Economics of Variable-Rate Fertilizer Application Carl Dillon Agricultural Economics

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

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

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 Where is the profit maximizing input level? P y = Price of output P x = Price of input Total Value Product (TVP) = TPP * P y Marginal Value Product (MVP) = MPP * P y Total Input Cost (TIC) = X * P x Marginal Input Cost (MIC) = P x

Production Economic Worksheet P y = 2 P x = 14

Input Decision Rule TVP = Total value product = P y *Y TIC = Total input costs = P x *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