# User:Jayasreev/Law of variable proportions/law of variable propotions

The law of variable proportion is the most important law in economics. Economists like Alfred Marshall, BenhamSamulson contributed maximium to this law.This law is based on short run production function. Let us start with the concept of a standard short run production function.

Prof. JAYASREE.V, SREE NARAYANA GURU COLLEGE OF COMMERCE, CHEMBUR.
LAW OF VARIABLE PROPORTIONS.
INTRODUCTION:
The law of variable proportion is the most important law in economics. Economists like Alfred Marshall, BenhamSamulson contributed maximium to this law.This law is based on short run production function. Let us start with the concept of a standard short run production function.
Q= f[ L, ]
Q→Output
f→ function of
L→Labour as the variable factor
→ Capital as the constant factor
→ constant technology.
Law of Variable Proportions:
→This is based on Short run Production Functio n.
→ some factors are fixed, others are variable.
→This is more applicable to agriculture.
Definitions of law.
The Law of Variable Proportions which is the new name of the famous law of Diminishing Returns.

→According to Stigler” "As equal increments of one input are added, the inputs of other productive services being held constant, beyond a certain point, the resulting increments of produce will decrease i.e., the marginal product will diminish".

→According to Paul Samulson "An increase in some inputs relative to other fixed inputs will in a given state of technology cause output to increase, but after a point, the extra output resulting from the same addition of extra inputs will become less".
The law of variable proportions states that as the quantity of one factor is increased, keeping the other factors fixed, the marginal product of that factor will eventually decline. This means that upto the use of a certain amount of variable factor, marginal product of the factor may increase and after a certain stage it starts diminishing. When the variable factor becomes relatively abundant, the marginal product may become negative.
Assumptions of Law.
→Constant technology--- This law assumes that technology does not change throughout the operation of the law.
→Fixed amount of some factors.—One factor of production has to be fixed for this law.
→ Possibility of varying factor proportions—This law assumes that variable factors can be --changed in the short run.
Terminology.
1,Total Product→ It is the total of output, resulting from efforts of all factors of production.
TP= P*Q
2Average Product→It is the total product per unit of the variable factor.
AP=TP/N
3.MarginalProduct→It is addition made to the Total Product as a result of production of one more unit of
output.
MP= TPn-- Tpn
Illustration of the Law.
We assume the land is the fixed factor in the short run, labour is the variable factor. Technology remains to be constant.The law states that as we increase the quantity of one input, which is combined with other fixed inputs, marginal physical productivity of variable input must eventually decline.
Following table explains the working of law.
Schedule:
Fixed Inputs (Land Capital) Variable Resource (labor) Total Produce (TP Quintals) Marginal Product (MP Quintals) Average Product (AP Quintals)
30
30 1
2 10
25 10
15 Increasing marginal return 10
12.5

30
30
30
30
30 3
4
5
6
7 37
47
55
60
63 12
10
8
5
3 Diminishing marginal returns 12.3
11.8
11.0
10.0
9.0

30
30
8
9 63
62 0
-1 Negative marginal returns 7.9
6.8

Diagrammatic Representation of Law.
Interpretation of the diagram and Table.
This law has THREE stages
1.Increasing Returns .
2. Diminishing Returns.
3. Negative Returns.
Increasing Returns:
In this stage, Average Product increases, Marginal Product increases and also Total Product. TP increases at more proportionate rate . TP increases from 10 to 25 units. This stage is known as increasing returns. This stage of increasing output by increasing labour does not last for a long time. This continues upto 3rdunits. The point F onwards TP increases at a diminishing rate. In the first stage, marginal product curve of a variable factor rises in a part and then falls. The average product curve rises throughout and remains below the MP curve. MP reaches maximum in this stage.
Diminishing Returns:

This is the most important stage in the production function. In stage 2, the total production continues to increase at a diminishing rate until it reaches its maximum point where the 2nd stage ends. In this stage both the marginal product (MP) and average product of the variable factor are diminishing but are positive. When TP reaches the maximum, MP is zero.MP intersects the X axis in this stage.
As more and more variable factors are used on fixed factor, marginal and average product begins to decrease. Factors of production are invisible. Economically this is the most viable area of production.
3.Negative Returns.
In the 3rd stage, the TP decreases. The TP, curve slopes downward (From point H onward). The MP curve falls to zero at point L2 and then is negative. When we increases the labour even after MP becomes zero, then MP becomes negative and it goes below the X axis.This is the most unviable region. In our table from 8th unit onwards, this stage starts.
Any sensible producer will stop the production in the second stage where AP and MP begins to decrease, but MP has not become negative.The producer will employ the variable factor (say labor) up to the point where the marginal product of the labor equals to the wage rate.

IMPORTANCE OF LAW.

→It helps to understand the input-output relationships. We can also find out the increase in TP as a result of additional labour.
→ The law also tells us the tendency of Diminishing Returns is applicable to all sectors including agriculture.
→The law also tells that however we increase variable factor on the fixed factor, TP will increase at a diminishing rate.

KEY POINTS.

yy

Recapitalisation:
1,Marginal product of a variable input is described as
a, Total product divided by number of variable unit.
b. additional output resulting from a one unit of variable factor.
c. additional output resulting from one unit increase in both in variable and fixed factors.
2. MP, AP, TP of a firm in the short run show the follow features:
a.when TP is increasing, AP and MP may be either rising or falling.
b. When MP is negative, TP and AP are falling.
c. When MP is rising, AP= MP and TP is rising.
3. The law of diminishing returns applies to
a, the short run but in the long run.
b. long run, not in the short run.
c. both short and long run.
4. When TP is maximum, MP is ----
a, Zero.
b. positive.
c. negative