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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
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