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qdemo7.gms : Nonlinear Simple Agricultural Sector Model QCP

This is a QCP version of the gamslib model DEMO7. The original NLP
formulation was concerned with good starting points. QCPs do not
need starting a point.

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 Type: QCP
$Title Nonlinear Simple Agricultural Sector Model (QDEMO7,SEQ=284) $Ontext This is a QCP version of the gamslib model DEMO7. The original NLP formulation was concerned with good starting points. QCPs do not need starting a point. 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 farmsize (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 plowes) natcon(c) domestic consumption (1000 tons) 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 $) Positive Variable xcrop,xlive,thire,flab,tlab,natcon,natprod, exports,imports Equations landbal(t) land balance (hectares) laborbal(t) labor balance (days) flabor(t) family labor balance (days) plow(s) land plowed (hectares per season) arev revenue accounting (dollars) ares reservation labor cost (dollars) acost total cost accounting (dollars) amisc misc cost accounting aplow alab labor cost accounting (dollars) lclover clover balance lstraw straw balance income income definition (dollars) proc(c) net production definition (tons) dem(c) national demand balance (1000 tons) objn objective function; landbal(t).. sum(c, xcrop(c)*a(t,c)) =l= land*fnum; laborbal(t).. sum(c, xcrop(c)*lc(t,c)) + sum(r, xlive(r))*llab =l= flab(t) + tlab(t); amisc.. mcost =e= sum(c, xcrop(c)*miscost(c)); alab.. labcost =e= sum(t, tlab(t)*twage); ares.. rescost =e= sum(t, flab(t)*rwage); aplow.. pcost =e= sum(s, thire(s)*trent); acost.. tcost =e= mcost + labcost + rescost + pcost; lclover.. xcrop("clover")*yield("clover") =g= sum(r, xlive(r)*lio("clover",r)); lstraw.. xcrop("wheat")*straw =g= sum(r, xlive(r)*lio("straw",r)); plow(s).. sum(c$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; flab.up(t) = famlab*fnum; Model demo7n QCP version/ landbal, laborbal, plow, ares, alab, acost, dem, proc, amisc, aplow, lclover, lstraw, objn /; option limcol=0,limrow=0; Solve demo7n maximizing cps using QCP;