Theory of production

1. Mir Mohammed Belal
Premier University
Chittagong
BBA (Hons)

2. Production function: The functional relationship between physical
inputs and physical output of a firm is known as production function.
Algebraically, production function can be written as p=f(Q),Q=f(L,K,M)
Where Q stands for the quantity of factors labor, capital and raw
materials respectively .
Types of production function:
2 types:
(1)Short run.
(2)Long run.
•Short run: The period when some input are constant and one on few in
variable.
•Long run: About 5 year all input are variable.

4. Product schedule:
Unit of labor TP AP MP
1 80 80 80
2 170 85 90
3 270 90 100
4 368 92 98
5 430 86 62
6 480 80 50
7 504 72 24
8 504 63 0
9 495 55 -9
10 480 48 -15

5. O X
TP
Y
1 2 3 4 5 6 7 8 9 10 Labor
Figure:1
50
100
150
200
250
300
350
400
450
500
550
TP

6. • The total product curve is shown by TP
in figure:-1. it will be seen that in the
beginning total curve rises at an
increasing rate. The stop of the TP curve
is rising in thee beginning a point total
product curve starts rising at a
diminishing variable factor is increased.

7. 1 2 3 4 5 6 7 8 9 10 X
0
-10
-20
100
90
80
70
60
50
40
30
20
10
AP
MP

8. • The average product are of a variable
factor first rises and it declines . That is
the average product are has been
inverted U shape. The marginal
product are first rises and the
diminishing variable factor is increased
and at a certain point MP is negative.

9.  Law of variable proportion
• Alfred Marshall: It refers input-output relation when
output is increased by varying the quantity of one input.
• Condition:
3 conditions_
1.Technology is constant.
2.Some inputs must be kept constant.
3.The possibility of varying the proportion.

10. Point of inflation
Y
O
MP
X
AP
TP
Unit of labor
TP,MP,AP
first
second third
F Ox axis
represent the
unit of factor,
OY axis
represent the
TP, AP and
MP.

11. •1st
stage: Total product increase, Marginal product increase
and average product also increase. Point F is point of
inflation, point of inflation means rate of change, rate of
change means before F TP increase, after F, TP increase –
decreasing rate. At point F MP is highest.
•2nd
stage: TP increase, AP decrease, MP decrease, At the end
of 2nd
stage TP highest, MP is zero.
•3rd
stage: TP decrease, AP decrease, MP decrease, but MP is
negative.

12. Expansion path/Scale line:
Expansion path
IQ1(200)
IQ2(300)
IQ3(400)
O M1 M2 M3 IC1 IC2 IC3
X
Y
N1
N2
N3
A
B
C
capital
labor

13. Ox represent the labor & and OY represent the capital.
There are thee ISO Quant ISO1. ISO2, ISO3, they
represent 200, 300, 400, unit. Three ISO cost IC1, IC2,
IC3. When OM labor & ON capital produce the output
level denoted by IQ1(200) unit & we get point A. The
OM1 & OM2 labor ON1 & ON2 capital produce the high
output level denoted by IQ2& IQ3 (300 & 400 unit) & we
get point B&C. The joining point A, B, C is called
expansion path.

14. ISO quant
• ISO quant indicates various combination of two factors of production
which give the same level of output per unit of time.
Schedule:
12 A
capital
8 B
5 C
3 D
2 E
O 1 2 3 4 5 X
labor
combin
ation
Factor
labor
Factor
capital
produc
tion
A 1 12 40
B 2 8 40
C 3 5 40
D 4 3 40
E 5 2 40
IQ

15. OX axes represent the labor and OY represent the
capital. IQ is an ISO quant curve. A consisting of
one unit of labor and 12 units of capital produce
the given 40 unit of output. Similarly B, C, D, E
consisting of 2, 3, 4 ,5 labor and 8, 5, 3, 2 unit of
capital produce the given 40 unit of output. The
every combination represented on it can produce
40 unit of output.

16. ISO quant map
an ISO quant map can be define the set of ISO quant curves that
show technically efficient combination inputs that can produce
different levels of output.
IQ1(40)
IQ2(60) IQ3(80)
IQ4(100)
Y
O
capital
X
labor

17. ISO cost line

18. 30
capital 25
20 ISO cost line
15
10
5
O 10 20 30 40 50 60 X
Labor
Y
ISO cost line:

19. Properties of ISO quant
There are three properties they are:-
a)ISO-quant is convex to the origin
b)Two ISO-quant can’t intersect.
c)ISO-quant slopes down word to the right.
(1) ISO-quant is convex to the origin: due to
diminishing MRTS this curve opposite to the
origin.

20. capital
Y
K
O labour X
IQ
Figure:1
MRTS>increasing
Y
IQ
K
O labor X
figure:2
MRTS>constant
IQ
X
laborO
Y
capital
Figure:3
OX represent the labor & OY
represent the capital in fig:1, 2,
3.Fig:1 is correct. Fig:2 is
constant. Fig:3 is state line. So
Fig 2&3 is not correct.

21. (2) Two ISO quant can’t intersect each other at any point:
C
B A
IQ2(60unit)
IQ1 (40 unit)
O Labor X
capital
Y
OX represent the labor &
OY represent the capital.
There is ISO quant there IQ
1 it represent 40 units
another IQ 2 represent 60
units. In IQ1 there is A two
point A and C. In IQ2 there
is two point B & C . There
are same production in
IC1 , B=C=60 units. C is the
different product in level in
the two productions.

22. (3)ISO quant slop down ward to the right:
This implies that the ISO quant is a negatively sloped curve. This is because when the
quantity of factors C is increased , the quantity of labor must be reduced so as to
keep the same level of output.
a
b
ISO (40)
Y
capital
O X1 X2 labor X
Figure:1
From the figure we find that as
the producer moves a to b, the
producer employed more
labor and less capital and its
represents 40 units of
production. It is show that an
IQ curves downward to the
right.

23.  Marginal rate of technical substitution(MRTS)
combinatio
n
Factor
labor
Factor
capital
product MRTS
A 1 12 40
B 2 8 40 4
C 3 5 40 3
D 4 3 40 2
E 5 2 40 1

24. O 1 2 3 4 5 x
Labor
12
8
5
3
2
1
Y
IQ
a
b
c
d
e
Factor
capital
OX represent the
labor & OY
represent the
capital. A, B, C, D &
E is an IQ curve. The
slope of labor will
increase. The slope
of labor will
decrease in capital.

25.  Return of scale
• Return of scale refers
different level of
production at different
factors of production..
There are three types of
returns to scale:-
a) Increasing returns to
scale: output increase in
greater than increase in
input.
b) Constant returns to
scale: output increase in
less same proportion as
input increase.
c) Decreasing return to
scale :output increase in
less proportion than
increase in input.
combin
ation
labor capital Total
return
Margina
l return
1 1 3 2 2
2 2 6 5 3
3 3 9 9 4
4 4 12 14 5
5 5 15 19 5
6 6 18 24 5
7 7 21 28 4
8 8 24 31 3
9 9 27 33 2

26. constant
Combination of factor
X
decreasingincreasing
Marginal
return
Y
5
4
3
2
1
O
1 2 3 4 5 6 7 8 9

27. • OX represent the combination of factor. OY
represent the marginal return. When the
combination of factor 1, 2, 3 then marginal return is
increasing the combination of factor 4, 5, 6 the
marginal return is constant. When the combination
of factor 7, 8, 9 the marginal return is decreasing.

28.  Efficiency of production/producers equilibrium.
The ability produced a good using the fewest resources possible.
Two kinds of efficiency of production.
(1)Cost minimization.
(2)Output minimization.
Least cost of combination/Cost minimization:
The producer is said to be in equilibrium when the chooses that combination of
factors that represent minimum cost & no tendency to rearrange.
Condition:
(1)Slope of ISO quant is equal to slope of ISO cost line.
(2) ISO quant is tangent to ISO cost.
(3)ISO quant is convex to origin.
(4)The production is fixed.

29. Equilibrium point
A
C
E
BD
N
O
M IC1 IC2 IC3 X
(100) (200) (300) labor
Y

31. Output maximization:
• Output maximization said to be in equilibrium when B
produces maximum output with given cost.
• There are four conditions:
1) Slope of ISO-quant is equal to slope of ISO cost line.
2) ISO-quant is tangent to cost line.
3) ISO-quant is convex to origin.
4) The total cost is fixed, I,E. suppose taka 300.

32. Y
X
A
C
B
N
O M ISO cost (300)
IQ3 (700)
IQ2 (600)
IQ1 (500)
Equilibrium point
Capital
Labor