Theories of Business Cycles (Part - 2) - Macroeconomics | Macro Economics - B Com PDF Download

5. Samuelson’s Model of Multiplier Accelerator Interaction:

The economists of post-Keynesian period emphasized the need of both multiplier and accelerator concepts to explain business cycles. Samuelson’s model of multiplier accelerator interaction was the first model that represents interaction between these two concepts.

In his model, Samuelson has described the way the multiplier and accelerator interact with each other for generating income and increasing consumption and demand of investment. He also describes how these two factors are responsible for creating economic fluctuations.

Samuelson used two concepts, namely, autonomous and derived investment, to explain his model. Autonomous investment refers to the investment due to exogenous factors, such as new product, production technique, and market.

On the other hand, derived investment refers to the increase in the investment of capital goods produced due to increase in the demand of consumer goods. When autonomous investment occurs in an economy, the income level also increases.

This brought the role of multiplier into account. The income level helps in determining the marginal propensity to consume. If the income level increases, then the demand for consumer goods also increases.

The supply of consumer goods should satisfy the demand for consumer goods. This is possible when the production technique is capable to produce a large quantity of products and services. This encourages organizations to invest more to develop advanced production techniques and increase production for meeting consumer demand.

Therefore, the consumption affects the demand of investment. This is referred as derived investment. This marks the starting of the acceleration process, which results in further increase in income level.

An increase in the income level would increase the demand of consumer goods. In this manner, the multiplier and accelerator interact with each other and make the income grow at a much higher rate than expected.

Autonomous investment leads to multiplier effect that result in derived investment. This is called acceleration of investment. Derived investment would make the accelerator to come into action. This is termed as multiplier-acceleration interaction.

Samuelson made certain assumptions for the explanation of business cycles. Some of the assumptions are that the production capacity is limited and consumption takes place after a gap of one year.

Another assumption made by him is that there would be a gap of one year between the increase in consumption and increase in the demand of investment. In addition, he assumed that there would be no government activity and foreign trade in the economy.

According to the assumption given by Samuelson that there would be no government activity and foreign trade, the equilibrium would be achieved when

Y_t = C_t + I_t

Where, Y_t = National income

C_t = Total consumption expenditure

I_t = Investment expenditure

t = Time period

According to the assumption that consumption takes place after a gap of one year, the consumption function would be represented as follows:

C_t = α Y_t-1

Where, Y_t-1 = Income for t-1 time period

α = ∆C/∆Y (multiplier propensity to consume)

Investment and consumption has a time lag of one year; therefore, the investment function can be expressed a follows:

I_t = b (C_t –C_t-1)

Where, b = capital/output ratio (helps in determination of acceleration)

By putting the value of C_t and I_t in the first equation of national income, we get

Y_t = α Y_t-1 + b (C_t – C_t-1)

If C_t = α Y_t-1, then C_t-1 = α Y_t-2. Putting the value of C_t-1 in the preceding equation, we get

Y_t = α Y_t-1 + b (α Y_t-1 -α Y_t-2)

Y_t = α (1 + b) Y_t-1 – abY_t-2 (equation for equilibrium)

With the help of preceding equation, the income level for past and future can be determined if the values of a, b and income of two preceding years are given. It can be depicted from the preceding equation that the changes in income level can be affected by the values of α and b.

The different combinations of α and b give rise to fluctuations in business cycles as shown in Figure-4:

In Figure-4, the areas A, B, C, and D represents the different phases of business cycles. The types of different cycles represented by A, B, C, and D are described in detail with the help of the following points:

A: Refers to the area at which the income level increases or decreases at the decreasing rate and arrive at a new equilibrium point. The change in the income level would be in one-direction only.

It results in damped non-oscillation, as shown in Figure-5:

B: Refers to the area in which points, a and b, together makes amplitude cycles that gradually become smaller. This process continues till the cycles get dissolve and economy reaches to equilibrium.

This represents damped oscillations, as shown in Figure-6:

C: Refers to the area in which points, a and b, together makes amplitude cycles that become larger.

This forms explosive cycles, as shown in Figure-7:

D: Refers to the area at which the income level is increasing or decreasing at the exponential rate. This process continues till cycles reach at the bottom.

It represents one-way explosion and results in explosive oscillations, as shown in Figure-8:

E: Refers to the point at which the oscillations are of equal amplitude.

Some of the drawbacks of Samuelson’s model are as follows:

a. Represents a simpler model that is not able to explain business cycles completely

b. Ignores other factors that influence business cycles, such as expectations of businessmen and taste and preferences of customers

c. Assumes that the capital/output ratio remains constant, which is not true.

6. Hicks’s Theory:

Hicks has associated business cycles to the growth theory of Harrod-Domar. According to him, business cycles take place simultaneously with economic growth; therefore, business cycles should be explained in association with the growth theory.

In his theory, he has used the following concepts to explain business cycles:

a. Saving-investment relation and multiplier concepts given by Keynes

b. Acceleration concept given by Clark

c. Multiplier-acceleration interaction concepts given by Samuelson

d. Growth model of Harrod-Domar

Hicks has also framed certain assumptions for describing business cycle concept.

The important assumptions of Hicks’s theory are as follows:

(a) Assumes an equilibrium rate of growth in a model economy where realized growth rate (Gr) and natural growth rate (Gn) are equal. As a result, the increase in autonomous investment is constant and is equal to the increase in voluntary savings. The equilibrium growth rate can be obtained with the help of rate of autonomous investment and voluntary savings.

(b) Assumes the consumption function given by Samuelson, which is C_t= α Y_t-1. As discussed earlier, according to Samuelson theory consumption takes place after a lag of one year. The time lag in consumption occurs due to the gap between income and expenditure and gap between Gross National Product (GNP) and non-wage income.

The gap between income and expenditure produces when income is ahead of expenditure. The gap between GNP and non-wage income produces when fluctuations in GNP occur more frequently than the fluctuations in non-wage income.

The saving function becomes the function of past year’s income. With the time lag between income and investment-saving, the multiplier process has a diminishing impact on business cycles.

(c) Assumes that autonomous investment is a function of output at present. In addition, autonomous investment is used for replacing capital goods. However, induced investment is regarded as the function of changes in output.

The change in output produces induced investment, which marks the beginning of the acceleration process. The acceleration process interrelates with the multiplier effect on income and consumption.

(d) Makes use of the words ceiling and bottom for explaining the upward and downward flow of business cycles. The ceiling on upward flow is a result of scarcity of resources required. On the other hand, the bottom on downward flow does not have a direct limit on contraction. However, an indirect limit is the effect of accelerator on depression.

Hicks’s theory can be explained with the help of Figure-9:

In Figure-9, the y-axis represents the logarithms of output and employment while x-axis represents the semi-logarithm of time AA line represents the autonomous investment that is rising at the same rate.

EE line shows the equilibrium line that is a multiple of autonomous investment. FF line expresses the full employment or the peak phase of economy, while LL line expresses the trough phase of an economy.

Hicks explains business cycles by assuming that the economy has reached to Po point of equilibrium path and autonomous investment is the result of innovation. The autonomous investment results in the increase of output.

Consequently, the economy moves upward from the equilibrium path. After a certain point of time, the autonomous investment brings the multiplier process at work, which further increases output and employment. The increased output makes the induced investment to work that further results in accelerator process to work.

The multiplier-accelerator interaction results in the growth of the economy. Consequently, the economy enters in the phase of expansion. The economy moves on the expansion path of P₀P₁. At point P₁, the economy is in full employment condition. Now, the economy cannot grow further, it can only move on the FF line.

However, it cannot remain at FF line because autonomous investment becomes constant; therefore, now at FF, only the normal autonomous investment would be produced. This infers that the expansion of the economy is governed by induced investment only.

When the economy reaches to point P₁, the increase in induced investment becomes stable and the growth of economy starts declining. This is because of the reason that the output produced at FF line is not sufficient for induced investment.

As a result the induced investment stops. The decline of the economy can be postponed, if the time lag between output and investment is of three to four years. However, the decline in output cannot be ceased. When the decline in output occurs at point P then the decline in output would continue till the economy reaches back to EE line.

After arriving at EE line, it would continue to fall further. The rate of decline in economy is very slow because disinvestment depends on the rate of depreciation. The decrease in output leads to the decline in the rate of depreciation.

The effect of reverse accelerator on the depression is not as frequent as in the case of expansion. During the path Q₁Q₂, the induced investment is nil while autonomous investment is less than normal. In addition, the indefinite decline of economy is represented by Q₁q. However, Q₁q is a very rare case that does not occur normally.

When the economy reaches to trough, it moves along the LL line, which is associated with AA line that represents autonomous investment. Therefore, output starts increasing again with the increase in autonomous investment.

Increase in output makes the accelerator to work again. This phase is termed as recovery phase. Along with accelerator, multiplier also comes into action and their interaction makes economy run on the growth path and reaches to equilibrium EE line again.

There are certain limitations of Hicks’s theory, which are as follows:

a. Fails to explain the reasons for linear consumption function and constant multiplier. When the economy is going through different phases of business cycles, the income is redistributed that affects the marginal propensity to consume, which further affects the multiplier process.

b. Suspects the constancy of multiplier in changing economic conditions. Without practical evidence, the accelerator and multiplier cannot be assumed to be constant.

c. Takes into consideration the abstract theory, which cannot be applied in the real world.