Answer 1

a)

Equilibrium Income: Y = C + I + G + X – M

C = 14 + 0.6Yd

where Yd = Y−T

           Yd = 0.6 (Y−(20+0.4Y)

           Yd = 0.6(Y − 20 − 0.4Y)

           Yd = 0.6(0.6Y − 20)

Therefore, C = 14 + 0.6(0.6Y − 20)]

Y = C + I + G + X – M

Y = 14 + 0.6(0.6Y − 20) + 20 + 20 +15 −(5 +0.1Y)

Y = 14 + 0.36Y − 12 +55 − 5−0.1Y

Y = 52 + 0.36Y − 0.1Y

Y = 52 + 0.26Y

Y − 0.26Y = 52

0.74Y = 52

Y = 70.27..........equilibrium output/income

b) 

Generally, Marginal Propensity to Import (MPI) is % of an extra dollar of income spent on imports by the consumer of a country as a whole.

It is given that C = 14 + 0.60Yd and the MPC = 0.60.

therefore, the remaining portion not spent for domestic consumption would show the marginal propensity to imports that is, (1- 0.60 = 0.40) m = 0.40.

This implies that ;

C = 14 + 0.60Yd and

IM = 0.40Y

out of each new dollar of income, $0.60 is spent, but of that $0.60, $0.40 is spent on foreign goods.

 Foreign trade multiplier or export multiplier$=\frac{1}{1-(0.6-0.4)}$ ; where m stands for marginal propensity to import

$=\frac{1}{1-0.6+0.4}$

$=1.25$......export multiplier

c)

At full employment AD=AS

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

$Y=14+0.6(Y-20-0.4Y)+20+20+15-5-0.1Y$

$Y+0.24Y-0.5Y=52$

$0.74Y=52$

$Y=70.2$

It is given that full employment is attained when AD=LRAS at Y=$100.

Therefore, there is a shortage of some amount hence the government needs to increase its expenditure.

Government multiplier = (1/1)-MPC

Change in Y=[(1/1)-MPC)]change in G

Change in Y=(100-70.2)=$29.2

29.2=(1/1-0.6)Change in G

Change in G=$11.8

If the full employment needs to be attained at $100 then the government needs to increase its expenditure by $11.8.

d)

Life cycle hypothesis states that the consumption of an individual depends upon his or her income during life time and not just current income.

Initially, income is lower (less than zero). Once an individual starts working the income increases and after retirement income decreases further but consumption is smooth throughout the age.