Economics of Variable-Rate
Fertilizer Application
Carl Dillon
Agricultural Economics
Discussion Outline
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Economic Basics
Input-Output Model or Production Function
Production Economic Analysis
Optimal Input Level Decision Rule
Sensitivity Analysis
Learning Outcomes
• You should be able to comprehend the
fundamentals of profit maximizing input
level
• Develop and apply the economically
optimal input decision rule
• Develop an economically optimal
recommendation map
• Conduct a sensitivity analysis
What is Precision Agriculture?
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Already been addressed
A new opportunity to make or lose money
Comprised of many different components
Not an all or nothing proposition
Of 108 studies by year 2000, 63% profitable
and 11% not with 23% mixed
Application of Economic
Principles
• 1. Acquire physical/biological data
(production technology)
• 2. Acquire price data (production
economics)
• 3. Apply appropriate decision-making rule
Marginal Concepts
• Management focuses on controllable factors
• Economics considers marginal aspects
• Marginal - incremental change, additional,
extra
Production Function
• Systematic representation of the output or
yield of a product corresponding to different
amounts of an input
• Table, graph, equation
• TPP, Y
• Physical relationship but important
Physical Product
• Total Physical Product = Yield
• Average Physical Product = TPP/X
• Marginal Physical Product =  TPP/  X
Production Function Worksheet
Input Level
TPP
APP
MPP
0
10
NA
NA
1
15
15
5
2
32
16
17
3
39
13
7
4
44
5
40
Production Function Worksheet
Input Level
TPP
APP
MPP
0
10
NA
NA
1
15
15
5
2
32
16
17
3
39
13
7
4
44
11
5
5
40
8
-4
Graphical Production Function
• How to draw a classical production function
• Stages of production
Total Physical Product Curve
Average and Marginal Physical
Product Curves
Stages and Relationships
Stage I
Stage II
Stage III
TPP 
TPP 
TPP 
MPP > APP
APP > MPP
APP > MPP
APP 
APP 
APP 
MPP , > 0
MPP  > 0
MPP  < 0
Production Function Points
• Inflection point at maximum MPP
• TPP maximum at MPP = 0
• A production function doesn’t necessarily
have all three stages
Law of Diminishing Marginal
Returns
• As additional units of a variable input are
used in combination with one or more fixed
inputs, MPP will eventually begin to decline
• The world can’t be fed from one acre
• Measured in MPP not TPP or APP
• Can begin with first unit
• IN stage one NOT the border of I and II
Adding Economics
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Where is the profit maximizing input level?
Py = Price of output
Px = Price of input
Total Value Product (TVP) = TPP * Py
Marginal Value Product (MVP) = MPP * Py
Total Input Cost (TIC) = X * Px
Marginal Input Cost (MIC) = Px
Production Economic Worksheet
Py = 2
Px = 14
X TPP TVP AVP MVP MIC TIC 
0 10 20 NA NA NA 0
20
1 15 30 30 10
14
14
16
2 32 64 32 34
14
28
36
3 39 78 26 14
14
42
36
4 44 88 22 10
14
56
32
5 40 80 16
14
70
10
-8
Input Decision Rule
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TVP = Total value product = Py *Y
TIC = Total input costs = Px*X
Profit = TVP - TIC
 Profit /  X = 0
 (TVP - TIC) /  X = MVP - MIC = 0
Input Decision Rule
• MVP=MIC for profit max
• NOT maximum yield if you want to
maximize PROFIT!
• Marginal benefits = Marginal cost
• An equality, not an equation
Economics of VRA
• Use MVP=MIC by spatial location for VRA
• Use land area weighted average MVP=MIC
for uniform rate profit maximization
• If change in net returns from VRA
outweighs cost of the technology then VRA
is profit maximizing
Some VRA Myths
• VRA will never result in higher total farm
input usage versus uniform rate
• An increase in input price always leads to
greater economic potential of VRA
• VRA requires a high amount of spatial
variability
Sensitivity Analysis
• Assessing the impacts of a change in the
decision-making environment on the
optimal decision
• Economic environment changes - output
price, input price
• Physical environment changes productivity
Conclusions
• Profit maximizing input level and yield
maximizing input level are different
• The optimal input level is a function of
output price and input price as well as the
underlying production function
• Input decision rule is MVP = MIC
• Sensitivity analysis can be useful