Econmic Help: equilirbrium level of income?

Question

Please guys I could not understand this. I really need some help!

C= 200 + 0.9Yd

Yd= Y - T

I = $200

G= $300

T= $150

X= 20

M= 20

Find the following:

(a) the equilirbrium level of income (Y)

(b) the equilirbrium level of consumption

(c) the marginal propensity to consume

(d) the value of the simple multiplier

(e) the equilirbrium level of income if taxes increase by $50

(f) the equilirbrium level of income if government spending decreases by $50 (ignore e in doing f)

please economists I need your help!

Answer 1

a)

Y=C+I+G+X-M

C=200+0.9(Y-150) =65+0.9Y

Y=65+0.9Y+200+300+20-20

0.1Y=565

Y=5650

b)

C=65+0.9Y=5150

c)

C=Ae+MPC*Yd

MPC=0.9

d)

ΔY/ΔG=1/(1-MPC)= 1/0.9=10/9≈1.1

e)

C=200+0.9(Y-200) =20+0.9Y

Y=20+0.9Y+200+300+20-20

0.1Y=520

Y=5200

f)

Y=65+0.9Y+200+250+20-20

0.1Y=515

Y=5150

Answer 2

Do u want the answers to be worked out or want to understand how the answers are derived?

What you have given is a set of macroeconomic equations:

C= 200 + 0.9Yd where C is Consumption and Yd is disposal income,

Yd= Y - T where Y is income and T is Tax given to Govt. out of Y.

I = $200 I is investment expenditure

G= $300, G is govt. expenditure,

T= $150

X= 20 where  X is Exports and

M= 20 is Imports.

Macro economic identity say, Y= C + I + G+ X - M, put the values you have already given above, you get,

Y= (200 + 0.9Yd) + 200+300+ 20 -20

or, Y = 0.9 Yd + 700 but Yd = Y-T= Y- 150.

So, Y = 0.9 (Y - 150) +700, or, Y= 0.9 Y - 0.9*150 +700, or,

0.1 Y = - 135- 700= 565. So, Y = 565/0.1= 5650/1= 5650. This is nothinh but the equilibrium level of income that satisfies all the equations you have given in the question.

So,

(a) the equilirbrium level of income (Y) = $ 5650.

(b) the equilirbrium level of consumption = $5150 derived as follows: 200 + 0.9Yd = 200 + 0.9 (Y-T) = 200 + 0.9 (5650 - 150 ) = 200+0.9 *5500

= 200 + 4950 = 5150

(c) the marginal propensity to consume = 0.9 derived as follows; dC/ dYd = d(200+0.9Yd)/dYd = 0 + 0.9= 0.9 or you can check increase Yd from say 100 to 110, C will change from 300 to 309 which means an icrease of 10 dollars in disposable income Yd leads to an increase in Concumption C by $9. The ratio of the cchange in consumption to change indisposable income is called the marginal propensity to consume and in this case equal 9/10=0.9

(d) the value of the simple multiplier: the formula for multiplier is given by 1/ (1- mpc)= 1/ (1-09) = 1 / 0.1 = 10/1 = 10

(e) the equilirbrium level of income if taxes increase by $50 is

Y=$5200

To derive this,we can go back to the process of solving the equations again. We had come to the following stage:  Y = 0.9 Yd + 700 but now Yd = Y-T= Y- (150+50). So,

Y = 0.9 (Y- 200) + 700 = 0.9 Y- 180 +700, 0r, 0.1 Y= 520, or,

Y= 520/0.1= 5200/1=5200.

There is a simple alternative to get this solution. Consider the macro identity Y= C + I + G+ X - M,or,

Y= 200 + 0.9 (Y-T) + I + G+ X - M .

If there is small change in T all other things remaining the same, we would get small change in Y

as DY= 0.9 DY -0.9DT which means 0.1DY = -0.9 DT , or,

DY/DT= - 0.9/0.1= -9. This is the tax multiplier. This means that in this case, an increase in taxes by $50 will reduce income by 9 times of $50 or by $450. So the new equlibrium Y will be previous equilibrium as derived in (a) $ 5650 -  $ 450..= $5200.

(f) the equilirbrium level of income if government spending decreases by $50 (ignore e in doing f) is Y= $5150

This is derived by going back to the equation solving process where we came to Y= C + I + G+ X - M, put the values you have already given above but now G= 300-50=250, you get,

Y= (200 + 0.9Yd+200+(300-50)+ 20 -20 , or, Y= 0.9Yd +650,

or, Y= 0.9 (Y- 150)+650, 0r, 0.1Y= -135+650 = 515, or,

Y= 515/0.1=5150,

This can also be derived more easily by using the autonomous expenditure multiplier derived as follows:Y= 200 + 0.9 (Y-T) + I + G+ X - M .

If there is small change in G all other things remaining the same, we would get small change in Y

as DY= 0.9 DY + DG which means 0.1DY = DG , or,

DY/DG= 1/ 0.1= 10.  This means that if govt expenditure decreases by $50, equlibrium level of income will also decrease by 10*$50= $500. So the new equilibrium will be the equilibrium Y found at (a) minus $500. Thus the new equilibrium income will be $5650- $500= $5150.

I hope the detailed workings will help you understand.