AAEC 2305
Fundamentals of Ag Economics
CHAPTER 3
Production Functions and
Product Curves
Factors of Production
 Inputs are generally designated as “X”
• 1) Fixed Inputs - factors must be
maintained (i.e. paid for, kept up, etc.)
whether pdn occurs or not (ex. - land,
buildings, heavy machinery, etc.)
• 2) Variable inputs - factors that vary as
the output level changes (ex. - labor,
fertilizer, seed, etc.)
Short vs. Long Run
 1) Immediate Short-Run:
Time span so
short that no resource changes can be
made. All factors of pdn are fixed.
 2) Short-Run: Time span such that some
factors are variable & some factors are
fixed.
 3) Long-Run: Time span so long that no
inputs are fixed.
Production Function (PF)
 Defn: The technical relationship between
inputs & output indicating the maximum
amount of output that can be produced
using alternative amounts of variable
inputs in combination with one or more
fixed inputs under a given state of
technology.
 Or, simply speaking, it is the technical
relationship between inputs & output
Product Curves
 Used to study PF
 Total Physical Product (TPP) - illustrates
relationship that exists between output and
one variable input, ceterus paribus
• Indicates total amount of output
produced at each level of input use
Product Curves (Cont.)
 Average Physical Product (APP) - shows
how much pdn, on average, can be obtained
per unit of the variable input with a fixed
amount of other inputs
• Indicates avg productivity of the inputs being
used - how productive is each input level on
average
APP = TPP / X
Product Curves (Cont.)
 Marginal Physical Product (MPP) -
represents the amount of additional (i.e.,
marginal) TPP obtained from using an
additional unit of variable input (X).
• The slope of the TPP curve
• We use the MPP to identify the rate of change
in output resulting from adding one more unit
of input
• MPP = ΔTPP / ΔX
Law of Diminishing Marginal
Physical Product
 Law of Diminishing Marginal Physical
Product: As additional units of one input
are combined with a fixed amount of other
inputs, a point is always reached where the
additional product received from the last
unit of added input will decline
Relationships between
Product Curves
 MPP is slope of TPP
 At Inflection Point (pt of diminishing mpp):
• TPP Δ’s from increasing at an increasing
rate to increasing at a decreasing rate
• Therefore, MPP reaches a maximum at
inflection point
Relationships between
Product Curves
 MPP = 0
occurs when TPP is maximum
 MPP is negative beyond TPP max

Relationships between
Product Curves
 APP measures the average productivity of
each unit of variable input being used
• Drawing a line from the origin which is
tangent to the TPP curve gives APP max
• At point where APP is max, MPP crosses
APP (MPP=APP)
Summary of Relationships
 When MPP > APP, APP is increasing
 When MPP = APP, APP is at a max
 When MPP < APP, APP is decreasing
 The relationship between TPP, APP, & MPP is
very specific. If we have COMPLETE
information about one curve, the other two
curves can be derived.
Stages of Production:
Rational & Irrational
 In stage I:
• TPP is increasing
• APP is increasing
• MPP increases, reaches a maximum &
decreases to APP
• IRRATIONAL STAGE BECAUSE APP IS STILL
INCREASING
Stages of Production:
Rational & Irrational
 In Stage II:
• TPP is increasing
• APP is decreasing
• MPP is decreasing and less than APP, but
still positive
• RATIONAL STAGE BECAUSE TPP IS STILL
INCREASING
Stages of Production:
Rational & Irrational
 In Stage III:
• TPP is decreasing
• APP is decreasing
• MPP is decreasing and negative
• IRRATIONAL STAGE BECAUSE TPP IS
DECREASING
Stage II of Production
 Note:
For each additional unit of X that is
being used within stage II, TPP is
increasing but APP is decreasing, resulting
in a trade-off between increased
production & decreased productivity for
each input. This trade-off is the core of
economic decision making and requires
the skills of the decision maker.
Effects of Technological Change
 We know that the PF gives the max amount
of output that can be produced by a firm
using a given technology.
 The PF can shift over time as a result of a
technological change
Effects of Technological Change
 Technological change refers to the
introduction of new technology that
increases output with the same amount of
resources (i.e., the TPP curve would shift
upward)
 The technological change that shifts the
TPP upward would result in a
corresponding upward shift in the APP &
MPP curves