The table above clarifies the law of variable proportions. In this table, land is considered a fixed factor, and labor is considered a variable factor. 

Keeping land fixed at 10 Ropanis and increasing the units of labor, total production increases at an increasing rate up to the third unit of labor. Then, total production increases at a decreasing rate up to the fifth unit of labor. After that, total production remains constant at the sixth unit of labor, and from the seventh unit, total production starts to decrease. 

Marginal production increases up to the third unit of labor and then starts to decrease. Marginal production is zero at the sixth unit of labor and then becomes negative. Average production increases up to the fourth unit of labor and then continuously decreases. 

Unlike marginal production, average production never becomes zero or negative.

The law of variable proportions can also be explained through the following graph:

In the graph above, the x-axis shows the units of labor, and the y-axis shows the total, average, and marginal production. 

The curves TP, AP, and MP represent the total production curve, average production curve, and marginal production curve, respectively.

Stages of the Law of Variable Proportions

The graph shows three stages of production. These stages can be explained as follows:

(a) Stage I: 

The first stage is also called the stage of increasing returns to the variable factor. At the beginning of this stage, total production increases at an increasing rate and, after a certain point, starts to increase at a decreasing rate. 

Also, in this stage, marginal production initially increases and reaches its maximum and then starts to decrease, but average production continuously increases. In the graph, total production is increasing at an increasing rate up to the third unit of labor and then starts to increase at a decreasing rate. 

Marginal production increases up to the third unit of labor and reaches its maximum, which is shown by point G. After that, marginal production starts to decrease. Average production is increasing up to the fourth unit of labor, and it reaches its maximum at this unit of labor. 

Average production is constant at the fourth unit of labor. At point E, marginal production and average production are equal. In other words, marginal production and average production are equal when labor is 4 units. The first stage ends at this point.

(b) Stage II: 

The second stage is also called the stage of diminishing returns to the variable factor. In this stage, total production increases at a decreasing rate and becomes maximum and then constant. 

It is clear from the graph that total production reaches its maximum at point C or the fifth unit of labor and becomes constant at point D or the sixth unit of labor. Also, average production is continuously decreasing. 

Marginal production becomes zero when total production is maximum and constant at the sixth unit of labor, which is shown by point F in the graph. The second stage ends when marginal production becomes zero. A rational producer chooses the second stage for production.

(c) Stage III: 

The third stage is also called the stage of negative returns to the variable factor. In this stage, total production continuously decreases. Average production also continuously decreases, but it never becomes zero or negative. 

In this stage, marginal production is negative because total production is decreasing. Therefore, the total production curve TP is sloping downwards from point D, and the marginal product curve (MP) goes below the x-axis.

The operating stage for a producer is Stage II: The Stage of Diminishing Returns.

Why does a producer operate in Stage II?

1. Efficient Use of Resources:

   • In Stage I, marginal production (MP) is increasing, meaning additional units of labor are highly productive. However, since average production (AP) is still rising, adding more labor can still be beneficial.

   • But in Stage III, marginal production becomes negative, meaning additional labor decreases total production, leading to inefficiency and wastage of resources.

2. Maximizing Output with Positive Marginal Returns:

   • In Stage II, total production is increasing at a decreasing rate, meaning additional labor still contributes positively to output.

   • Marginal production (MP) is decreasing but remains positive, ensuring that each additional worker still adds to total production.

3. Point of Maximum Total Production:

   • The producer should operate before marginal production becomes zero (end of Stage II), as beyond this point, adding more labor will not increase output.

Thus, a rational producer operates in Stage II, where total production is maximized while still achieving positive marginal returns.