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function equilibrium
syms K2 K3 Rg1 Rg2 Rg3 Rg4 P1 P2 P3 P4 PI1 PI2 PI3 PI4 a H2 H3 H4 Ra2 Ra3 Ra4 kg1 kg2 kg3 kg4
f1=K2*PI2^2-PI4;
f2=PI1*PI2*K3-PI3;
f3=Rg1-a*kg1*(P1-PI1);
f4=Rg2-a*kg2*(P2-PI2);
f5=Rg3-a*kg3*(P3-PI3);
f6=Rg4-a*kg4*(P4-PI4);
f7=Ra2-a*H2*(PI2)^(3/2);
f8=Ra4-a*H4*PI4;
f9=Ra3-a*H3*PI3;
f10=Rg1+Rg3-Ra3;
f11=Rg2+Rg3+2*Rg4-Ra2-Ra3-2*Ra4
[PI1 PI2 PI3 PI4 Rg1 Rg2 Rg3 Rg4 Ra2 Ra3 Ra4]=solve(f1,f2,f3,f4,f5,f6,f7,f8,f9,f10,f11)
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