Economics of Variable-Rate Fertilizer Application

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 WorksheetPy = 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