LECTURE IV

PRODUCTION PRINCIPLES

Production Principles

The Production Principles to be discussed include:

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)

Yield (Bags/acre)

0 50

40 75

80 105

120 115

160 123

200 128

240 124

Production Function

Yield

0

50

100

150

0 100 200 300

Yield

Production Function 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)

Added output or Marginal Physical Product (MPP)

0 50

40 75 25

80 105 30

120 115 10

160 123 8

200 128 5

240 124 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 FunctionThe 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: 0.75(200) + 0.0042(2002) – 0.000023(2003)

= 134 bags per acre.

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)

Maize yield, (Bags/acre)

Marginal Product

0 0 0

40 35 35

80 75 40

120 110 35

160 133 23

200 134 1

240 104 -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 Total Physical Product (TPP)/Units of output

Added output/MPP

1 1 1

2 3 2

3 6 3

4 10 4

5 15 5

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 Total Physical Product (TPP)/Units of output

Added output/MPP

1 2 2

2 4 2

3 6 2

4 8 2

5 10 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 Total Physical Product (TPP)/Units of output

Added output/MPP

1 5 5

2 9 4

3 12 3

4 14 2

5 15 1

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 returnsThe 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 ReturnsAs 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.