Question

Consider the following economy and use the Keynesian model to answer the questions.

Round off answers to two decimals. Final values are expressed in millions of rands.

C=250 million+0.9Yd
I=175 m
G=310 m
X=170 m
Z=120m
T=0.25Y
Yf= R3 100 m
Equilibrium income:Y=C + I + G +(X-Z)
Disposable income:Yd=(1-t)Y

1. Calculate the multiplier

2. Calculate the equilibrium level of income based on the calculated value of the multiplier in 1

3. By approximately how much should investment spending be raised to achieve full employment

4. How will the multiplier and the equilibrium level of income change by including induced imports (m=0.11)?

Answer 1

Q1) The Keynesian Multiplier says that an increase in the investment leads to a more than proportionate increase in the income which leads to an increase in the consumption. The MPC or the marginal propensity to consume is the change in the total consumption due to the change in income = dC/dY. It can be determined by the consumption function which is of the form: C = autonomous consumption + MPC * Y_d, where Y_d = disposable income. The investment multiplier is given by the formula, 1/MPS, i.e. Marginal Propensity to Save, as the amount of investment depends on the amount of savings. So, in this case:

C = 250 + 0.9 Y_{d ,} so, MPC = 0.9 , MPS = 1- 0.9 = 0.1,

So, Kenesian Investment Multiplier = 1/MPS = 1/(1-MPC) = 1/0.1 = 10.

This implies that every one unit increase in investment will increase the income/output by 10 units.

2) The equilibrium level of income is given by Y* = C + I + G + (X-Z) , - (1)

Also, disposable income Y_d = Y - T,  i.e. personal income - taxes,

So, substituting all the values in eqn (1)

So, Y = 250 + 0.9(Y-0.25Y) + 175 + 310 + (170-120) ,

Y = 785 + 0.675Y, 0.325Y = 785, Y* = 2,415.38 million rands

This is the equilibrium level of income.

3) Now, the full employment level of Y = Y_f = 3100 million rands

So, the increase in income/output needs to be 3100 - 2415.38 = 684.62

So, as per the investment multiplier we calculated, 684.62 million of increase in income/output can be achieved by an increase in 694.62/10 = 68.46 million of investment.

4) The kenesian multiplier also has another form. Marginal Propensity to Save is the change in savings due to change in income. MPC + MPS = 1, Marginal Propensity to Tax is the change in tax as per change in income and can be found by the form =dT/dY,  T = MPT*Y, MPM is the Marginal Propensity to Import, dIm/dY, and change in imports as per change in the income.

So, in this case, MPS = 1-0.9 = 0.1, MPT = 0.25, MPM = 0.11,

So, the Keynesian Multiplier = 1/(MPS + MPT + MPM)

Multplier = 1/(0.1+0.25+0.11) = 1/0.46 = 2.17

So, the vaue of the multplier is changing (decreasing) from 10 to 2.17, by including induced imports.

So, now the imports equation will be Z = 120 + MPM*Y = 120 +0.11Y

So, now calculating the equilbrium income:

Y = Y* = C + I + G + (X-Z)

= 250 + 0.9(Y-0.25Y) + 175 + 310 + (170-120-0.11Y)

Y = 785 + 0.675Y - 0.11Y ,

Y - 0.565Y = 785, 0.435Y = 785 , Y* = 1,804.6 million rands.

So, this is how the equilibrium income changes(decreases) by including induced imports.