Law of variable proportion/ law of diminishing returns:

It states that, if one factor is used more and more, keeping the other factors constant. The total output will increase at increasing rate in the beginning and then afterwards it increases at diminishing rate and eventually decreases absolutely.

When other things remaining the same, “As labour and capital are applied in the cultivation of land, causes less than proportionate increase in the amount of produced raised, unless it happen to coincide an improvement in the art of agriculture” or “If equal increments of one factor of production to other factors of production are applied, which are kept at a certain level, then the resulting additional output will decline beyond some point”. The law indicates an important relationship since it is that where a farmer would like to operate rationally. For example, the farmer is producing in the first area where the marginal product increases, then he can increase the average productivity by applying more of inputs and thus he has a strong incentive to use more unit of this input to get out this range. When application of further doses may cause the total output to decrease. So farmer keeps himself from that range due to declining marginal productivity.

Assumptions:

• Constant technology
• Short run
• Homogeneous factors
• Variable input ratio

Three stages of production

Based on the law of variable proportion, there is increasing return in the early period, if one input is changing and some other inputs are kept fixed. Then, after a certain point the production increases with constant rate, then production increases on decreasing rate then the production reaches at maximum. If we further try to increase variable inputs, the production goes on decreasing. Such production function is also termed as the classical production function.

According to classical production function, there are three stages or production which is described as follows:

Input (X)	Total product (Y) (TP)	Average product Y/X (AP)	Marginal product dY/dX(MP)
0	0
1	2	2	2
2	5	2.5	3
3	9	3	4
4	14	3.5	5
5	19	3.8	5
6	23	3.833333	4
7	26	3.714286	3
8	28	3.5	2
9	29	3.222222	1
10	29	2.9	0
11	28	2.545455	-1
12	26	2.166667	-2

Elasticity of production (Ep):

It is a measure of responsiveness of output to changes in input. The elasticity of production refers to the proportionate change in output as compared to proportionate change in input.

Ep = Percentage change in output/ Percentage change in input.

Ep = ((Change in output/ Initial output) * 100) / ((Change in input/ Initial input) * 100)

i.e., ((Δ Y/ Y) * 100)/(( Δ X/X) * 100)

= (Δ Y/Y)/( Δ X/X) = (Δ Y/Y) (X/ Δ X) = (Δ Y/ Δ X) * (X/Y),

By rearranging we have,

ΔY/ ΔX * (X/Y) = ((Δ Y / Δ X)/( Δ Y/ Δ X) = MPP/APP

The elasticity of production is the ratio of marginal physical product to average physical product.

Ep = 1, Constant returns. (MPP = APP), at the end of Ist stage of production

EP > 1, increasing returns (I stage of production)

EP < 1, Diminishing returns (II stage of production)

Ep = 0, When MPP = 0 and TPP maximum (At the end of IInd stage)

EP < 0, Negative returns (IIIrd stage of production)

The relationships of TP, MP and AP can be expressed as;

1. When the output is increasing, marginal product is positive.

2. When the total product is maximum, marginal product is zero.

3. When the total product is decreasing, marginal product is negative.

4. When the total product is increasing at increasing rate, the marginal product is increasing; and

5. When the total product is increasing at decreasing rate, the marginal product is decreasing but positive.

Region I:

The first phase of production is characterized by more additional production per unit of input used i.e. there is higher marginal product (MP). But the average product (AP) is lesser than the marginal product and AP increases throughout this reason due to increased efficiency of the variable inputs. Thus, this region holds from the point of origin up to the point where MP remains greater than AP. The AP increases throughout this region indicating that the efficiency of all the units of variable input keeps increasing. The total product (TP) is increasing at increasing rate at first then at decreasing rate. After certain time AP equals MP, it is the end point of first stage. In this region the elasticity of production (EP) is greater than one due to increased efficiency of variable input.

Region II:

Throughout the second region the marginal product goes down and lowers than the average product. This is the region obtains when MP is decreasing and is less than AP. In this region, at the starting point MP is equal to AP and elasticity of production is 1. Then the marginal product goes down and becomes zero. The decreasing rate of MP indicates that the additional product obtained by additional variable inputs diminishes. In this region, total product (TP) increases but at decreasing rate and the elasticity of production (EP) is greater than zero but less than 1.

Region III:

This region begins when there is the highest level of total product (TP) and MP becomes zero and crosses zero point i.e. MP becomes negative. Negative MP occurs when so much excessive quantity of the variable input is used but the total output begins to decrease continuously. In this region, the elasticity of production (EP) is always less than zero or negative.

Rational Stage of Production:

When a farmer is undertaking production on his farm, his prime objective is to maximize his returns. The TP curve indicates only total production but MP curve represents rate of returns. Therefore the position of MP is very important for deciding how much to produce. Therefore the rational stage of production is always stage II. The reason behind it is that in this stage MP and AP both are positive, MP declines but positive. Similarly, elasticity of production (EP) is less than one but it also positive. Therefore farmer should take production in this stage for maximizing the potential returns.

Irrational stages of production:

Stage I and III are the irrational stage of production. If production is taken in stage III it will result in loss, because MP and EP are negative and TP also decreases continuously. If farmer produces in this reason he will incur double loss i.e. reduced production and unnecessary additional cost of input. In case of stage I, though TP, MP, AP and EP all are indicating increasing trend, it is irrational stage of production. The reason behind it is that if production is ceased in this stage, the producer or farmer will not in loss but he/she will lose the potential possible returns. This is opposite to rationality. Hence these two stages are irrational stage of production.