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Complementarity

This primer explores the concepts of complementarity, substitution, and synergy in the context of sustainable agriculture. It discusses how positive and negative spillover effects among inputs, outputs, and netputs can influence productivity and resource management. Through analyzing functional relationships, the piece emphasizes the importance of holistic thinking in farming practices. By recognizing the interdependencies in agricultural systems, practitioners can design strategies that enhance productivity while minimizing negative impacts, leading to more sustainable outcomes for communities and environments.

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Complementarity

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  1. Complementarity An Economic/Analytical Primer Sustainable AG Application

  2. Definitions: • Complementarity: • The positive “spillover” (marginal) impacts of one context on another. • Substitution: • The negative “spillover” (marginal) impacts of one context on another. • Synergy: • Uses complementarity/substitution among parts to add value and/or reduce costs. • The whole is greater than the sum of it’s parts!!!

  3. PRIMAL = “Quantity” Space • Production and/or Distance Function: • Functional relationship between inputs and outputs. • Q1 = f (Q2, Q3, x1, x2, x3). • Substitute versus Complement Relations w.r.t.: • Inputs • Outputs • Netputs!!! • Inputs versus outputs is arbitrary from a whole farm/systems perspective!!!

  4. DUAL = “Value” Space • Cost, Revenue, Profit Functions. • Functional relationship between netputs and values. • P3= f (Q1, Q3, x1, x2, x3). • Substitute versus Complement Relations w.r.t. Netputs!!! • Generally: Value = Price

  5. 2nd Order Metrics: Netputs • Marginal Product: • Amount of netput (or value) for one more unit of another netput. • 1stderivative: • MPx1 = ∂Q1/∂x1, MPx2 = ∂Q1/∂x2, MPx3 = ∂Q1/∂x3. • ∂Q1/∂Q2, ∂Q1/∂Q3. • Substitute versus Complement: • 2ndderivativedescribe how MP of one netput is affected by second netput (a spillover effect). • ∂MPx1/∂x2 = ∂2Q1/∂x1∂x2.

  6. Netput Complements • How is marginal productivity of one netput affected by a second netput ??? • IF ∂MPx1/∂x2 = ∂2Q1/∂x1∂x2 > 0 • THEN, the second netput, x2, enhances the marginal productivity of the first netput, x1. • This is netput complementarity • AND, the foundation of “design for” UpCycle synergy.

  7. Netput Substitutes • How is marginal productivity of one netput affected by a second netput ??? • IF ∂MPx1/∂x2 = ∂2Q1/∂x1∂x2 < 0 • THEN, the second netput, x2, reducesthe marginal productivity of the first netput, x1. • This is netput substitution • AND, the foundation of “design against” Green Chemistry synergy.

  8. Sustainable Ag Examples • Netput “spillovers”: • UpCycle design to reduce entropy • Entropy: a negative marginal product due to lower level (energy) use • Tillage/rotation/cover crops • Increase (design for): soil structure, infiltration, biotic health/diversity, carbon sequestration and (slow release) nutrient cycling, etc. • Decrease (design against): soil/water/nutrient/GHG loss. • Look for Spillovers in Space/Time/Form!!! • THINK: “whole farm”/P3systems context…..

  9. Sustainable AG Implications • THINK SYSTEMS/NETPUTS: • Environment & Societalversus “Economic” • Hierarchical  emergent properties…. • Stocks versus Flows • Longer versus shorter run…. • Duality to “time value of $$$” dilemma??? • Technical versus Biological Nutrients (UpCycle) • Design to MIN(entropy)/MAX(solar capture/store) • Weak(er) versus Strong Metrics: • Still need “measure to manage”….

  10. Sustainable AG Implications • THINK P3 (place, people, profit) VALUE “mappings” as Functions…. • Full generality(advanced analytics/metrics) • functions = “correspondences” • benefit (versus profit/etc.) functions • Traditional: Production/Cost/Revenue/Profit • Triple Bottom LineExpansions??? • “enlightened” (green/spiritual) dualitymappings??? • P3 Benefit Function mappings…. • Duality need to invert (stand on head)…..

  11. THINK P3 (place, people, profit) VALUE “mappings” as Functions…. • Value Function: P3(place, people, profit) = f( )

  12. Sustainable AG Implications • THINK P3 (place, people, profit) VALUE “mappings” as Functions…. • Sustainable AG: • Value Function: P3(place, people, profit) P3 = f(Community Vitality, Cover Crops, Conservation Tillage, Nutrient Management, Crop/Lvstk/Landscape Diversity, On-Farm Energy (Conserve/Produce), Water/Wetland Mgmt, Marketing, Whole Farm/Systems Approach, Grazing, Ecological Pest/Weed Mgmt (IPM))

  13. Sustainable AG Implications • THINK P3 Empirical/Discrete Derivatives!!! • Simulate (cross-shock) P3 Benefit Correspondences • Footprint Metrics: carbon, water, N|P|K|S, land • Think: 2nd (applied, discrete)derivatives!!! • Innovate!!! • Develop, expand, refine, calibrate, validate “new and improved” P3 metrics!!! • Social/interpersonal metrics!!! • Measure to Manage!!! • UpCycle design/manage for synergy…

  14. Implications • Identify potential +/- netput synergies: • Note substitute/complement dynamics can change with the levels (hierarchy) of the component contexts. • ALSO: Δ Space/Time/Form • Via Dialogue With Major Players/Stakeholders Across Whole System • Supply Chain  Circle  Spiral (UpCycle) • Identify potential design/management values/objectives/strategies/tactics/metrics (in this order) to exploit these synergies (bio-mimicry!!!)

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