agreste.gms : Agricultural Farm Level Model of NE Brazil

Description

This is a farm level model of the north east region of brazil. There is
only one farm type - medium sized. There are 3 types of land and risk
on revenue is considered.


Reference

  • Kutcher, G P, and Scandizzo, P L, The Agricultural Economy of Northeast Brazil. The Johns Hopkins University Press, Baltimore and London, 1981.

Small Model of Type : LP


Category : GAMS Model library


Main file : agreste.gms

$title Agreste Farm Level Model of NE Brazil (AGRESTE,SEQ=88)

$onText
This is a farm level model of the north east region of brazil. There is
only one farm type - medium sized. There are 3 types of land and risk
on revenue is considered.


Kutcher, G P, and Scandizzo, P L, The Agricultural Economy of Northeast
Brazil. The Johns Hopkins University Press, Baltimore and London, 1981.

Keywords: linear programming, agricultural economics, farming, crop yields, livestock
$offText

$sTitle Set Definitions
Set
   c       'crops'               / cotton-h   'cotton-herbaceo'
                                   banana     'banana'
                                   sugar-cane 'sugar-cane'
                                   beans-arr  'beans-de-arranca'
                                   beans-cor  'beans-de-corda'
                                   oranges    'oranges'
                                   manioc     'manioc'
                                   corn       'corn'
                                   sisal      'sisal'                                      /
   p       'cropping activities' / crop-02    'cotton-herbaceo'
                                   crop-05    'banana'
                                   crop-10    'sugar cane'
                                   crop-15    'oranges'
                                   crop-16    'manioc'
                                   crop-17    'corn'
                                   crop-19    'sisal'
                                   crop-25    'beans-de-corda   corn'
                                   crop-29    'cotton-herbaceo  beans-de-arranca corn'
                                   crop-30    'cotton-herbaceo  beans-de-corda   corn'
                                   crop-33    'beans-de-arranca corn'
                                   crop-36    'beans-de-arranca manioc           corn'     /
   s       'land types'          / good       'flat and near water or humid and low lying'
                                   medium     'hilly or more arid than good'
                                   pasture    'cultivated pasture or tree crops'           /
   tm      'months' / jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec           /
   sc(s)   'crop lands'                     / good, medium            /
   r       'livestock feeding alternatives' / rec-1*rec-3             /
   ty      'year'                           / 1960*1969               /
   dr      'family consumption bundle alternatives' / one, two, three /
   km      'technology characteristics' / equipment, fertilizer, seeds, sprouts, itech     /
   ps(p,s) 'process-land possibilities';

Alias (s,sp);

Parameter
   landc(s)    'land data                                      (ha)' / good     8.775
                                                                       medium  11.64
                                                                       pasture 21.92  /
   rations(r)  'livestock rations feeding alternative (cr per head)' / rec-1   5.141
                                                                       rec-2  21.646
                                                                       rec-3  49.845  /
   xcropl(p,s) 'limits on cropping activities';

xcropl("crop-19","good")   = 0.036;
xcropl("crop-19","medium") = 0.298;

Table ldp(s,s) 'land downgrading possibilities'
                good  medium
   good            1
   medium         -1       1
   pasture                -1;

* land requirements for livestock seems high but ok - pg 65 para 3
Table lio(s,r) 'land requirements for livestock feed alternatives (ha per head)'
                rec-1  rec-2  rec-3
   medium       1.407   .611   .631
   pasture       .209  2.03    .9  ;

Table labor(p,tm) 'labor requirements for cropping (man-days per ha)'
                     jan    feb    mar    apr    may    jun    jul    aug    sep    oct
   crop-02          4.79  10.89  18.70   9.83   8.03  20.95  15.67  15.48  11.35   8.38
   crop-05          8.24   0.89   5.43   3.31  11.13  10.33   3.27   2.65   5.47   3.67
   crop-10          5.78   3.37   4.03   7.09   4.64   5.91   7.67   9.23   5.93   9.05
   crop-15          2.00   2.36   4.13   2.13   7.18   5.88   3.21   9.20   6.89   3.30
   crop-16          5.71   7.60   7.28   8.15   8.48  10.71   9.34  12.76   8.93  10.22
   crop-17          9.19  14.42  10.59  12.01   3.47  10.75   5.88   7.30   4.14   4.25
   crop-19          1.22   1.11   0.56   0.78   1.19   0.44   1.89   3.04   2.93   4.99
   crop-25         12.46  11.35  24.38  22.03  16.91   9.47  10.97   9.70   4.93   6.41
   crop-29          5.54  10.30   9.24   8.97  15.82  13.00  14.74  10.64   5.64   4.90
   crop-30          9.18   3.94  16.15  23.69  28.12  20.58  17.73  15.06   4.58   9.76
   crop-33          6.87  10.19  10.61   9.14  18.38  11.50   9.22  13.36   3.85   3.87
   crop-36          7.44  10.21   9.63  16.18  20.11  16.86  14.86  14.00   8.04   6.69

   +                 nov   dec
   crop-02          8.23  4.54
   crop-05          3.18  1.44
   crop-10          7.59  6.37
   crop-15          9.70  8.87
   crop-16          6.18  8.34
   crop-17          3.49  2.11
   crop-19          7.73  9.44
   crop-25          0.53  0.89
   crop-29          4.73  4.92
   crop-30          7.39  2.67
   crop-33          2.65  1.09
   crop-36          5.49  5.26;

Table llab(tm,r) 'labor requirement for livestock feed (man-days per head)'
                  rec-1  rec-2  rec-3
   jan            4.261  1.873  1.933
   feb            2.854  1.262  1.302
   mar             .040   .040   .040
   apr             .040   .040   .040
   may             .040   .040   .040
   jun             .040   .040   .040
   jul             .040   .040   .040
   aug             .040   .040   .040
   sep             .040   .040   .040
   oct             .040   .040   .040
   nov            7.075  3.095  3.195
   dec            7.075  3.095  3.195;

Table cbndl(c,dr) 'consumption bundles (tons per bundle)'
                    one    two  three
   beans-arr       .225   .152   .15
   manioc          .965  2.64    .935
   corn            .235   .232   .581;

Table crev(c,ty) 'crop revenue time series (cr per ha)'
                  1960  1961  1962  1963  1964  1965  1966  1967  1968  1969
   banana         6399  8193  9215  8581  7988  7228  5923  6738  7221  7842
   sugar-cane     1667  1899  1898  2230  2265  2067  1499  1903  1901  1929
   beans-cor       546   585  1091   651   470   621   605   518   519   772
   manioc          986  1543  2658  1639  1146  1380  1357  1702  1560  1580
   corn            267   378   544   329   320   351   310   322   294   349;

Parameter
   price(c)    'crop reference prices       (cr per kg)'
               / cotton-h  1.9 , banana    4   , sugar-cane 35
                 beans-arr 2.5 , beans-cor 1.5 , oranges    10
                 manioc     .17, corn       .15, sisal       1 /
   ravg(c)     'average crop revenues       (cr per ha)'
   prdev(c,ty) 'price deviations for crops (cr per ton)';

* wage data: pg 159
* working capital: is this correct: = 6.4 * 1113
* family labor available: correct?

Scalar
   fwage  'family reservation wage rate (cr per man-month)' /   75   /
   twage  'temporary labor wage rate    (cr per man-month)' /  250   /
   pwage  'permanent labor wage rate     (cr per man-year)' / 2054   /
   vsc    'value of self-consumption       (cr per bundle)' /  934   /
   wcbar  'working capital                            (cr)' / 7123.2 /
   famlab 'family labor              (man equivalent wrks)' /   70.5 /
   lprice 'livestock price                   (cr per head)' /  211   /
   vetpr  'cost of veterinary service        (cr per head)' /   1    /
   dpm    'man-days per man month'                          /   25   /
   phi    'risk factor';

* some of these yields look odd: medium land has higher land than good

Table yield(p,c,s) 'crop yields (kg per ha)'
                         good  medium
   crop-02.cotton-h       848     569
   crop-05.banana         221     174
   crop-10.sugar-cane      45      30
   crop-15.oranges         92
   crop-16.manioc        4456    3964
   crop-17.corn           725     563
   crop-19.sisal         2244    1666
   crop-25.beans-cor      251     211
   crop-25.corn           373     264
   crop-29.cotton-h       269     149
   crop-29.beans-arr      285     221
   crop-29.corn           536     544
   crop-30.cotton-h       403     133
   crop-30.beans-cor      115     352
   crop-30.corn           361     212
   crop-33.beans-arr      274     260
   crop-33.corn           594     442
   crop-36.beans-arr      288     287
   crop-36.manioc        3408    1031
   crop-36.corn           503     328;

ps(p,s)   = yes$sum(c, yield(p,c,s));
ravg(c)   = sum(ty, crev(c,ty))/card(ty);
prdev(c,ty)$ravg(c)  = 1000*price(c)*(crev(c,ty)/ravg(c) - 1);
phi       = 1;

display ravg, prdev;

Table techc(p,km) 'cropping technology requirements (cr per ha)'
                   equipment  fertilizer  seeds  sprouts
   crop-02                            31     91
   crop-05                                            45
   crop-10                            36
   crop-15                           106      1      184
   crop-16                            20
   crop-17                            42     55
   crop-29                 4          22              19
   crop-30                                   27
   crop-33                11          42
   crop-36                            98      6        1;

Parameter
   pcost(p) 'cropping technology costs (cr per ha)'
   a(p)     'cropping constants';

pcost(p) = sum(km, techc(p,km));

display pcost;

a(p) = 1;
a(p)$sum(s, yield(p,"cotton-h",s)) = 0;

display pcost, a;

$sTitle Model Definition
Variable
   xcrop(p,s) 'cropping activities                             (ha)'
   xliver(r)  'livestock activity defined on feed techniques (head)'
   xlive      'livestock production                          (head)'
   lswitch(s) 'land downgrading                                (ha)'
   xprod(c)   'crop production                                (ton)'
   cons(dr)   'on-farm consumption                            (ton)'
   sales(c)   'crop sales                                     (ton)'
   flab(tm)   'family labor                              (man-days)'
   tlab(tm)   'temporary labor                           (man-days)'
   plab       'permanent labor                            (workers)'
   rationr    'livestock ration requirements                   (cr)'
   pdev(ty)   'positive price deviations                       (cr)'
   ndev(ty)   'negative price deviations                       (cr)'
   yfarm      'farm income                                     (cr)'
   revenue    'from crop and livestock sales                   (cr)'
   cropcost   'accounting: cropping activities cost            (cr)'
   labcost    'accounting: labor costs - including family      (cr)'
   vetcost    'accounting: veterinary services cost            (cr)';

Positive Variable xcrop, xliver, lswitch, sales, cons, flab, tlab, plab, pdev, ndev;

Equation
   landb(s) 'land balance'
   lbal     'livestock balance                        ( )'
   rliv     'livestock ration requirements definition ( )'
   mbalc(c) 'material balance: crops                  ( )'
   dprod(c) 'crop production definition               ( )'
   cond     'on farm consumption definition           ( )'
   labc(tm) 'labor supply-demand relation             ( )'
   ddev(ty) 'crop price deviation definition          ( )'
   income   'farm income definition                   ( )'
   arev     'accounting: revenue definition           ( )'
   acrop    'accounting: cropping cost definition     ( )'
   alab     'accounting: labor cost definition        ( )'
   awcc     'accounting: working capital requirements ( )'
   avet     'accounting: veterinary costs            (cr)';

landb(s)..     sum(p$ps(p,s), a(p)*xcrop(p,s))$sc(s)
            +  sum(sp, ldp(s,sp)*lswitch(sp))
            +  sum(r, lio(s,r)*xliver(r))
           =l= landc(s);

lbal.. xlive   =e= sum(r, xliver(r));

rliv.. rationr =e= sum(r, rations(r)*xliver(r));

mbalc(c)..     sum((s,p), yield(p,c,s)*xcrop(p,s))/1000
           =g= sales(c) + sum(dr, cbndl(c,dr)*cons(dr));

dprod(c).. xprod(c) =e= sum((p,s), yield(p,c,s)*xcrop(p,s))/1000;

labc(tm)..     sum((p,s)$ps(p,s), labor(p,tm)*xcrop(p,s))
            +  sum(r, llab(tm,r)*xliver(r))
           =l= flab(tm) + tlab(tm) + dpm*plab;

cond..     sum(dr, cons(dr)) =e= 1;

ddev(ty).. sum(c, prdev(c,ty)*sales(c)) =e= pdev(ty) - ndev(ty);

arev..   revenue  =e= lprice*xlive + 1000*sum(c, price(c)*sales(c));

acrop..  cropcost =e= sum((p,s)$ps(p,s), pcost(p)*xcrop(p,s));

alab..   labcost  =e= (fwage*sum(tm, flab(tm)) + twage*sum(tm, tlab(tm)))/dpm + pwage*plab;

awcc..   cropcost + rationr + vetcost + twage/dpm*sum(tm, tlab(tm)) + pwage*plab =l= wcbar;

avet..   vetcost =e= vetpr*xlive;

income.. yfarm   =e=   revenue + vsc*sum(dr, cons(dr)) - labcost - rationr - vetcost
                     - cropcost - phi*sum(ty, pdev(ty) + ndev(ty))/card(ty);

Model agreste 'farm level model' / all /;

xcrop.up(p,s)$xcropl(p,s) = xcropl(p,s);
flab.up(tm) = famlab;

solve agreste maximizing yfarm using lp;

phi = 0;

solve agreste maximizing yfarm using lp;