# Saving - Investment Parity

It facilitates in fetching the impartiality amidst saving and investment. If there is a deviation amidst saving and investment and hike in investment tends to a hike in earnings via the multiplier process by more than the hike in initial investment. Consequently, the hike in earnings, saving also hikes and equals investment.

Let us work out few illustrations which explains us the concept of multiplier.

__Illustration 29__

With the following information you are required to ascertain the equilibrium income of the economy and the value of the multiplier.

C = 100 + 0.8Yd

I = 200

G & T = 150 each

Where, C, I and Yd are consumption, investment and disposable income respectively.

__Solution__

- Since G = T, budget of the government is balanced.

Y = C + I + G

C = a + bYd = a + b (Y – T)

Substituting the values of C, I and G we have:

Y = 100 + 0.8(Y – 150) + 200 + 150

= 100 + 0.8Y – 120 + 200 + 150

= 330 + 0.8Y

Y – 0.8Y = 330

0.2Y = 330

Y = 330 / 0.2

**Thus, equilibrium level of income is 1,650**

Value of Multiplier is

__ 1 __ = __ 1 __

1 – b 1 – mpc

= __ 1 __

1 – 0.8

= 1 / 0.2

**Hence the value of multiplier is 5**

__Illustration 30__

In an economy, the marginal propensity to consume is 0.80. the tax is a lump sum tax or, in other words, not related to income level. Find the change in the equilibrium output for the following:

- Increase in government expenditure by $20 millions
- Increase in taxes by $30 millions
- Increase in transfers by $20 millions

__Solution__

We have

GM = __Δ Y__ = __ 1 __

Δ G 1 – b

And b = 0.80 and Δ G = 20

Thus,

__Δ Y__ = __ 1 __ = 100

20 1 – 0.80

**Thus, for a $20 million increase in the level of increase of government expenditures,
the equilibrium output increases by $100 millions.**

We have

GT = __ΔY__ = __ -b __

Δ T 1 – b

And b = 0.80 and Δ T = 30

Thus,

__ΔY__ = __-
0.80 __ = -120

30 1 – 0.8

**Thus for a $30 million increase in taxes, the equilibrium output decreases by
120 millions.**

When transfers are at $20 millions

__ΔY__=

__0.80__= 80

20 1- 0.80

**Thus a 20 million increase in transfers increases the equilibrium output by
$80 millions.**

__Illustration 31__

Presume the level of autonomous investment in an economy is $ 400 millions and consumption function of the economy is C = 160 + 0.75Y. Ascertain the following.

- The Equilibrium level of income

- The increase in national income if investment increases by $50 millions

__Solution__

For equilibrium level of income

Y = C + I

Where C = 160 + 0.75Y …..Equation (1)

I = 400 millions

Substituting the values of C and I in Equation (1) we have

Y = 160 + 0.75Y + 400

Y – 0.75Y = 160 + 400

0.25Y = 560

Y = 560 / 0.25

**Equilibrium level of income is therefore equal to $2,240 millions.**

The next condition to be satisfied is an increase in investment with 50 millions and it depends on the size of multiplier. The size of multiplier is determined by the value of marginal propensity to consumer.

In the given consumption function C = 160 + 0.75Y marginal propensity to consume is equal to 0.75 or fractionally ¾.

Thus multiplier is equal to __ 1 __

1 – mpc

= __ 1 __ = 4

1 – ¾

**Thus with increase in investment by 50 millions, national income will hike
by 50 x 4 = 200 millions.**

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**Other topics under Consumption, Investment and Saving functions:**

- Accelerator theory of Investment
- Average Propensities, Marginal Propensity to Save
- Camouflaged Redundancy
- Classical Vs. Keynesian Models of income and Employment
- Concept of multiplier
- Consumption Function
- Complex Multiplier
- Criticisms of Keynesian Thesis
- Drift Theory of Consumption
- Foreign Trade Multiplier
- Government Expenditure
- Investment Function
- Jorgenson's Neoclassical Notion of Investment
- Keynesian Postulations and Underdeveloped Countries
- Keynesian Theory of Income, Output and Employment
- Model of National Income Determination
- Principle of Acceleration and the Super Multiplier
- Principle of Acceleration and the Super Multiplier - Part I
- Thrift, Marginal Competence of Capital
- Saving Function
- Saving and Investment Equality
- Some New Theories of Investment
- Theory of Consumption Function
- Unemployment and Full Employment