# In this post, we shall focus our attention on the laws of returns.

At the end of this topic, you should be able to:

 identify the three types of returns we have in production relationships.

 explain the laws of returns

 use table, graph and mathematics to illustrate the three laws of returns.

In attempt to either maximize output or profit, farmers combine varying levels of input factors in the production process. This various levels of input usage by farmers allow the operations of the laws of returns.

The usefulness of this concept lies in its role as a classifying device. It provides a convenient way of classifying particular types of technological condition.

In a resource allocation involving one variable input factor while keeping the other factors fixed, three different types of relationships can be identified: increasing returns, constant returns and decreasing returns. These relationships can be discussed using written words, tables, graphs and mathematics.

## Law Of Increasing Returns

Law of increasing returns is a situation in the production process in which each successive unit of variable input adds more and more to the output. That is, every addition to variable input adds more and more to the output. In other words, every addition of variable input to the fixed factors in the production process yield more to the total output than the previous unit of output. This situation in the production process can also be illustrated in a tabular form.

Table 2: Hypothetical Example of increasing Return

From Table 2, addition of one unit of variable factor to 1 unit of input, yielded marginal returns of 5. Addition of one unit to the second variable factor yielded marginal returns of 10 and from 10 to 15 and 15 to marginal returns of 20. Every additions of one unit of variable factor yielded more than the previous marginal returns.

This relationship can also be expressed graphically thus:

Input (X)

Output (Y)

TP

Fig. 2: Graphical Illustration of Increasing Returns

This relationship can also be expressed in mathematical form thus:

ΔY1 < ΔY2 < ΔY3 < ΔY4 < ΔY5

ΔX1 ΔX2 ΔX3 ΔX4 ΔX5

This shows that the marginal return in out Y1 and variable input X1 is less than the marginal returns involving output Y2 and variable input X2 and so on.

## Law of Constant Returns

The law of constant returns states that without varying the proportions in which the factor of production area combined, there is an increase in output proportionate to the increase in the total quantity of factors employed. In other words, the addition of each successive unit of the variable factor to the fixed factors adds the same to the output. For example if all the quantities of all the inputs used in producing a given  output is increased by 10 percent and then output increased by the same 10 percent, then the returns is said to be constant.

Each successive unit of variable input added results in an equal quantity of additional output.

This relationship can be expressed in a tabular form.

Table 3: Hypothetical Illustration of Constant Returns.

Table 3 showed that addition of one unit of variable input factor continuously yield marginal returns of 5, i.e every addition of one unit of variable input factor yielded the same marginal returns of 5 units.

This relationship can also be expressed in a graphical form by plotting output against the corresponding values of variable input factors.

Fg.3: Graphical Illustration of constant Return.

The graph showed a linear relationship producing a straight line curve. The relationship can also be expressed in a mathematical form using algebraic equation

ΔY1 = ΔY2 = ΔY3 = ΔY4 = ΔY5

ΔX1 ΔX2 ΔX3 ΔX4 ΔX5

This shows that the marginal returns in output Y1 and variable input X1 is exactly the same as in other relationships.

The condition of constant returns is unlikely to be met in agricultural business.

## Law of Decreasing Returns

The law of decreasing returns states that the addition of each successive unit of the variable input to the fixed inputs in the production process, adds less and less to the total output than the previous unit. Alternatively, it can be stated that for each addition to the variable factor the addition to the total output declines. This law can further be illustrated thus: suppose that the quantities of all the inputs used in producing a given output are increased for example by 10 percent and if output increases by smaller proportion e.g a percent or less, then return to scale is said to be decreasing. Decreasing returns can also be expressed in a tabular form

Table 4: Hypothetical Illustration of Decreasing Returns

From Table 4, addition of 1 unit of X to the initial unit of X, yielded marginal returns of 25 units. Addition of 1 unit of X to the second variable input yielded less marginal returns of 20. Every subsequent additions of one unit of variable factors yielded less than the previous marginal returns.

This relationship can equally be represented in a graphical form.

Fig. 4: Graphical Representation of Decreasing Returns

The graph depicts a concave relationship to the x-axis. We can also express this relationship between variable input factor and output in algebra form as follows:

ΔY1 > ΔY2 > ΔY3 > ΔY4 > ΔY5

ΔX1 ΔX2 ΔX3 ΔX4 ΔX5

Mathematically, this relationship shows that the marginal returns in output Y1 and variable input X1 is more than the marginal returns involving output Y2 and input X2 and son on.

SELF-ASSESSMENT EXERCISE

List and explain the three types of returns in production relationships

## CONCLUSION

This post focused on the laws of returns. In this topic we identified three major types of returns in production process. These returns can be increasing, constant or decreasing. Knowledge of these relationships is very important in agricultural production because it provides a convenient way of classifying particular types of technological condition.

## SUMMARY

The main points discussed in this post include the followings:

Relationships between variable input factors and output can be classified into three: increasing returns, constant returns and decreasing returns

In the stage of increasing returns each successive unit of variable input adds more and more to the output

Increasing returns can be expressed algebraically as:

ΔY1 < ΔY2--------------------ΔYn

ΔX1 ΔX2 ΔXn

In constant returns, addition of each successive unit of variable factor to the fixed factors adds the same to the output.

Constant returns can be expressed algebraically as follows:

ΔY1 = ΔY2--------------------ΔYn

ΔX1 ΔX2 ΔXn

In decreasing returns, each addition to the variable factor, the addition to the total output declines.

vii. Decreasing returns can be expressed algebraically as follows:

ΔY1 ˃ ΔY2--------------------ΔYn

ΔX1 ΔX2 ΔXn

The three classifications can be expressed in written words, tabular form, graphical form and algebraic form.

ASSIGNMENT

With the aid of tables, graphs and algebra differentiate between the laws of increasing, constant and decreasing returns.

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