The SIMPLE KEYNESIAN MODEL

OF INCOME DETERMINATION

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Session Outline

• Consumption and savings function

• Investment function

• Multiplier analysis (incl. Multiplier process)

• Acceleration principle

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Consumption and Savings Function

• The level of private disposable income is the chief determinant of

private consumption and saving , which, in the absence of government

is equal to total income. i.e., at higher levels of income the private

sectors will both consume more and save more and vice versa.

• But, consumption and saving are determined by many factors in

addition to the level of disposable income.

• Other important factors that influence the consumption and savings

function are:

– Stock of Wealth

– Expectations

– Taxation Policy

– Distribution of Income

– Age Composition

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Investment Function• Investment is the most volatile of all the major

components of aggregate demand (output), because of the multiplier mechanism.

• Capital investments (new buildings, new machineries, inventory etc) are made either out of own resources or borrowings .

• If borrowing is used, interest has to be paid on the sum borrowed. This is called `Debt financing’. That does not mean that in the case of self- financing, own resources, come free of cost. With `self financing’ the investor sacrifices the interest that he could otherwise have earned.

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Investment Function….

• Investments are made with an objective to earn profit.

• Interest is the price, profit is the reward for investment.

• The expected rate of profit from investment is called ‘marginal

efficiency of capital’ or ‘marginal productivity of investment’.

• A rational investor will compare the profits earned with the rate of

interest to be paid on the funds borrowed.

• The investor would decide to invest only if the expected profit from

investment (marginal efficiency of capital) is higher than the rate of

interest to be paid.

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Investment Function…

We conclude that the volume of investment in an economy mainly depends on two important factors:– Marginal efficiency of capital– Interest rates

Of the two factors , MEC has a greater influence on the volume of investment

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Other Factors Affecting Investment Demand

• Acquisition and operating cost

The initial expenditure incurred on capital goods and the

cost of maintenance of these goods, are important

aspects for estimating the rate of net profitability of any

investment. Such initial expenses increase the cost of

installation, with limited return on investment. If these

costs decline, the expected net profits go up.

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Other Factors Affecting Investment Demand

– Operating costs are often company specific, while the

company may not have any control on its initial

expenses.

– Operating costs are driven by wage rates, which are

influenced by the trade union policies of the company.

Thus, an increase in the acquisition and operating cost

reduces the expected net profitability, thereby reducing

investment demand.

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Other Factors Affecting Investment Demand

• Taxes

– Profits earned by a business after paying all

the charges against Interest and Taxes, is the

true yardstick for measuring prospective

investment. Therefore, an increase in the

rates of taxes would reduce the profitability of

an investment, while a decrease would make

the investment attractive

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Other Factors Affecting Investment Demand

• Change in Technology– Technological progress, process of development of

new products, improvement in the quality of performance of the existing products and development of a new method of production- all these, act as a stimulant to the investment climate. Development of a new machine, for instance would help to reduce the cost of production, improve the quality of the product and increase the expected rate of profit earned from such an investment. In short, a rapid degree of technological innovation drives the demand for new investment in the economy.

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Other Factors Affecting Investment Demand• Stock of Capital Goods in Hand

– Stock of capital goods in hand influences the investment demand

in just the same way as the stock of consumer goods in hand

affects the household consumption-savings decision. To the

extent that a given industry is well equipped with productive

facilities and inventory of finished goods, money remains blocked

in that industry, thus affecting return on investment. Any industry

with such a kind of problem would be forced to accept lesser

profits. With lower rates of return, incremental investments into

the industry would also be less. Thus an excess or inadequate

availability of stock of capital determines investment demand in

the economy.

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Other Factors Affecting Investment Demand

– Ratchet effect is the commonly observed

phenomenon that some processes cannot go

backwards once certain things have

happened, by analogy with the mechanical

ratchet that holds the spring tight as a clock is

wound up.

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Steady State Level of Consumption in the Long Run

Consumption function, Ct = a + bYdt + gCt -1

[Where Ct = Consumption expenditure for the current year;

a = Autonomous consumption; b = Short run MPC;

Ydt= Disposable personal income for the current year;

g = Coefficient indicating the relation between current period consumption and previous period consumption ;

Ct-1= Previous period consumption expenditure]

Since Ct = Ct-1

Ct = a + bYdt + gCt Or, Ct (1 – g) = a + bYd

t

Or, Ct = [{a/(1-g)} + {b/(1-g). Ydt}]

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Process of Multiplier

How does the process of multiplier work beginning from the initial injection?

Increase in autonomous spending adds to incomes, which in turn are spent partly on other goods and services, leading to increase in income. Part of this increased income is again spent on goods and services, causing further increase in income. This process continues uninterruptedly with a smaller sum of income passed on at each phase.

The magnitude of this increase is determined by how much income is passed on at each phase.

This in turn is dependent on the rise in consumption spending (ΔC/ΔY) or the marginal propensity to consume for a unit rise in disposable income.

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Process of MultiplierThe change in total income (ΔY) = Change in

autonomous expenditure (ΔE) + the induced change in consumption (ΔC).

Symbolically, ΔY = ΔE + ΔC

We know that MPC = = ΔC/ΔY

Or, ΔC = MPC. ΔY

Thus, ΔY = ΔE + ΔC = ΔE + . ΔY

Or, ΔY (1 - ) = ΔE

Or, k (multiplier) =

Where, MPS = the marginal propensity to save

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Multiplier AnalysisIllustration: If consumption function is given by C = 50 + 0.5Y, what is the change in equilibrium income for an increase of Rs.100 crores in autonomous government expenditure?

Solution:With the increase of autonomous government expenditure by Rs.100 crores, the demand income increases by Rs.100 crores in the first phase. This induces a demand of Rs.50 crores in the second phase due to consumption of 0.5 or 50% of increased income; Rs.25 crores in the third phase; Rs.12.5 in the fourth phase; Rs.6.25 in the fifth phase; 3.125 in the sixth phase; and so on. Thus, the total increase in equilibrium income (ΔY) = 100 + 50 + 25 + 12.5 + 6.25 + 3.125 + 1.5625 + 0.78125 + … = 200

Multiplier x ΔE = 2001005.0

1100

5.01

1100

1

1

xxx

MPC

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Multiplier Process (For an Increase of Rs.100 in Autonomous Investment)

Stages MPC x Change in Income Rise in Income Total Income

1 100 100 100

2 0.5x 100 50 150

3 0.5x 50 25 175

4 0.5x 25 12.5 187.5

5 0.5x 12.5 6.25 193.75

6 0.5x 6.25 3.125 196.875

7 0.5x 3.125 1.5625 198.4375

8 0.5x 1.5625 0.78125 199.2188

9 0.5x 0.7815 0.39 199.6088

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Multiplier Process

0

50

100

150

200

250

0 1 2 3 4 5 6 7 8 9

Phases (Stages)

Ris

e in

Inco

me

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Uses and Limits of the MultiplierUses

– The Multiplier process by indicating different phases of trade cycles helps the business community to plan its transactions accordingly.

– Multiplier analysis acts as an important tool for the modern governments in formulating economic policies.

– A government, by multiplier analysis, can know the quantity of investment that has to be made to reach full employment level.

– The Multiplier principle shows the importance of deficit budgeting

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Uses and Limits of the MultiplierLimitations

• Multiplier process works only when there is adequate availability of consumer goods.

• Full value of multiplier is achieved only when various increments in investments are repeated at regular intervals.

• The full value of the multiplier can be achieved only when there is no change in the MPC during the process of income propagation.

• While estimating the multiplier in a country, we assume that the country has no trade relations with others. If there are trade relations with other countries, then the multiplier estimated may be more or less than its real value.

• To realize the full value of multiplier, it is assumed that there are no time lags between the receipt of income and its spending. But, this is not possible in real life.

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Acceleration PrincipleAcceleration principle is concerned with the changes in investment and its

ultimate effect on gross product or income. Although J.M. Keynes

discussed the principle of multiplier, he did not make any reference to

acceleration principle in his General Theory.

Acceleration principle (principle of magnified derived demand) is based on

the induced investment; the principle states that the demand for durable

goods (investment) is derived from the demand for final goods and

services produced by them. For example, if demand for consumption

goods increases, it induces an additional demand for capital goods.

Thus the concept of acceleration shows the functional relationship

between changes in demand for final goods (consumption goods) and

the consequent changes in the demand for capital goods (capital goods

– e.g. machines).

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Acceleration Principle

This functional relationship can be expressed as

Acceleration principle = ΔK/ΔY (Change in Investment ‘divided by’

Change in Income)

The working of “Acceleration Principle” is similar to that of “Multiplier Principle”.