Tutorial 2 Memo
1. Considering the following equations:
a) C=C0+cYd
b) I=I
c) G=G
Use the algebra to derive the equilibrium output (Y) and indicate which part is called
autonomous spending and explain why it is referred to as autonomous.
Z=C+I+G
In equilibrium Y=Z
Y=C+I+G
Y= C0 +c1Yd +I+G
Y=C0 +c1(Y-T) +I+G
Y=C0 +c1Y – c1T +I+G
Y-c1Y = C0 -c1T +I + G
Y (1-c1) = C0 -c1T + I + G
1
Y= [C0 - c1T +I+G]
1−c 1
The autonomous part is [C0 - c1T +I+G] and is referred to as autonomous spending because it
is independent of income.
2. Suppose investment decreases. Explain, using the appropriate graph, what the impact will
be on equilibrium income and demand.
The graph explains that when investment decreases, firms decrease their production,
decreasing the wages that they pay workers. Household income decreases from y to y 1 which
reduces the purchasing power parity that consumers have and this leads to a decrease in the
demand for goods and services from Y to Y1 and ultimately the demand curve Z shifts
downwards to ZZ
3. Suppose an increase in autonomous consumption. Explain, using the appropriate graph,
what the impact will be on equilibrium income and demand.
Demand, Z;
Production, Y
ZZ’
Y’
ZZ
45
Income, Y
Y Y1
The graph explains that when autonomous consumption increases, there is a greater demand
for goods which is depicted by the increase in demand from ZZ to ZZ’. Firms have to
increase production to meet this increase in demand, hence the production of goods increases
from Y to Y’ which ultimately leads to an increase in income from Y to Y1.
4. Assume a single economy with only consumption, investment and government.
Given the following:
C = 270 + 0.8 (Y – 100)
I = 250
G = 150
a) Calculate the size of the multiplier
1 1
M= = =5
1−c 1 1−0.8
b) Calculate equilibrium income
Y=Z
Y = C+I+G
Y = 270+0.8(Y-100) + 250+150
Y = 270+0.8Y- 80+250+150
Y = 590+0.8Y
Y – 0.8Y = 590
0.2Y = 590
1
Y= x 590
0.2
Y = 5 X 590
Y = 2950
c) Calculate the autonomous consumption
Remember that Y = M x A [A = autonomous consumption]
From (1) M = 5
From (2) Y = M x A
2950 = 5 x A
2950
A=
5
A = 590
Or Y=MxA
1
Y= [C0 - c1T +I+G]
1−c 1
Therefore, we can say:
A = Co – c1T + I + G
A = 270 - 0.8 (100) + 250 + 150
A = 270 – 80 + 250 + 150
A = 590
d) What is the disposable income?
Yd = Y – T
Yd = 2950 – 100
Yd = 2850
e) Calculate consumption
C = C0 + c1Yd
C = 270 + 0.8 (Y – T)
C = 270 + 0.8 (2950 – 100)
C = 2550
f) Suppose a change in government spending, it is now G=110. Calculate the new
equilibrium income.
∆ G=150−110
∆ G=40
∆ Y =M x ∆ G
∆ Y =5 x 40
∆ Y =200
thus :Y 2=Y 1−∆ Y
Y2 = 2950 – 200
Y2 = 2750
Or
Y = 270 + 0.8 (Y – 100) + 250 + 110
Y = 270 + 0.8Y – 80 + 250 + 110
Y = 550 + 0.8Y
Y – 0.8Y = 550
0.2Y = 550
Y = 2750
g) Considering the change in equilibrium income, how does this affect consumption?
C = 270 + 0.8Yd
C = 270 +0.8 (2750 -100)
C = 2390
Because of the decrease in government expenditure 40, this affected the equilibrium level of
income which then became R2750. This change affected consumers’ disposable income,
which ultimately affects their basket of goods (how much they can afford). Hence
consumption decreased from 2550 to 2390.
4. Assume a simple economy with only consumption, investment and government. Further
suppose the marginal propensity to save (b)=0.4, autonomous consumption (a) = R80,
Investment (I)=R150, Government spending (G) =R150 and tax rate (T)=100
a) Calculate the size of the expenditure multiplier.
1 1
M= = =2.5
MPS 0.4
b) Calculate the equilibrium income
Y = M x [C0 - c1T+ I +G]
Y = 2.5 x [80 - 0.6 (100) + 150 + 150]
Y = 2.5 x [380 – 60]
Y = 2.5 x [320]
Y = 800
c) Calculate the disposable income
Yd = Y – T
Yd = 800 – 100
Yd = 700
Bonus Question!
5. C=180 +0.4Yd
I= 140
G =140
T=100
t= 0.25
Hint: the tax identity is T = T + tY
Using algebra, solve the following variables
a. Equilibrium income (Y)
Y=C+I+G
Y = 180 + 0.4Yd + 140 + 140
Y = 180 + 0.4 (Y – T) + 140 + 140
Y = 180 + 0.4 [Y – (T + tY)] + 140 + 140
Y = 180 + 0.4 [Y – (100 + 0.25Y)] + 280
Y = 180 + 0.4 [Y – 100 – 0.25Y] + 280
Y = 180 + 0.4Y – 40 – 0.1Y + 280
Y = 420 + 0.3Y
Y – 0.3Y = 420
0.7Y = 420
Y = 600
b. Induced consumption
IC = C1Yd
IC = C1 [600-100-0.25(600)]
IC = 140
c. Consumption expenditure (C)
Yd = Y – T
Yd = Y – [100 + 0.25Y]
Yd = Y – 100 – 0.25Y
Yd = 600 – 100 – 0.25 (600)
Yd = 350
Hence C = 180 + 0.4Yd
C = 180 + 0.4 (350)
C = 320
Or C = C0 + C1(Yd)
C= 180 + 140
C = 320
