UNIT 2 – WORKSHEET
1.
Assume consumption is represented by the following: C = 400 + .75Y. Also assume that
planned investment (I) equals 100.
C = 400 + .75Y
I = 100
(a) Given the information, calculate the equilibrium level of income.
ANSWER:
Recall in Equibrium Y = AE
AE
Where AE = C + I
Therefore AE = 400 + 0.75Y + 100
2,400
So
AE = 500 + 0.75Y
Y = 500 + 0.75Y
Y – 0.75Y = 500
0.25Y = 500
Y = 500 / 0.25
Y = 2,000 (equibrium Income)
Y=AE
2,000
AE = 500 + 0.75Y
500
2,000
2,400
(b) Given the information, calculate the level of consumption and saving that occurs at
the equilibrium level of income.
ANSWER
If C = 400 + 0.75Y and Y = 2,000
Then C = 400 + 0.75(2,000)
C = 400 + 1,500
C = 1,900
Saving?... recall that Y = C + S,
Therefore S = Y – C
S = 2,000 – 1,900
S = 100
(c) Suppose planned investment increases by 100. Calculate the new equilibrium level
of income. Given your answer, what is the size of the multiplier for this economy?
ANSWER
If C = 400 + 0.75Y I = 200
Then in Equilibrium
Y
Y=C+I
Y = 400 + 0.75Y + 200
= 600 + 0.75Y
Y – 0.75Y = 600
Y = 600 / 0.25
Y = 2,400
The multiplier = 1 / 1-MPC or
ch Y / ch I
Therefore the Multiplier = 1 / (1 – 0.75)
= 1 / 0.25 = 4
Or
Multiplier = (2,400 – 2,000) / (200 – 100)
= 400 / 100 = 4
UNIT 3A – WORKSHEET
1.
In a closed economy with a public sector prove that S + T = I + G.
ANSWER:
Note Y = C + S + T
And AE = C + I + G
Now in Equilibrium Y = AE
Therefore C + S + T = C + I + G
Then C would cancel each other, leaving
S+T=I+G
Withdrawals = Injections
Y – T = Yd = Disposable Income
2.
Assume an economy is represented by the following:
G = Spending & T = Tax
If G = T …. ... Balance budget
G > T…… Budget Deficit
G < T ……. Budget Surplus
(a) Calculate the equilibrium level of output.
ANSWER:
In Equilibrium Y = AE
Where AE = C + I + G
AE = 100 + 0.9Yd + 200 + 1,000
= 1,300 + 0.9Yd
But Yd = Y – T (disposable Income)
Hence AE = 1,300 + 0.9(Y - 1000)
= 1,300 + 0.9Y – 0.9(1,000)
= 1,300 + 0.9Y – 900
AE = 400 + 0.9Y
Therefore in Equilibrium
Y = 400 + 0.9Y
Y – 0.9Y = 400
0.1Y = 400
Y = 400 / 0.1
Y = 4,000 (Equilibrium Income)
(b) Based on your analysis in Part (a), calculate the levels of consumption and saving
that occur when the economy is in equilibrium.
ANSWER
If C = 100 + 0.9Yd and Y = 4,000
Then C = 100 + 0.9(Y – T)
C = 100 + 0.9(4,000 – 1000)
= 100 + 0.9(3000) = 100 + 2,700
C = 2,800
If Y = C + S + T
Then S = Y – C – T
S = 4,000 – 2,800 – 1,000
S = 200
Y
4,000
=C +S
+T
= 2,800 + 200 + 1,000
Disposable = Y – T = 4,000 – 1,000 = 3,000
(c) Now suppose planned investment rises by 100. Calculate the new equilibrium
level of income. Given your answer, what is the size of the multiplier?
ANSWER
In equilibrium Y = AE
Where AE = C + I + G
= 100 + 0.9Yd + 300 + 1,000
= 1,400 + 0.9(Y - T)
= 1,400 + 0.9(Y – 1,000)
= 1,400 + 0.9Y – 0.9(1,000)
= 1,400 + 0.9Y – 900
AE = 500 + 0.9Y
So since Y = AE in equil.
Y = 500 + 0.9Y
Y – 0.9Y = 500
0.1Y = 500
Y = 500 / 0.1
Y = 5,000
Multiplier = 1 / 1-MPC (1 / MPS) or ch Y / ch I
1 / 1-MPC
Multiplier = 1 / (1 – 0.9)
= 1 / 0.1
= 10
ch Y / ch I
Multiplier = (5,000 - 4,000) / (300 – 200)
= 1,000 / 100
= 10