1. Economics of Variable-Rate Fertilizer Application
Carl Dillon
Agricultural Economics

2. Discussion Outline Economic Basics
Input-Output Model or Production Function
Production Economic Analysis
Optimal Input Level Decision Rule
Sensitivity Analysis

3. 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

4. What is Precision Agriculture?
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

5. Application of Economic Principles
1. Acquire physical/biological data (production technology)
2. Acquire price data (production economics)
3. Apply appropriate decision-making rule

6. Marginal Concepts Management focuses on controllable factors
Economics considers marginal aspects
Marginal - incremental change, additional, extra

7. 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

8. Physical Product Total Physical Product = Yield
Average Physical Product = TPP/X
Marginal Physical Product =  TPP/  X

9. Production Function Worksheet

10. Production Function Worksheet

11. Graphical Production Function
How to draw a classical production function
Stages of production

12. Total Physical Product Curve

13. Average and Marginal Physical Product Curves

14. Stages and Relationships

15. Production Function Points
Inflection point at maximum MPP
TPP maximum at MPP = 0
A production function doesn’t necessarily have all three stages

16. 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

17. Adding Economics 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

18. Production Economic Worksheet Py = 2 Px = 14

19. Input Decision Rule TVP = Total value product = Py *Y
TIC = Total input costs = Px*X
Profit = TVP - TIC
 Profit /  X = 0
 (TVP - TIC) /  X = MVP - MIC = 0

20. 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

21. 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

22. 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

23. 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

24. 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