Answer to Question #187868 in Macroeconomics for chaoh

Question

Investment expenditure = 56 Government expenditure = 50 Autonomous Consumption = 100 Net exports = (30) MPS = 0.44. Required: i. Find the consumption and savings functions and indicate your assumptions of the model used. 4mks ii. Find the equilibrium level of national income 4m

Answer 1

Solution:

i). Find the consumption and savings functions and indicate assumptions of the model used.

Consumption function = autonomous consumption + MPC (After tax income)

C = a + bY

a = autonomous consumption (consumption when national income is zero) = 100

b = Marginal Propensity to Consume = 1 – 0.44 = 0.56

Y = After tax income (Y – T), we assume T = 0.3Y

Therefore:

C = 100 + 0.56(Yd)

C = 100 + 0.56(Y – T)

C = 100 + 0.56(Y – 0.3Y)

C = 100 + 0.56Y – 0.168Y

C = 100 + 0.392Y

 

Savings function = Y – C

S = Y – C

S = Y – (a + bY)

S = Y – a – bY

S = -a +Y – bY

S = -a + (1 – b) Y

Therefore:

S = -100 + (1 – 0.56) Y

S = -100 + 0.44Y

Assumptions made include the following:

·        Autonomous consumption is the consumption when national income is equal to zero.

·        The tax rate is assumed to be 0.3.

·        The marginal propensity to consume is b and it is equal to 1 – MPS.

 

ii). Find the equilibrium national income.

At equilibrium: AE = Y

Y = C + I + G + X – M

Where: C = 100 + 0.392Y

I = 56

G = 50

X-M = -30

Therefore:

Y = 100 + 0.392Y + 56 + 50 – 30

Y = 100 + 56 + 50 – 30 + 0.392Y

Y = 176 + 0.392Y

Y – 0.392Y = 176

0.608Y = 176

Y = $\frac{176}{0.608}$

Y = 289.47

The equilibrium national income = 289.47