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PRODUCTION THEORY
Whatever the objective of the firm, achieving maximum efficiency in production or minimizing costs
for a given level of production is a key concern of managers
...
The key questions
mangers face in their efforts to minimize production costs are:
i)

How can production be optimized or costs minimized?

ii)

How does output respond to change sin the inputs?

iii)

How does technology matter in reduction of costs of production?

iv)

How can the least-cost combination of inputs be achieved?

v)

Given the technology, what happens to the rate of return when more plants are added to
the firm?

The theory of production, using models answers the above questions by providing tools and
techniques to analyze real life production conditions and to find solutions to practical business
problems
...
This can be generally expressed as Q  f ( L, Ld , K , M , T , t ) where: L is labour; Ld
is land; K is capital; M is raw materials; T is technology, and t is time

For ease of analysis, economists usually reduce the number of inputs to capital (K), and labour (L)
...
This implies that the quantity
produced depends on the amount of labour and capital employed
...
Each firm, depending on the product produced will
therefore have a long-run and a short-run period
...
The firm can only increase output by increasing labour
...
There are therefore
two production functions, the short-run and the long-run production functions
...
67

4

44

15

11

5

55

11

11

6

60

5

10

7

62

2

8
...
75

9

61

-1

6
...
90

Stage I

Stage II

Stage III

The above information can also be presented graphically as follows which also shows the
relationships between the TP, MP and AP
...
of workers)

The Law of Diminishing Returns
The TP shows the law of diminishing returns
...
The marginal product of each
additional worker increases and total output increases at an increasing rate
...
This is
because there is a limited number of ways of achieving greater labour specialization and each
additional worker introduces crowding effects
...


Relationship Between the TP, MP, and AP, and the Stages of Production
Several relationships between the TP, MP and AP can be seen form the graph
...
TP increases at an
increasing rate
...

Stage II: Decreasing Returns: TP continues to increase but at a decreasing rate as the marginal
product starts to decline
...
The stage ends where MP of
labour is zero and output is maximized
...

The firm should not operate in stages I and II
...


Determining the Optimal Use of the Variable Input (Labour)
To maximize output, a firm should employ more workers until MP of labour is zero at which point
TP is at its maximum
...
The
firm cannot get free labour and is required to pay wages
...


From our demand analysis, we have seen that profit is maximized where MR=MC
...
So the profit will be
maximized where MW=MR
...
This is the
value of the product resulting from the marginal unit of the variable input (labour)
...

MRP=MPL*P

Assuming a perfectly competitive product market where each unit produced is sold at 10 shillings and
that the labour market is also competitive so that each worker is paid 50 shillings
...

Number of

Total Product

Marginal Product

Marginal Revenue

workers (L)

(TP)

(MPL)

Productivity
(MRPL = MPL*P)

0

0

-

-

1

6

6

60

2

16

10

100

3

29

13

130

4

44

15

150

5

55

11

110

6

60

5

50

7

62

2

20

8

62

0

0

9

61

-1

-10

10

59

-2

-20

An economic activity should be expanded so long as the marginal benefits (revenue) exceed the
marginal cost
...


Graphic Presentation
Below ON workers the MRP exceeds the MW or Marginal Factor Cost (MFC)
...
The firm should
employ more workers until ON
...
The optimal number of workers to employ is therefore ON
...
This results in
an expansion of the scale of production
...
This is either a graphic or an algebraic function representing all
the various combinations of the two inputs that can be used to produce a given level of output
...


MRTS  

K
L

Given that:

MPL 

Q
Q
 L 
L
MPL

and
MPK 
Then:

Q
Q
 K 
K
MPK

Q
Q MPL MPL
K MPK
MRTS 


*

Q
L
MPK Q MPK
MPL

Isocost Lines
A firm will seek to produce a given output level using a combination of inputs that will minimize the
cost of production given the prices of the inputs
...
4L  0
...
This
occurs at the point of tangency between the two curves so that the slopes are the same, ie:
MPL PL
MPL MPK



MPK PK
PL
PK

Graphic Presentation

Capital

A

C
K1

B

L1

Q1

Labour

To minimize costs, the firm will produce the desired level of output at the lowest possible cost
...


Returns to Scale
This refers to the behaviour of output in response to a proportional and simultaneous change in
inputs
...
When a
firm expands its scale of production there are three possible outcomes:
i)

Total output may increase more than proportionately
...


iii)

Total output may increase less than proportionately
...


ii)

Constant returns to scale
...


K

K

200

K

200
30
00
100
0

100
0
10 20

L

a) Increasing returns to scale

200

100
10
0

0

20
0

10 20 L
b) Constant returns to scale

15
0
10
0

100
0
10 20

L

c) Decreasing returns to scale

Increasing returns to scale arise due to the opportunity for increase specialization of labour and
capital while decreasing returns are associated with management and coordination challenges that
come in as the firm grows

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