$title	A Simple Partial Equilibrium Trade Model with Corner Solutions

set	r	Regions /r1*r50/;
alias (r,rr);

parameter	cost(r)		Production cost
		c(r,rr)		Export cost
		alpha(r)	Demand coefficient;

*	Generate a random dataset:

cost(r)	= uniform(0.75,1.5);
c(r,rr) = uniform(0.25,0.75);
alpha(r) = uniform(1,5);

positive
variables	p(r)	Market price
		x(r,r)	Trade flows
		y(r)	Production;

equations eq_x, eq_y, mkt;

eq_x(r,rr)..	p(r) + c(r,rr) =g= p(rr);

eq_y(r)..	cost(r) =g= p(r);

mkt(r)..	y(r) + sum(rr, x(rr,r)-x(r,rr)) =e= alpha(r) * p(r)**(-2);

p.lo(r) = 0.01;
p.l(r) = 1;
y.l(r) = 1;

*	The model statement indicates complementarity between 
*	variables and equations.  Zero profit conditions for
*	trade and production are associated with quantities 
*	shipped and produced.  Market clearance conditions are
*	associated with market prices:

model peq /eq_x.x, eq_y.y, mkt.p/;

*	Eliminate degeneracy:

x.fx(r,r) = 0;

solve peq using mcp;

parameter	equil	Equilibrium values;
equil(r,"y") = y.l(r);
equil(r,"p") = p.l(r);
equil(r,"export") = sum(rr, x.l(r,rr));
equil(r,"import") = sum(rr, x.l(rr,r));
display equil;



----     52 PARAMETER equil  Equilibrium values

              y           p      export      import

r1        6.226       0.879       1.417
r2                    1.229                   1.798
r3                    1.157                   1.917
r4        3.162       0.976
r5        3.229       0.969
r6        5.157       0.918
r7        4.748       1.012
r8                    1.165                   1.389
r9       21.634       0.800      16.592
r10       2.157       1.125
r11                   1.097                   3.739
r12                   1.100                   4.011
r13                   1.108                   1.742
r14                   1.177                   3.611
r15       6.160       0.848
r16                   1.146                   1.417
r17       6.034       0.870
r18       5.311       0.938
r19                   1.049                   2.387
r20                   1.043                   3.135
r21       4.298       1.020
r22       1.225       1.014
r23       5.112       0.849
r24       8.839       0.863       2.283
r25       3.072       1.192
r26                   1.052                   3.001
r27       2.092       0.923
r28                   1.051                   2.774
r29                   1.097                   3.620
r30       2.216       0.978
r31      18.598       0.833      12.101
r32       2.813       1.127
r33      10.160       0.870       3.619
r34                   1.065                   3.023
r35       2.316       0.949
r36       1.885       0.964
r37                   1.170                   1.821
r38                   1.088                   0.973
r39                   1.121                   2.283
r40                   1.075                   4.316
r41       2.649       1.060
r42       5.389       0.838
r43       2.264       0.986
r44      22.181       0.785      16.296
r45       1.688       1.004
r46       7.005       0.887       1.389
r47                   1.129                   2.014
r48                   1.149                   2.320
r49                   1.137                   2.406
r50       5.017       0.973