Agricultural
Production
Economics
LECTURE 2
What Is a Production Function?
A production function describes the technical relationship that
transforms inputs (resources) into outputs (commodities).
1. 𝑦 = 𝑓 𝑥
2. 𝑦 = 2𝑥
3. 𝑦 = 𝛼 + 𝛽1 𝑥 + 𝛽2 𝑥 2 + 𝑒
Ref: pp 14-16 (textbook)
Fixed Versus Variable Inputs and the
Length of Run
How can it be determined if an input should be treated as fixed or
variable?
Variable input: farm manager can control the level of use. E.g.
Fertilizer
Fixed input: farmer has no control over the amount available. E.g.
land
Note: If the length of time were sufficient to do this, the land input
might be treated as a variable input.
Ref. pp 17-18
Fixed Versus Variable Inputs and the
Length of Run
Functional form:
𝑦 = 𝑓(𝑥1 ⃓𝑥2 , 𝑥3 , 𝑥4 , 𝑥5 , 𝑥6 )
Variable Fixed input
Output
input
Fixed Versus Variable Inputs and the
Length of Run
The categorization of inputs as either fixed or variable:
It dependents on the concept of time-
Long run: time of sufficient length such that all inputs to the
production function can be treated as variable
Very short run: so short period of time that none of the inputs are
variable
Short run: a period of time long enough such that a few of the inputs
can be treated as variable, but most are fixed.
Intermediate run: A period long enough so that many, but not all
inputs are treated as variable
Fixed Versus Variable Inputs and the
Length of Run
These categories again are somewhat arbitrary
How long is the short run?
The answer would probably be that the short run is a period of time
sufficiently long that some inputs can be treated as variable, but
sufficiently short such that some inputs can be treated as fixed
Does this imply a length of time of a day, a week, a month, or a crop
production season?
The length of time involved could be any of these
Ref: p-18
The Law of Diminishing Return
It’s the fundamental to all of production economics
The law can be named as the law diminishing marginal return
This law states that as units of an 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.
As units of the variable input are added to units of the fixed inputs,
the proportions change between fixed and variable inputs.
The law of diminishing returns has sometimes been referred to as
the law of variable proportions.
Ref: P 19
The Law of Diminishing Return
Marginal and Average Physical
Product
Marginal physical product (MPP) is the change in output
associated with a 1 unit increase in the input.
The MPP of input 𝑥𝑖 might be referred to as 𝑀𝑃𝑃 𝑥𝑖 .
MPP representing the incremental change in TPP, can be
either positive or negative.
Marginal and Average Physical
Product
Average physical product (APP): The ratio of output to input.
𝑦
That is, APP = .
𝑥
Suppose that the production function is
y = f(x).
Δ𝑦
MPP is by the expression , where the ∆ denotes change.
Δ𝑥
Δ𝑦
The expression can be read as "the change in y (∆ y) with
Δ𝑥
respect to a change in x (∆ x)."
For the same function APP is expressed either as y/x or as
f(x)/x
Marginal and Average Physical
Product
Ref: p 22
MPP and Marginal Product Function
Total physical product (TPP) function
𝑦=𝑓 𝑥
Marginal physical product (MPP) function
𝑑𝑦 ′
𝑑𝑇𝑃𝑃
=𝑓 𝑥 = = 𝑀𝑃𝑃
𝑑𝑥 𝑑𝑥
Ref: pp 22-24
Neoclassical
Production
Function
Neoclassical Production Function
As the use of input x1 increases, the productivity of the input
at first increases. The function turns upward, or increases, at
first at an increasing rate.
Then a point called the inflection point occurs. This is where
the function changes from increasing at an increasing rate to
increasing at a decreasing rate. The inflection point marks the
end of increasing marginal returns and the start of diminishing
marginal returns.
Neoclassical Production Function
Finally, the function reaches a maximum and begins to turn
downward.
Beyond the maximum, increases in the use of the variable
input x1 result in a decrease in total output (TPP). This would
occur in an instance where a farmer applied so much fertilizer
that it was actually detrimental to crop yields.
Ref: pp 27-28
MPP for Neoclassical Production
Function
At first, as the productivity of input x1 increases, so MPP
function must be increasing.
At inflection point MPP is maximum that is the productivity of
additional unit input x1 is at its greatest.
After the inflection point, the marginal product of x1 declines
and the MPP function must also be decreasing.
The marginal product of x1 is zero (MPP=0) at the point of
output maximization, and
MPP is negative thereafter.
Ref: p 28
APP for Neoclassical Production
Function
APP increases with the increase in input
APP reaches a maximum at a point after the inflection point
but before the point in which
output is maximized.
At APP maximum point, MPP intersects the APP from above
that is APP=MPP
After that APP decreases with increase in inputs
APP never be negative
Ref: p 28
Single Input Production Elasticity
Δ𝑦 Δ𝑥
Elasticity (𝐸𝑝 ) =( )ൗ( )
y 𝑥
Δ𝑦 𝑥
Or (𝐸𝑝 ) =( . )
Δ𝑥 𝑦
1 𝑀𝑃𝑃
Or (𝐸𝑝 ) = MPP. =
𝐴𝑃𝑃 𝐴𝑃𝑃
Ref: pp 33-34
Elasticities of Production for a Neoclassical
Production Function
Ep >1 until MPP=APP
Ep greatest when MPP/APP greatest
Ep greatest when MPP maximum
Ep <1 beyond MPP=APP
Ep =0, when MPP = 0
Ep <0 when MPP<0
These are the unique characteristics of
neoclassical production function
Ref: p35
