$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. Keywords: linear programming, nonlinear programming, farming, agricultural economics, market behavior $offText Set c 'crop' / wheat, clover, beans, onions, cotton, maize, tomato / cl 'livestock feed' / clover, straw / t 'month' / jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec / r 'feeding recipes' / rec-1 , rec-2 / s 'seasons' / summer, winter / sc(s,c) 'season crop mapping' / summer.(cotton,maize,tomato) winter.(wheat,clover,beans,onions) / cn(c) 'crops sold in national market' ce(c) 'export commodities' cm(c) 'import commodities'; Table a(t,c) 'months of land occupation by crop (hectares)' wheat clover beans onions cotton maize tomato jan 1. 1. 1. 1. feb 1. 1. 1. 1. mar 1. .5 1. 1. .5 apr 1. 1. 1. 1. may 1. .25 1. .25 jun 1. 1. jul 1. 1. .75 aug 1. 1. 1. sep 1. 1. 1. oct 1. .5 1. nov .5 .25 .25 .5 .75 .75 dec 1. 1. 1. 1. Table lc(t,c) 'crop labor requirements (man-days per hectare)' wheat clover beans onions cotton maize tomato jan 1.72 4.5 .75 5.16 feb .5 1. .75 5. mar 1. 8. .75 5. 5. apr 1. 16. 19.58 5. may 17.16 2.42 9. 4.3 jun 2.34 2. 5.04 jul 1.5 7.16 17. aug 2. 7.97 15. sep 1. 4.41 12. oct 26. 1.12 7. nov 2.43 2.5 7.5 11.16 12. 6. dec 1.35 7.5 .75 4.68 ; Table lio(cl,r) 'livestock input output matrix' rec-1 rec-2 clover 1.3 2.0 straw 1.6 .8; Table demdat(c,*) 'demand data' ref-p ref-q elas exp-p imp-p * ($) (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; Scalar 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$(demdat(c,"imp-p") < inf); cm("clover") = no; price(c) = demdat(c,"ref-p"); pe(ce) = demdat(ce,"exp-p"); pm(cm) = demdat(cm,"imp-p"); beta(cn)$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; Variable 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; Equation 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; Model 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. * the LP has many solutions: find one with moderate domestic consumption natcon.up(c) = 1e5; solve demo7f maximizing yfarm using lp; natcon.up(c) = INF; 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;