**Definition: **The **Multiplier-Accelerator Interaction Theory** came into existence when the theorist of the Keynesian tradition stresses on multiplier process in economic fluctuations while J.K. Clark emphasized on the role of acceleration in the business fluctuations.

But however, Paul Samuelson, the post-Keynesian business cycle theorists asserted that neither the multiplier theory nor the principle of acceleration alone is adequate to analyze the business cycle fluctuations. And hence, proposed the **Multiplier-Accelerator Model**, also called as **Hanson-Samuelson Model**.

The multiplier-Accelerator model is based on the Keynesian multiplier, a consequence of the assumption that the **level** of economic activity decides the consumption intentions and the accelerator theory of investment which is based on the assumption that the investment intentions depend on the **pace **with which the economic activities grow.

The Samuelson’s model is the first step towards integrating the theory of multiplier and principle of acceleration. This theory shows how well these two tools are integrated to generate income, so as to have an increased consumption and investment demands more than expected and how these reflect the changes in the business cycle. To understand Samuelson’s model one needs to know the difference between the Autonomous and Derived Investments.

**Autonomous investment** is the investment undertaken due to the external factors such as new inventions in technology, production process, production methods, etc. While, the **Derived Investment** is the investment, particularly in capital equipment, is undertaken to meet the increase in consumer demand necessitating new investment.

With an increase in the autonomous investment, the income of people rises and the process of multiplier begins. With increased incomes, the demand for the consumer goods also increases depending on the marginal propensity to consume. And if the firm has no excess production capacity, then its existing capital will stand inadequate to meet the increased demand. Therefore, the firm will undertake new investment to meet the growing demand. Thus, an increase in consumption creates a demand for investment, and this is called as **Derived Investment**. This marks the beginning of the **acceleration process.**

When the derived investment takes place, the income rises, in the same manner, it does when the autonomous investment took place. With an increased income, the demand for the consumer goods also increases. This is how, the multiplier process and principle of acceleration interact with each other, such that income grows at a faster rate than expected.

In short, the exogenous factors (external origin) lead to autonomous investment, which results in the multiplier effect. This multiplier effect creates the derived investment, which results in the acceleration of investment. **Samuelson made the following assumptions in the analysis of this interaction process:**

- There is no excess production capacity.
- At least one-year lag in the consumption.
- At least one-year lag in the increase in demand for consumption and investment.
- No government intervention, and no foreign trade.

**Samuelson’s model of business fluctuations is presented below:**

Given the assumption (4), the economy is said to be in equilibrium when,

**Y _{t} = C_{t} +I_{t } ………. (A)**

Where, Y_{t} = national income, C_{t }= total consumption expenditure, I_{t} = total investment expenditure, all in a period ‘t’.

Given the assumption (2), the consumption function can be expressed as:

**C _{t} =a Y_{t-1} ……….. (B)**

Where, Y_{t-1}= income in period t-1, and a = marginal propensity to consume (mpc).

Investment is a function of consumption with a one-year lag, and is expressed as:

**I _{t} = b (C_{t} – C_{t-1}) ……… (C)**

Where, b = capital/output ratio. Here parameter ‘b’ determines the accelerator.

By substituting equation (B) for C_{t} and equation (C) for I_{t}, the equilibrium equation can be written as:

**Y _{t} = a Y_{t-1} + b (C_{t} – C_{t-1})**

Note: C_{t}= a Y_{t-1} and C_{t-1} = a Y_{t-2}**. **By substituting these values, the equilibrium equation can be rewritten as:

**Y _{t} = a Y_{t-1} + b(a Y_{t-1} – a Y_{t-2})**

Further, simplifying this equation:

**Y _{t} = a (1 +b) Y_{t-1} – abY_{t-2})**

**Samuelson’s model suffers from the following criticisms:**

- The critics feel that it is far too simple a model to explain what all happens during the economic fluctuations. They are of an opinion that the model has been developed on highly simplifying assumptions.
- Samuelson stresses on the role of multiplier and accelerator and the interaction between them as a fundamental cause of business fluctuations. Thus, like other theories, it has also ignored the other important factors that play a crucial role in a cyclical process, such as producer’s expectations, change in the psychology of businessmen, change in consumer’s tastes and preferences and the exogenous factors.
- One of the major criticism of this model is that it is assumed that the capital/output ratio remains constant while there are chances of change in this ratio during expansion and depression.
- Finally, the cyclical patterns suggested in this model do not confirm the real world experience.

In spite of these bottlenecks, Samuelson’s model is acclaimed as a sound attempt to integration between the Keynesian multiplier theory and Clarke’s acceleration principle, that fairly explains the causes of fluctuations in the business cycles.** **

Atiq Sohail says

Very helpful for me