Question #72776

Consider the following model of national income determination
C = 300 + 0.75 (Y-T)
T = 100
I = 475
G = 150
i) List the entire exogenous and endogenous variable. (2 marks)
ii) Solve for the equilibrium value for all the endogenous variables. (2 marks)
iii) Suppose government expenditure increase by 50 find the new equilibrium values of the endogenous variables. Assume the economy of Kenya is described by the following information
Y = C + I + G (x - M) x = 20
C=20+0.8Yd M = 4 + 0.3Y
T = 30 Yd=Y-T
G = 22 I = 30 (8 marks)

Expert's answer

1) C = 300 + 0.75 (Y-T), T = 100, I = 475, G = 150.

i) Exogenous variables: T, I;

Endogenous variables: C, Y.

ii) Solve for the equilibrium value for all the endogenous variables.

Y = C + I + G,

Y = 300 + 0.75(Y - 100) + 475 + 150,

Y = 850 + 0.75Y,

0.25Y = 850,

Y = 3400.

C = 300 + 0.75(3400 - 100) = 2775.

iii) If G = 150 + 50 = 200, then:

Y = 300 + 0.75(Y - 100) + 475 + 200,

Y = 900 + 0.75Y,

0.25Y = 900,

Y = 3600.

C = 300 + 0.75(3600 - 100) = 2925.

2) Y = C + I + G + (X - M), X = 20,

C = 20 + 0.8Yd, M = 4 + 0.3Y, T = 30, Yd = Y - T, G = 22, I = 30, so:

Y = 20 + 0.8(Y - 30) + 30 + 22 + (20 - 4 - 0.3Y),

Y - 0.8Y + 0.3Y = 64,

0.5Y = 64,

Y = 128.

i) Exogenous variables: T, I;

Endogenous variables: C, Y.

ii) Solve for the equilibrium value for all the endogenous variables.

Y = C + I + G,

Y = 300 + 0.75(Y - 100) + 475 + 150,

Y = 850 + 0.75Y,

0.25Y = 850,

Y = 3400.

C = 300 + 0.75(3400 - 100) = 2775.

iii) If G = 150 + 50 = 200, then:

Y = 300 + 0.75(Y - 100) + 475 + 200,

Y = 900 + 0.75Y,

0.25Y = 900,

Y = 3600.

C = 300 + 0.75(3600 - 100) = 2925.

2) Y = C + I + G + (X - M), X = 20,

C = 20 + 0.8Yd, M = 4 + 0.3Y, T = 30, Yd = Y - T, G = 22, I = 30, so:

Y = 20 + 0.8(Y - 30) + 30 + 22 + (20 - 4 - 0.3Y),

Y - 0.8Y + 0.3Y = 64,

0.5Y = 64,

Y = 128.

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