Complementarity

An Economic/Analytical Primer

Sustainable AG Application

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!!!

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!!!

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

2nd Order Metrics: Netputs• Marginal Product:

– Amount of netput (or value) for one more unit of another netput.

– 1st derivative:• MPx1 = ∂Q1/∂x1, MPx2 = ∂Q1/∂x2, MPx3 = ∂Q1/∂x3.

• ∂Q1/∂Q2, ∂Q1/∂Q3.

• Substitute versus Complement:– 2nd derivative describe how MP of one netput is

affected by second netput (a spillover effect).• ∂MPx1/∂x2 = ∂2Q1/∂x1∂x2.

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.

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, reduces the marginal productivity of the first netput, x1.

– This is netput substitution

• AND, the foundation of “design against” Green Chemistry synergy.

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”/P3 systems context…..

Sustainable AG Implications• THINK SYSTEMS/NETPUTS:

– Environment & Societal versus “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”….

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 Line Expansions???

• “enlightened” (green/spiritual) duality mappings???• P3 Benefit Function mappings….• Duality need to invert (stand on head)…..

THINK P3 (place, people, profit) VALUE “mappings” as Functions….

• Value Function: P3(place, people, profit) =

f( )

•

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))

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…

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!!!)