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demo7.gms : Nonlinear Simple Agricultural Sector Model

This is the last in a series of agricultural farm level and sector
models, this model simulates the market behavior of the sector
using a partial equilibrium framework. The technique is
the maximization of consumers and producers surplus.
Reference:
Small Model of Types: NLP lp
$Title Nonlinear Simple Agricultural Sector Model (DEMO7,SEQ=92a) $Ontext This is the last in a series of agricultural farm level and sector models, this model simulates the market behavior of the sector using a partial equilibrium framework. The technique is the maximization of consumers and producers surplus. Kutcher, G P, Meeraus, A, and O'Mara, G T, Agriculture Sector and Policy Models. The World Bank, 1988. $Offtext Sets c crop / wheat, clover, beans, onions, cotton, maize, tomato/ cl livestock feed / clover, straw / t month / jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec / r feeding recipes / rec-1, rec-2 / s seasons / summer, winter / sc(s,c) season crop mapping / summer.(cotton,maize,tomato) winter.(wheat,clover,beans,onions) / cn(c) crops sold in national market ce(c) export commodities cm(c) import commodities Table a(t,c) months of land occupation by crop (hectares) wheat clover beans onions cotton maize tomato jan 1. 1. 1. 1. feb 1. 1. 1. 1. mar 1. .5 1. 1. .5 apr 1. 1. 1. 1. may 1. .25 1. .25 jun 1. 1. jul 1. 1. .75 aug 1. 1. 1. sep 1. 1. 1. oct 1. .5 1. nov .5 .25 .25 .5 .75 .75 dec 1. 1. 1. 1. Table lc(t,c) crop labor requirements (man-days per hectare) wheat clover beans onions cotton maize tomato jan 1.72 4.5 .75 5.16 feb .5 1. .75 5. mar 1. 8. .75 5. 5. apr 1. 16. 19.58 5. may 17.16 2.42 9. 4.3 jun 2.34 2. 5.04 jul 1.5 7.16 17. aug 2. 7.97 15. sep 1. 4.41 12. oct 26. 1.12 7. nov 2.43 2.5 7.5 11.16 12. 6. dec 1.35 7.5 .75 4.68 Table lio(cl,r) livestock input output matrix rec-1 rec-2 clover 1.3 2.0 straw 1.6 .8 Table demdat(c,*) demand data ref-p ref-q elas exp-p imp-p * ($) (1000t) ($) ($) wheat 100 2700 -.8 140 beans 200 900 -.4 270 onions 125 700 -1. 40 inf cotton 350 2100 -1. 300 inf maize 70 3800 -.5 85 tomato 120 500 -1.2 60 inf Scalars fnum number of farms in sector /1000/ land farm size (hectares) / 4. / famlab family labor available (days per month) / 25 / dpm work days per month / 25 / rwage reservation wage rate (dollars per day) / 3 / twage temporary labor wage (dollars per day) / 4 / llab livestock labor requirements (days per month) / 2 / trent tractor rental cost (dollar per hectare) / 40 / hpa land plowed by animals (hectares per animal) / 2 / straw straw yield from wheat /1.75 / Parameters yield(c) crop yield (tons per hectare) / wheat = 1.5, clover = 6 , beans = 1, onions = 3 cotton = 1.5, maize = 2, tomato = 3 / miscost(c) misc cash costs (dollars per hectare) / wheat = 10, beans = 5, onions = 50 cotton = 80, maize = 5, tomato = 50 / price(c) reference (observed) price (dollars) pe(c) commodity export prices (dollars) pm(c) commodity import prices (dollars) alpha(c) demand curve intercept beta(c) demand curve gradient; cn(c) = yes$demdat(c,"ref-p"); ce(c) = yes$demdat(c,"exp-p"); cm(c) = yes$(demdat(c,"imp-p") lt inf ); cm("clover") = no; price(c) = demdat(c,"ref-p"); pe(ce) = demdat(ce,"exp-p"); pm(cm) = demdat(cm,"imp-p"); beta(cn)$demdat(cn,"ref-q") = demdat(cn,"ref-p")/demdat(cn,"ref-q")/ demdat(cn,"elas"); alpha(cn) = demdat(cn,"ref-p") - beta(cn)*demdat(cn,"ref-q"); demdat(cn,"dem-a") = alpha(cn); demdat(cn,"dem-b") = beta(cn); Display cn,cm,ce,price,pe,beta,alpha,demdat; Variables xcrop(c) cropping activity (hectares) yfarm farm income (dollars) revenue value of production (dollars) mcost misc cash cost (dollars) pcost tractor plowing cost labcost labor cost (dollars) rescost family labor reservation wage cost (dollars) tcost total farm cost including rescost flab(t) family labor use (days) tlab(t) temporary labor (days) xlive(r) livestock activity (units) natprod(c) net production (tons) thire(s) tractor rental (hectares plowed) natcon(c) domestic consumption (1000 tons) natprice(c) domestic price (dollars per ton) exports(c) national exports (1000 tons) imports(c) national imports (1000 tons) cps consumers and producers surplus valpro value of net production at ref prices employ employment generated (man-years) tradebal net exports (1000 $) Positive Variable xcrop,xlive,thire,flab,tlab,natcon,natprod, exports,imports Equations landbal(t) land balance (hectares) laborbal(t) labor balance (days) flabor(t) family labor balance (days) plow(s) land plowed (hectares per season) arev revenue accounting (dollars) ares reservation labor cost (dollars) acost total cost accounting (dollars) amisc misc cost accounting aplow alab labor cost accounting (dollars) lclover clover balance lstraw straw balance income income definition (dollars) dem(c) national demand balance (1000 tons) pdef(c) price definition arevn revenue accounting (1000 $) arevf revenue accounting: fixed price model (1000 $) valproc value of net production definition (1000 $) proc(c) net production definition (tons) employc employment definition (man-years) tradebalc trade balance definition (1000 $) objn objective function; landbal(t).. sum(c, xcrop(c)*a(t,c)) =l= land*fnum; laborbal(t).. sum(c, xcrop(c)*lc(t,c)) + sum(r, xlive(r))*llab =l= flab(t) + tlab(t); amisc.. mcost =e= sum(c, xcrop(c)*miscost(c)); alab.. labcost =e= sum(t, tlab(t)*twage); ares.. rescost =e= sum(t, flab(t)*rwage); aplow.. pcost =e= sum(s, thire(s)*trent); acost.. tcost =e= mcost + labcost + rescost + pcost; lclover.. xcrop("clover")*yield("clover") =g= sum(r,xlive(r)*lio("clover",r)); lstraw.. xcrop("wheat")*straw =g= sum(r,xlive(r)*lio("straw",r)); plow(s).. sum(c$sc(s,c), xcrop(c)) =l= sum(r, xlive(r))*hpa + thire(s); proc(c).. natprod(c) =e= xcrop(c)*yield(c); dem(cn).. natcon(cn) =e= natprod(cn) + imports(cn)$cm(cn) - exports(cn)$ce(cn); objn.. cps =e= sum(cn, alpha(cn)*natcon(cn) + .5*beta(cn)*sqr(natcon(cn))) + sum(ce, exports(ce)*pe(ce)) - sum(cm, imports(cm)*pm(cm)) - tcost; * the next 5 equations are only reporting or accounting definitions. * they do not effect the model. arevn.. revenue =e= sum(cn, alpha(cn)*natcon(cn) + beta(cn)*sqr(natcon(cn)) + exports(cn)*pe(cn)$ce(cn)); arevf.. revenue =e= sum(cn, natprod(cn)*price(cn) + (exports(cn)*(pe(cn)-price(cn)))$ce(cn)); valproc.. valpro =e= sum(c, natprod(c)*price(c)); income.. yfarm =e= revenue - tcost + rescost; employc.. employ =e= (sum(t, sum(c, xcrop(c)*lc(t,c))) + sum(r, xlive(r)*llab))/dpm/12; tradebalc.. tradebal =e= sum(cn, exports(cn)*pe(cn)$ce(cn) - imports(cn)*pm(cn)$cm(cn)); pdef(cn).. natprice(cn) =e= alpha(cn) + beta(cn)*natcon(cn); flab.up(t) = famlab*fnum; Models demo7f fixed price / landbal, laborbal, plow, ares, arevf, alab, acost, dem, employc, proc, valproc, amisc, aplow, lclover, lstraw, income, tradebalc / demo7n nonlinear / landbal, laborbal, plow, ares, arevn, alab, acost, dem, employc, proc, valproc amisc, aplow, lclover, lstraw, income, tradebalc, pdef, objn /; * find a good starting point for the nlp by solving a fixed price * lp model. Solve demo7f maximizing yfarm using lp; natprice.l(cn) = demdat(cn,"ref-p"); * the first lp found a good primal starting point. we can help * the nlp step to provide some additional dual information. * the equation arevf is replaced by arevn and pdef is new and * should be binding. pdef.m(cn) = 1; arevn.m = arevf.m; Solve demo7n maximizing cps using nlp;