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Forest and Agricultural Sector Optimization Model (FASOM)

Forest and Agricultural Sector Optimization Model (FASOM). Basic Mathematical Structure. Linear Programming. FASOM can solve up to 6 Million Variables (j), 1 Million Equations (i). Important Equations. Objective Function Resource Restrictions Commodity Restrictions

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Forest and Agricultural Sector Optimization Model (FASOM)

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  1. Forest and Agricultural Sector Optimization Model (FASOM) Basic Mathematical Structure

  2. Linear Programming FASOM can solve up to 6 Million Variables (j), 1 Million Equations (i)

  3. Important Equations • Objective Function • Resource Restrictions • Commodity Restrictions • Intertemporal Transition Restrictions • Emission Restrictions

  4. Objective Function Maximize + Area underneath demand curves - Area underneath supply curves - Costs ± Subsidies / Taxes from policies The maximum equilibrates markets!

  5. Market Equilibrium Price Supply Consumer Surplus P* Producer Surplus Demand Q* Quantity

  6. Basic Objective Function Terminal value of standing forests Discount factor Consumer surplus Resource surplus Costs of production and trade

  7. Consumer and Resource Surplus

  8. Economic Principles • Rationality ("wanting more rather than less of a good or service") • Law of diminishing marginal returns • Law of increasing marginal cost

  9. Demand function price • Decreasing marginal revenues • uniquely defined by • constant elasticity function • observed price-quantity pair (p0,q0) • estimated elasticity  (curvature) Area underneath demand function Demand function p0 sales q00 q0

  10. Land Supply Forest Inventory Processing Demand Water Supply CS Domestic Demand PS Labor Supply Implicit Supply and Demand Feed Demand Animal Supply National Inputs Export Demand Import Supply Economic Surplus Maximization

  11. Production and Trade Cost

  12. ResourceAccounting Equations(r,t,i)

  13. Physical Resource Limits(r,t,i)

  14. Commodity Equations (r,t,y) Demand  Supply

  15. Industrial Processing (r,t,y) • Processing activities can be bounded (capacity limits) or enforced (e.g. when FASOM is linked to other models)

  16. Forest Transistion Equations • Standing forest area today + harvested area today <= forest area from previous period • Equation indexed by r,t,j,v,f,u,a,m,p

  17. Emission Accounting Equation(r,t,e)

  18. Environmental Policy or

  19. Duality restrictions (r,t,u) Observed crop mixes • Prevent extreme specialization • Incorporate difficult to observe data • Calibrate model based on duality theory • May include „flexibility contraints“ Crop Mix Variable No crop (c) index! Crop Area Variable Past periods

  20. Miscellaneous • GAMS • Systematic Model Check • Linearization • Alternative Objective Function

  21. Linear Program Duality

  22. Reduced Cost Shadow prices Objective Function Coefficients Technical Coefficients

  23. Variable Decomposition Example (not from FASOM) ## Landuse_Var(Bavaria,Sugarbeet) SOLUTION VALUE 1234.00 EQN AijUiAij*Ui objfunc_Equ350.00 1.0000 350.00 Endowment_Equ(Bavaria,Land) 1.0000 90.000 90.000 Endowment_Equ(Bavaria,Water) 250.00 0.0000 0.0000 Production_Equ(Bavaria,Sugarbeet) -11.000 40.000 -440.00 TRUE REDUCED COST 0.0000

  24. Variable Decomposition Example (not from FASOM) ## Landuse_Var(Bavaria,Wheat) SOLUTION VALUE 0.00000 EQN AijUiAij*Ui objfunc_Equ 350.00 1.0000 350.00 Endowment_Equ(Bavaria,Land) 1.0000 250.00 250.00 Endowment_Equ(Bavaria,Water) 250.00 0.0000 0.0000 Production_Equ(Bavaria,Wheat) -1.0000 89.000 -89.000 TRUE REDUCED COST 511.00

  25. Complementary Slackness Opt. Slack Variable Level Shadow Price Opt. Variable Level Reduced Cost

  26. Solution Decomposition Insights • Why is an activity not used? • How do individual equations contribute to the variable‘s optimality?

  27. Current work • Land management adaptation to policy & development • Externality mitigation (Water, Greenhouse Gases, Biodiversity, Soil fertility) • Stochastic formulation (extreme events) • Land use & management change costs • Learning and agricultural research policies • Investment restrictions

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