MODEL:
   ! General Equilibrium Model of an economy in LINGO,  (GENEQLBM);
   ! Data based on Kehoe, Math Prog, Study 23(1985);
   ! Find clearing prices for commodities/goods and
     equilibrium production levels for processes in an economy;
   ! Keywords: Equilibrium, General equilibrium, Complementarity constraints;
SETS:
    GOOD: PRICE, H;
    SECTOR;
    GXS( GOOD, SECTOR): ALPHA, W;
    PROCESS: LEVEL, RC;
    GXP( GOOD, PROCESS): MAKE;
   ENDSETS
   DATA:
   ! There are 4 goods, 4 sectors. In general need not be same;
     GOOD = 1..4; SECTOR = 1..4;
   ! Demand curve parameter for each good i & sector j;
    ALPHA =
      .5200  .8600  .5000  .0600
      .4000  .1     .2     .25
      .04    .02    .2975  .0025
      .04    .02    .0025  .6875;
   ! Initial wealth of good i held by sector j;
     W =
      50     0      0      0
       0    50      0      0
       0     0    400      0
       0     0      0    400;
   PROCESS= 1   2;  ! There are two processes to make goods;
   ! The processes are linear, with
     amount produced of good i per unit of process j;
     MAKE =
           6   -1
          -1    3
          -4   -1
          -1   -1;
   ! Weights for price normalization constraint;
     H = .25 .25 .25 .25; ! Make simple average = 1;
   ENDDATA
   !-----------------------;
   ! Variables:
      LEVEL(p) = level or amount at which we operate
                 process p.
      PRICE(g) = equilibrium price for good g.
         RC(p) = reduced cost of process p 
               = cost of inputs to process p - revenues from outputs
                 of process p,  per unit;

   ! The objective function is optional.
     Arbitrarily maximize some price;
     MAX = PRICE(1);

   ! For each good G must have supply = demand, i.e.,
      initial amount + production = sum over sectors, S,
      of amount demanded of G at given prices;
    @FOR( GOOD( G):
      @SUM( SECTOR( M): W( G, M))
      + @SUM( PROCESS( P): MAKE( G, P) * LEVEL( P))
      = @SUM( SECTOR( S):
              ALPHA( G, S) * 
        @SUM( GOOD( I): PRICE( I) * W( I, S))/ PRICE( G));
        );

   ! Each process at best breaks even, RC is constrained >= 0;
    @FOR( PROCESS( P):
      RC(P) = @SUM( GOOD( G): - MAKE( G, P) * PRICE( G));
   ! Complementarity constraint to enforce that
     if process does not break even(RC > 0), then
      do not use it. Also, if use it, then RC = 0;
      RC(P)*LEVEL(P) = 0;
        );

   ! Prices scale to 1. otherwise there is an infinity of solutions;
     @SUM( GOOD( G): H( G) * PRICE( G)) = 1;
END