LECTURE IV
PRODUCTION PRINCIPLES
Production Principles

The Production Principles to be
discussed include:

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


Production Function
Law of Diminishing Returns
Production Costs and Farm Receipts
Profit maximization
Risk and uncertainty
Production Function
 Production
function describes the
technical relationship that transforms
inputs (resources) into output
(commodities).
 The production function is expressed
as:
Y
= f (X1 -n) where
Y is an output
 X is an input

Production Function
 Total
yield or output varies with the
quantities of inputs used in the
production process.
 Management must decide the amount
of production and the amount and kinds
of inputs to be used, because
production does not vary evenly as
inputs are fed uniformly into the
production process.
Production Function

The range of the function consists of each
output level (Y) that result from each level of
input (X) being used.
 Y = f (X) meets the mathematicians definition
of a function but is a very general form for a
production function.
 It is not possible to determine exactly how
much output (Y) would result from a given
level of input (X).
 The specific form of the function f (X) would
be needed, and f(X) could take on many
specific forms for example Y= 2X or Y= 1/X
Production Function
 The
production function can be used to
describe the production of maize in
response to the use of nitrogen fertilizer.
 The specific data below shows this
relationship.
Table1: Corn Yield Response to
Nitrogen
Quantity of Nitrogen
(Kg/Acre)
0
Yield (Bags/acre)
40
75
80
105
120
115
160
123
200
128
240
124
50
Production Function
Yield
150
100
Yield
50
0
0
100
200
300
Production Function

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
For each nitrogen application level, a single yield is
defined.
The yield level is sometimes referred to as total
physical product (TPP) resulting from the nitrogen
that is applied.
A problem exists with the interpretation of the data
contained in the table above.
The exact amount of maize (TPP) that will be
produced if a farmer decides to apply 120 kg of
nitrogen per acre can be determined from the table,
but what happens if the farmer decides to apply 140
kg of nitrogen per acre?
A yield has not been assigned to this nitrogen
application level.
Production Function

A simple solution might be to interpolate
between the known values.
 If 120 kgs per acre produces 115 bags of
maize, and 160 kgs of nitrogen produces 123
bags of maize, the yield at 140 kgs of
fertilizer might be (115 + 123)/2 giving rise to
119 bags (140 = (120+160)/2).
 However, incremental increases in nitrogen
application do not provide equal incremental
increases in maize production throughout the
domain of the function.
Production Function

There is no doubt that some nitrogen is
available in the soil from decaying organic
material and nitrogen applied in previous
seasons, and nitrogen need not be applied in
order to get back the first 50 bags of maize.
 The first 40 kgs of nitrogen applied produces
addition 25 bags of maize for a total of 75
bags; the next 40 kgs produces 30 bags of
maize for a total of 105 bags but the
productivity of the remaining 40 kgs
increments in terms of maize production
declines as shown in Table 2 below.
Table 2: Marginal Physical
Product
Quantity of
Nitrogen
(Kg/Acre
Yield
(Bags/acre)
0
40
80
120
160
200
240
50
75
105
115
123
128
124
Added output
or Marginal
Physical
Product (MPP)
25
30
10
8
5
4
Production Function

Following this rationale, it seems unlikely that
140 kgs will yield 119 bags.
 A more likely guess would be 120 or 121
bags.
 These are only guesses.
 In reality, no information about the behaviour
of the function is available at nitrogen
application levels other that those listed in the
table.
 A yield of 160 bags per acre, at a nitrogen
application level of 140 kgs per acre, could
result or for that matter any other yield.
Production Function
 Suppose
instead that the relationship
between the amount of nitrogen that is
applied and maize yielded is described
by:
Y
= 0.75X + 0.0042X2 – 0.000023X3 Where
Y = Maize yielded (Total Physical Product) in
bags per acre
 X = Nitrogen applied in Kgs per acre.

Production Function
 The
major advantage is that it is
possible to calculate the resultant maize
yield at any fertilizer application level.
For example, maize yielded when 200
kgs of fertilizer is applied would be:
+ 0.0042(2002) – 0.000023(2003)
= 134 bags per acre.
 0.75(200)
Production Function
 The
function is continuous and there are
no nitrogen levels where maize yield
cannot be calculated.
 The additional output (marginal product)
resulting from an extra kg of nitrogen
applied can be calculated.
 Calculate the yields of maize and
Marginal Product at the following
nitrogen application rates for the
Production Function Y = 0.75X +
0.0042X2 – 0.000023X3.
Table 3:Maize Yields at various
Nitrogen Application Rates
Quantity of
Nitrogen
(Kgs/acre)
0
40
80
120
160
200
240
Maize yield,
(Bags/acre)
Marginal
Product
0
35
75
110
133
134
104
0
35
40
35
23
1
-30
Production Function

The results in table 3 differ from those in table
1 in that if a farmer applied no nitrogen to the
maize (as is shown in table 1), a yield of 50
bags per acre is obtained.
 It is assumed that there is some residual
nitrogen in the soil on which the maize is
grown.
 The nitrogen is in the soil because of
decaying organic material and leftover
nitrogen from fertilizers applied in past years.
 As a result, the data in table 1 reveal higher
yields at low nitrogen application levels than
do the data obtained in table 3
Types of Production Responses
 There
are three types of production
responses to an input or factor of
production
 Increasing
returns to a variable factor.
 Constant returns to a variable factor.
 Decreasing returns to a variable factor.
 Increasing
marginal returns
(productivity) occur when each unit of
added input produces more product
than the previous unit of input as shown
in table 4 below.
Table 4: Increasing Marginal
Returns
Unit of Input
Added
output/MPP
1
Total Physical
Product
(TPP)/Units of
output
1
2
3
2
3
6
3
4
10
4
5
15
5
1
Types of Production Responses
 In
the case of increasing marginal
returns the second unit of input adds
one more unit of product than the first
one while the third adds three etc as
shown in Table 4.
 Constant marginal returns occur when
each additional unit of input always
yields the same amount of additional
product
Table 5: Constant Marginal
Returns
Unit of Input
Added
output/MPP
1
Total Physical
Product
(TPP)/Units of
output
2
2
4
2
3
6
2
4
8
2
5
10
2
2
Types of Production Responses
 With
constant marginal returns there is
thus no need for more input.
 Decreasing marginal returns occur
when each additional unit of input yields
a relatively smaller amount of additional
product.
Table 6: Decreasing Marginal
Returns
Unit of Input
Added
output/MPP
1
Total Physical
Product
(TPP)/Units of
output
5
2
9
4
3
12
3
4
14
2
5
15
1
5
Law of Diminishing Returns

From Tables 2 and 3 it can be see that the
increment or marginal product increases at
an increasing rate with additional increase in
nitrogen application to a certain point and
then starts to increase at a decreasing rate.
 This is due to the law of diminishing returns
which is fundamental to all production
economics.
 The law is synonymous with the law of
Diminishing Marginal Returns because it
deals with what happens to the incremental
or marginal product as units of inputs or
resources are added.
Law of diminishing returns
 The
Law of diminishing returns states
that as units of a variable input are
added to units of one or more fixed
inputs, after a point each incremental
unit of the variable input produces less
and less additional output.
 If incremental units of nitrogen fertilizer
were applied to maize, after a point
each incremental unit of nitrogen
fertilizer would produce less and less
additional maize yield (Tables 2&3).
Law of Diminishing Returns

Were it not for the law of diminishing returns,
a single farmer could produce all the maize
required in the world, merely by acquiring all
of the available nitrogen and applying it to
his/her farm.
 The law of diminishing marginal returns is
important in the allocation resources to
products.
 It applies widely and explains why we cannot
produce all the food we need from a single
plot of land.
 It is likely to apply as farming population
pressure increases on a fixed area of land.
Law of Diminishing Returns
 As
the labour input rises, the marginal
product per person is likely to fall,
unless new, more productive systems of
farming can be found.
 Generally, the average product
(productivity), of a variable input
diminishes along with the marginal
product when inputs are increased.
Law of Diminishing Returns

The point where total product is at a
maximum and marginal product is zero is
sometimes known as the technical optimum
or technically the best choice.
 It represents the highest attainable yield per
acre of land.
 However, this point ignores the costs involved
thus it may not necessarily be the economic
optimum.