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

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

• 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 WorksheetPy = 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 -8 14 70 10

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

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