Answer:
a) The equilibrium value of Y is 41,180.
b) The value of autonomous consumption (c0) is 12557.
c) The value of MPC is 0.5.
d) The value of MPS is 0.5.
e) The value of APC is 0.70
f) The value of APS is 0.30
g) Private saving is 32286; Public saving is -1305; and National saving is 30981
h) Multiplier = 2
i) The equilibrium value of Y increases by $300.
j) The equilibrium value of Y decreases by $150.
k) The equilibrium value of Y increases by $150.
Explanation:
Note: The model is not complete as the figures in it are omitted. The complete model of the economy is therefore provided before answering the question as follows:
C = 12557 + 0.5YD
I = 2281
G = 10199
T = 8894
The explanation of the answers is now given as follows:
a) What is the equilibrium value of Y?
YD = Y - T .............. (1)
Equilibrium value of Y can be obtained using the following formula:
Y = C + G + I ............................ (2)
Substituting all the values into equation (2), we have:
Y = 12557 + 0.5YD + 2281 + 10199 ………………….. (3)
Substituting equation (1) into equation (3), we have:
Y = 12557 + 0.5(Y – T) + 2281 + 10199 ……………… (4)
Substitute T = 8894 into equation (4) and solve for Y, we have:
Y = 12557 + 0.5(Y – 8894) + 2281 + 10199
Y = 12557 + 0.5Y – (0.5 * 8894) + 2281 + 10199
Y – 0.5Y = 12557 – (0.5 * 8894) + 2281 + 10199
(1 - 0.5)Y = 20590
0.5Y = 20590
Y = 20590/0.5
Y = 41,180
b) What is the value of autonomous consumption (c0)?
From C = 12557 + 0.5YD, the value of autonomous consumption (c0) is 12557.
c) What is the value of MPC?
From C = 12557 + 0.5YD, the value of MPC is 0.5.
d) What is the value of MPS?
MPS = 1 – MPC = 1 – 0.5 = 0.5
e) What is the value of APC?
YD = Y – T = 41180 – 8894 = 32286
C = 12557 + 0.5YD = C = 12557 + (0.5 * 32286) = 28,700
APC = C / Y = 28700 / 41,180 = 0.70
Note: This is not part of the answer but just additional information. Sometimes, YD is used. Then, we have:
APC = C / YD = 28700 / 32286 = 0.89
f) What is the value of APS?
APS = 1 – APC = 1 – 0.70 = 0.30
Note: This is not part of the answer but just additional information. If YD is used to calculate APC as it can be done sometimes, then we have:
APC = C / YD = 28700 / 32286 = 0.89
APS = 1 – APC = 1 – 0.89 = 0.11
g) Calculate private saving, public saving and national saving.
Private saving = Y – T = 41180 – 8894 = 32286
Public saving = T – G = 8894 – 10199 = -1305
National saving = Private saving + Public saving = 32286 -1305 = 30981
h) Calculate the multiplier.
Multiplier = 1 / MPS = 1 / 0.5 = 2
i) What happens to the equilibrium value of Y if G increases by $150?
Change in Y = Increase in G * Multiplier = $150 * 2 = $300
Since it is positive, it implies that the equilibrium value of Y increases by $300
j) What happens to the equilibrium value of Y if T increases by $150, and G remains at its original value of ?
Tax multiplier = - MPC/MPS =-0.5/0.5 = -1.0
Change in Y = Increase in T * Tax multiplier = $150 * (-1.0) = -$150
Since it is negative, it implies that the equilibrium value of Y decreases by $150.
k) What happens to the equilibrium value of Y if both G & T increase by $150 from their original amounts?
Change in Y = Change in Y as a result of change in G + Change Y as a result change in T = $300 + (-$150) = $300 - $150 = $150
Since it is positive, it implies that the equilibrium value of Y increases by $150.
