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Production function
A production function provides the relationship between out put and various
factors of production. A production function is a functional relation between
the inputs and out put.
The production function can be classified as per time period. There can be
short run production function and the long run production function. Between
time periods the nature of factors can change.
In the long run all factors change; when all factors change there can be large
changes in the out put can be brought, the technology can change, the cost
structure may be totally renewed. So, the expression of long run production
function will be
Quantity of out put,
Q = f ( Labor, raw material, power, land, buildings, machinery / T)
Where T, is technology; an embedded (associated) factor of production. It is
the qualitative description of capital,
In the short run certain factors are fixed certain other variable. Fixed factors
remain fixed even with changing out put. On the other hand variable factors
change with changes in the out put. So the expression of production function
will have fixed and variable factors.
Quantity of out put,
Q, = f ( labor, raw material, power/ F , T)
Where F represents the fixed factors which remain unchanged in the short
run and T is the level of technology given and constant.
Dr.Ranga Sai
First Year BMM Semester I, Economics (w.e.f. June 2009) 16
The short run production function will always carry the expression fixed and
variable, separately.
Law of variable proportions
The law of variable proportions studies the relationship between one
variable factor and the out put. It studies the behavior of out put for changing
variable factor. It deals with a short run production function with one
variable factors with all other factors are given and kept constant.
Q, = f ( labour / F , T)
Where F represents the fixed factors which remain unchanged in the short
run and T is the level of technology given and constant.
According to the law of variable proportions, ‘all other factors remaining
constant, if the usage of one variable factor increases, the out put will
increase rapidly, then slowly and finally decreases’.
Labour
Units
Total
Product
TP
Average
Product
AP
Marginal
Product
MP
Production
Elasticity
Stages of production
1 5 5 0 Increasing
2 8 4 3 Ep>1 returns
3 15 5 7 I Stage
4 24 6 9
5 30 6 6
6 30 5 0 Ep<1 Diminishing returns
II Stage
7 28 4 -2 Ep<0 Negative returns
III Stage
A production function provides the relationship between out put and various
factors of production. A production function is a functional relation between
the inputs and out put.
The production function can be classified as per time period. There can be
short run production function and the long run production function. Between
time periods the nature of factors can change.
In the long run all factors change; when all factors change there can be large
changes in the out put can be brought, the technology can change, the cost
structure may be totally renewed. So, the expression of long run production
function will be
Quantity of out put,
Q = f ( Labor, raw material, power, land, buildings, machinery / T)
Where T, is technology; an embedded (associated) factor of production. It is
the qualitative description of capital,
In the short run certain factors are fixed certain other variable. Fixed factors
remain fixed even with changing out put. On the other hand variable factors
change with changes in the out put. So the expression of production function
will have fixed and variable factors.
Quantity of out put,
Q, = f ( labor, raw material, power/ F , T)
Where F represents the fixed factors which remain unchanged in the short
run and T is the level of technology given and constant.
Dr.Ranga Sai
First Year BMM Semester I, Economics (w.e.f. June 2009) 16
The short run production function will always carry the expression fixed and
variable, separately.
Law of variable proportions
The law of variable proportions studies the relationship between one
variable factor and the out put. It studies the behavior of out put for changing
variable factor. It deals with a short run production function with one
variable factors with all other factors are given and kept constant.
Q, = f ( labour / F , T)
Where F represents the fixed factors which remain unchanged in the short
run and T is the level of technology given and constant.
According to the law of variable proportions, ‘all other factors remaining
constant, if the usage of one variable factor increases, the out put will
increase rapidly, then slowly and finally decreases’.
Labour
Units
Total
Product
TP
Average
Product
AP
Marginal
Product
MP
Production
Elasticity
Stages of production
1 5 5 0 Increasing
2 8 4 3 Ep>1 returns
3 15 5 7 I Stage
4 24 6 9
5 30 6 6
6 30 5 0 Ep<1 Diminishing returns
II Stage
7 28 4 -2 Ep<0 Negative returns
III Stage