PRODUCTION FUNCTION

Q1. What is meant by variable factor and fixed factor? Give two examples of each.
Answer: Production is the result of combined efforts of the factors of production. These factors
may be fixed or variable.

A fixed factor is one, whose quantity cannot readily be changed in response to desired changes in
output or market conditions in the short run. Its quantity remains the same, whether the level of
output is more or less or zero. Buildings, land, machinery, plants and top management are some
common examples of fixed factors.

A variable factor, on the other hand, is one whose quantity may be changed in response to a
change in output. Raw materials, ordinary labour, power, fuel, etc. are examples of variable
factors. Such factors are required more, when output is more; less, when output is less and zero,
when output is nil.

Q 2. What is meant by returns to a factor? State the law of diminishing returns to a factor.
Ans: When a firm increases production in the short run by increasing the use of a variable factor,
other factors remaining fixed, it is known as the short-run production function or returns to a
factor or law of variable proportions.
In economics, diminishing returns is the decrease in the marginal (incremental) output of
a production process as the amount of a single factor of production is incrementally increased,
while the amounts of all other factors of production stay constant.
The law of diminishing returns states that in all productive processes, adding more of one factor
of production, while holding all others constant ,will at some point yield lower incremental per-
unit returns.

It states: when output is increased by employing additional units of the variable factor (fixed
factor remaining constant) MP of the variable factor must ultimately start declining, even when it
tends to rise initially. This is also known as law of diminishing marginal product.

Q 3. Explain the relationship between marginal product and average product using
diagram.
Relationship between Average product and Marginal Product
• Initially AP and MP production goes on increasing
• AP increase when MP is greater than AP
• At maximum AP=MP
• AP decrease when MP is less than AP
.
 •

Q4. What does the law of variable proportions show? State the behaviour of total product
and marginal product according to this law.
Ans: The law of variable proportion states that if the inputs of one resource is increased by equal
increment per unit of time while the inputs of other resources are held constant, total output will
increase, but beyond some point the resulting output increases will become smaller and smaller.
Behaviour of TP: The law of variable proportion states that other factors of production remain
constant, as more and more units of variable factor is employed in the beginning total product
(TP) increases at increasing rate, then increases at a decreasing rate and ultimately declines.
Behaviour of MP: The law of variable proportion states that other factors of production remain
constant, as more and more units of variable factor is employed in the beginning Marginal
product (MP) increases , then decreases and ultimately becomes negative.

Q: State the relation between TP and MP

Relationship between Total product and Marginal Product
• Initially, TP and MP production goes on increasing
• When MP increases, TP increases at increasing rate.
• When MP is constant, TP increases at the constant rate.
• When MP decreases, TP increases at diminishing rate.
• TP is maximum when MP is zero
• TP is negative when MP decline. (See the above diagram)

Q5. Explain the law of variable proportions, giving reasons. Use diagrams.

The law of variable proportion states that other factors of production remain constant, as more
and more units of variable factor is employed in the beginning total product (TP) increases at
increasing rate, then increases at a decreasing rate and ultimately declines.
In short, the effect on total production/ marginal production in short run when variable factor is
increased is called the law of variable proportion.
Law of variable proportions is based on following assumptions:
(i) Constant Technology:
The state of technology is assumed to be given and constant. If there is an improvement in
technology the production function will move upward.
(ii) Factor Proportions are Variable:
The law assumes that factor proportions are variable. If factors of production are to be combined
in a fixed proportion, the law has no validity.
(iii) Homogeneous Factor Units:
The units of variable factor are homogeneous. Each unit is identical in quality and amount with
every other unit.
(iv) Short-Run:
The law operates in the short-run when it is not possible to vary all factor inputs.
By keeping land as a fixed factor, the production of variable factor i.e., labour can be shown with
the help of the following table:

I phase: MP increases, due to which TP increases at increasing rate. AP also increases.

The stage lasts where the MP is maximum.
Reasons:
a. Better utilization of the fixed input with increase in variable input,
b. Benefits of division and specialization of the variable input used, say, labour, c.
Indivisibility of fixed input.
II phase: MP decreases, due to which TP increases but at decreasing rate. AP also reaches
at maximum and start decreasing. The stage lasts till the TP is maximum and MP is zero.
Reasons:
Optimum combination between fixed and variable inputs is disturbed with increasing use of the
variable input,
b. After a certain level of employment of the variable input, the benefits from the
division of labour will diminish leading to diminishing return.
Imperfect substitutability between fixed input and variable input

Q. What are the reasons for the law of variable proportions?

Ans: Condition or Causes of Applicability:
There are many causes which are responsible for the application of the law of variable
proportions.
They are as follows:
1. Under Utilization of Fixed Factor:
In initial stage of production, fixed factors of production like land or machine, is under-utilized.
More units of variable factor, like labour, are needed for its proper utilization. As a result of
employment of additional units of variable factors there is proper utilization of fixed factor. In
short, increasing returns to a factor begins to manifest itself in the first stage.
2. Fixed Factors of Production.
The foremost cause of the operation of this law is that some of the factors of production are fixed
during the short period. When the fixed factor is used with variable factor, then its ratio
compared to variable factor falls. Production is the result of the co-operation of all factors. When
an additional unit of a variable factor has to produce with the help of relatively fixed factor, then
the marginal return of variable factor begins to decline.
3. Optimum Production:
After making the optimum use of a fixed factor, then the marginal return of such variable factor
begins to diminish. The simple reason is that after the optimum use, the ratio of fixed and
variable factors become defective. Let us suppose a machine is a fixed factor of production. It is
put to optimum use when 4 labourers are employed on it. If 5 labourers are put on it, then total
production increases very little and the marginal product diminishes.
4. Imperfect Substitutes:
Mrs. Joan Robinson has put the argument that imperfect substitution of factors is mainly
responsible for the operation of the law of diminishing returns. One factor cannot be used in
place of the other factor. After optimum use of fixed factors, variable factors are increased and
the amount of fixed factor could be increased by its substitutes.
Such a substitution would increase the production in the same proportion as earlier. But in real
practice factors are imperfect substitutes. However, after the optimum use of a fixed factor, it
cannot be substituted by another factor.

Q6. Define production function. Distinguish between short run and long run production
function.
The functional relationship between inputs and outputs refers to the Production Function. It
refers to the maximum quantity a firm can produce per unit of time with a given amount of
inputs when best production techniques are available.
“Production Function is the relationship between physical inputs and physical output of a
firm”. Watson
It can be expressed in terms of graph, table, and equation.
Y=f(L,K,S)
Y – Output (production) L-labor K-capital S-land
Time Periods
Short Run– it is the time period when fixed factors cannot be changed. In short, run fixed factors
remain same and variable factor changes. Law of variable proportion applies here.
Long Run– it is the time period when all the factors of production (fixed and variable) can be
changed. In the long run law of returns is applied.
Short term production function
In a short run production function, one input is variable and all other inputs are constant. The
behavior of output when one input is changed and other inputs are fixed is known as Returns to
factor.
Long-term production function
In a long run production function, all inputs are variable. When all the inputs used in the
production of a commodity changed simultaneously in the same proportion and leads to change
in output, it is known as the long-term production function. The behavior of output when all the
factors of production changes are known as Returns to scale.

Q7. Explain the law of variable proportions with the help of a diagram /numerical
example .
Answer given above