Answer to Question #217304 in Macroeconomics for Sahil khan

Question

S=-80+0.25Y, and import function is is given as 100-0.05Y then find

a. At what level of equilibrium level of income and consumption will occur?
b. If government expenditure increase bye 55 crore and government imposes the lump sum taxes worth 15 crore what impact will it have on consumption and income
c. What will happen to imports if government raises the import duty by 10%
d. Calculate the multipliers of government expenditure and foreign trade

Answer 1

a.). First derive the consumption function:

Saving function = -80 + 0.25Y

S = Y – C

Y = S + C

Y = -80 + 0.25Y + C

-80 + 0.25Y – Y = C

-80 – 0.75Y = C

C = 80 + 0.75Y

Consumption function = 80 + 0.75Y

Equilibrium level of income: AD = AS

Y = C + I + G + X – M

Y = 80 + 0.75Y + 100 – 0.05Y

Y = 80 + 100 + 0.75Y + 0.05Y

Y = 180 + 0.80Y

Y – 0.80Y = 180

0.20Y = 180

Y = 900

Equilibrium level of income = 900

 

b.). If the government imposes the lump-sum taxes worth 15 crore, both the consumption function and income will decrease since there will be a reduction in disposable income. An increase in government expenditure by 55 crores on the other hand will result to an increase in equilibrium national income.

 

The new consumption and equilibrium income will be as follows:

C = 80 + 0.75 (Y – T) = 80 + 0.75(Y – 15) = 80 + 0.75Y – 11.25

C = 80 + 0.75Y – 11.25

New equilibrium income:

Y = C + I + G + X – M

Y = 80 + 0.75Y – 11.25 + 55 + 100 – 0.05Y

Y – 0.75Y – 0.05Y = 80 + 55 + 100 – 11.25

0.20Y = 223.75

Y = 1,118.75

New equilibrium national income = 1,118.75

 

c.). The imports will increase by 10% if the government raises the import duty by 10%. That is the cost of imports will be much higher.

 

d.). Government expenditure multiplier = $\frac{\triangle Y } {\triangle G }$

 

Change in income = 1,118.75 – 900 = 218.75

Change in government expenditure = 55 – 0 = 55

Government expenditure multiplier = $\frac{218.75}{55}$ = 3.98

Government expenditure multiplier = 4

 

Foreign trade multiplier = $\frac{1}{MPS + MPI}$

Where: MPS = Marginal propensity to save

            MPI = Marginal propensity in income

MPS = 0.25

MPI = Change in imports/Change in income

Change in income = 1,118.75 – 900 = 218.75

 

Change in imports:

Previous import = 100 – 0.05Y = 100 – 0.05(900) = 100 – 45 = 55

New import = 100 – 1.05Y = 100 – 0.005(900) = 100 – 4.5 = 95.5

Change in import = 95.5 – 55 = 40.5

Foreign trade multiplier = $\frac{1}{(0.25 + 40.5)} = \frac{1}{40.75}$ = 0.025

Foreign trade multiplier = 0.025