THEORY OF PRODUCTION
A production function shows a technical relationship between inputs and outputs. Supposing that the
production of good X requires input of capital, labour and land using functional notation we can write
Qx=f (K, L, LD)
Where:
Qx=output of x per time period
F=the functional relationship
K,L,LD=Services of capital labor and land
The short and long run
The short run is that period of time over which the input of at least one factor of production cannot
be varied. Those factors which can be varied in the short run (labor, raw materials and fuel) are called
variable factors. Those which cannot be varied (capital and land are called fixed factors). The long
run is that period of time over which the input of all factors is variable factors in the long run.
NB: The actual length of the long run does not correspond precisely to any particular time period.
Short run changes in production. As a firm increases its level of production in the short run, it
eventually comes up against “the law of diminishing returns.”
Illustration
Consider farmer growing maize in 1 acre of land and with a given quantity of capital and assume that
neither the land nor the capital can be varied in the short run. Assume also that the state of technology
is constant and that labor is homogeneous i.e. Each worker is exactly like any other worker.
The production function can be written as:-
QM=f (L, K, LD)
No. of workers Total Product(TP) Average product MP
(AP)
1 4 4 4
2 14 7 10
3 25.5 8.5 11.5
4 40 10 14.5
5 60 12 20
6 72 12 12
7 77 11 5
8 80 10 3
9 81 9 1
10 75 7.5 -6
P=TP
L
MP=the change in total product resulting from the employment of an additional worker.
MP=ΔTP
ΔL
It is apparent that MP of a labor is at a maximum when five workers are employed, the 5th worker
adds 20 tones to the total maize output. After this point the MP of labor declines. The result that both
the average and the marginal product of labor eventually declines as more and more units of labor
are added to a fixed amount of other factors in an illustration of the” law of diminishing returns .”
Theory of Production – NOTES @DOUGLAS Page 1
, The law of diminishing return states that as additional units of a variable factor are added to a given
quantity of fixed factors, with a given state of technology, the average and the marginal products of
the variable factor will eventually decline.
Average and
Marginal
Products
AP
MP
NO. Of workers
The AP and MP are smooth because of the discrete nature of the data. If we had used continuous data
so that the labor input could be increased in very small quantities, we would have obtained smooth
curves for AP and MP
Average
And
Marginal
Product A B
O Number of workers
MP reaches maximum at point A. This is known as the point of diminishing marginal returns.
Similarly the point at which AP reaches maximum is B and is known as the point of diminishing
average returns
NB - AP begins to fall before AP does. In fact the MP cuts the AP at maximum point on the AP
Theory of Production – NOTES @DOUGLAS Page 2
A production function shows a technical relationship between inputs and outputs. Supposing that the
production of good X requires input of capital, labour and land using functional notation we can write
Qx=f (K, L, LD)
Where:
Qx=output of x per time period
F=the functional relationship
K,L,LD=Services of capital labor and land
The short and long run
The short run is that period of time over which the input of at least one factor of production cannot
be varied. Those factors which can be varied in the short run (labor, raw materials and fuel) are called
variable factors. Those which cannot be varied (capital and land are called fixed factors). The long
run is that period of time over which the input of all factors is variable factors in the long run.
NB: The actual length of the long run does not correspond precisely to any particular time period.
Short run changes in production. As a firm increases its level of production in the short run, it
eventually comes up against “the law of diminishing returns.”
Illustration
Consider farmer growing maize in 1 acre of land and with a given quantity of capital and assume that
neither the land nor the capital can be varied in the short run. Assume also that the state of technology
is constant and that labor is homogeneous i.e. Each worker is exactly like any other worker.
The production function can be written as:-
QM=f (L, K, LD)
No. of workers Total Product(TP) Average product MP
(AP)
1 4 4 4
2 14 7 10
3 25.5 8.5 11.5
4 40 10 14.5
5 60 12 20
6 72 12 12
7 77 11 5
8 80 10 3
9 81 9 1
10 75 7.5 -6
P=TP
L
MP=the change in total product resulting from the employment of an additional worker.
MP=ΔTP
ΔL
It is apparent that MP of a labor is at a maximum when five workers are employed, the 5th worker
adds 20 tones to the total maize output. After this point the MP of labor declines. The result that both
the average and the marginal product of labor eventually declines as more and more units of labor
are added to a fixed amount of other factors in an illustration of the” law of diminishing returns .”
Theory of Production – NOTES @DOUGLAS Page 1
, The law of diminishing return states that as additional units of a variable factor are added to a given
quantity of fixed factors, with a given state of technology, the average and the marginal products of
the variable factor will eventually decline.
Average and
Marginal
Products
AP
MP
NO. Of workers
The AP and MP are smooth because of the discrete nature of the data. If we had used continuous data
so that the labor input could be increased in very small quantities, we would have obtained smooth
curves for AP and MP
Average
And
Marginal
Product A B
O Number of workers
MP reaches maximum at point A. This is known as the point of diminishing marginal returns.
Similarly the point at which AP reaches maximum is B and is known as the point of diminishing
average returns
NB - AP begins to fall before AP does. In fact the MP cuts the AP at maximum point on the AP
Theory of Production – NOTES @DOUGLAS Page 2
