$title A General Equilibrium Version of the von Thunen Model (VONTHMGE,SEQ=156)

$onText
A General Equilibrium Version of the von Thunen Model.

Mackinnon, J, A Technique for the Solution of Spatial Equilibrium
Models. Journal of Regional Science 16, 3 (1976), 293-307.

Keywords: mixed complementarity problem, general equilibrium model, von Thunen model,
          agricultural policy, GAMS - MPSGE framework
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Set
   R 'regions'     / R1*R12 /
   C 'commodities' / WHEAT, RICE, CORN, BARLEY /
   H 'households'  / WORKER, OWNER, PORTER     /;

Scalar
   LTOT 'labor endowment'     / 30 /
   TRNS 'transport endowment' / 20 /;

Parameter
   D(R)       'distance to region R'
   A(R)       'area of region R'
   T(C)       'transport requirement'
   PHI(C)     'cost function scale parameter'
   BETA(C)    'cost function share parameter'
   ALPHA(*,H) 'demand function share';

D(R) = 5*(2*ord(R) - 1);
A(R) = 2*pi*D(R);

Table MISC(*,*)
           WHEAT  RICE   CORN   BARLEY  LEISURE
   PHI     1      2      3      4
   BETA    0.9    0.7    0.5    0.3
   T       0.015  0.006  0.004  0.01
   WORKER  0.2    0.3    0.1    0.3         0.1
   OWNER   0.3    0.3    0.2    0.2
   PORTER  0.6    0.2    0.1    0.1            ;

PHI(C)     = MISC("PHI",C);
BETA(C)    = MISC("BETA",C);
T(C)       = MISC("T",C);
ALPHA(C,H) = MISC(H,C);
ALPHA("LEISURE",H) = MISC(H,"LEISURE");

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$MODEL:VONTHUN

$SECTORS:
   Y(C,R)      ! OUTPUT LEVEL

$COMMODITIES:
   WL          ! WORKER WAGE
   WP          ! PORTER WAGE
   P(C)        ! MARKET PRICE
   PK(R)       ! RENTAL RATE

$CONSUMER:
   PORTER
   WORKER
   OWNER

$AUXILIARY:
   IP(R)       ! INTERVENTION PURCHASE (BOUNDS PRICE)

$PROD:Y(C,R) s:0 a:1
   O:P(C)    Q:PHI(C)
   I:WL      Q:BETA(C) a:
   I:PK(R)   Q:(1 - BETA(C)) a:
   I:WP      Q:(T(C)*D(R))

$DEMAND:PORTER s:1
   E:WP      Q:TRNS
   D:P(C)    Q:ALPHA(C,"PORTER")

$DEMAND:WORKER s:1
   E:WL      Q:LTOT
   D:P(C)    Q:ALPHA(C,"PORTER")
   D:WL      Q:ALPHA("LEISURE","PORTER")

$DEMAND:OWNER s:1
   E:PK(R)   Q:A(R)
   E:PK(R)   Q:-1    R:IP(R)
   D:P(C)    Q:ALPHA(C,"OWNER")

$CONSTRAINT:IP(R)
   PK(R) =g= 0.001*WL;
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$sysInclude mpsgeset VONTHUN

$include VONTHUN.GEN
solve VONTHUN using mcp;