the range of three function arguments is between 0 and 1, boundaries excluded Thanks again Lorenzo Rocco, Ph.D. School of Economics University of Padova Italy

the range of three function arguments is between 0 and 1, boundaries excluded Thanks again Lorenzo Rocco, Ph.D. School of Economics University of Padova Italy

This is the code: restart; > numsol:=proc(eta,tau,lambda,beta,gamma0,cA,cB,VVAA,VVBB) > local lambda_H, lambda_L, yAH, yAL, yBL, yBH, psi, g, Sigma, focA, focB, focvA, focvB, sys: > global vA,vB,lAH,lBL,lAL,lBH: > lambda_H:=1+lambda+beta*(1-eta): > lambda_L:=1+lambda+beta*eta: > yAH:=1+(lambda_H-1)*tau: > yAL:=1-tau: > yBL:=1+(lambda_L-1)*tau: > yBH:=1-tau: > lBH:=(eta-vA*lAH)/vB: > lAL:=(1-eta-vB*lBL)/vA: > psi:=x->1-exp(-x): > g:=x->(1+x)*exp(-x): > Sigma:=(1-psi(lAH))*(1-psi(lAL))*yAL-(1-psi(lBL))*(1-psi(lBH))*yBH: > focA:=(1-psi(lAH))*(yAH-yAL)+Sigma-gamma0/eta*(3*vA*lAH-eta*(1+vA/(vA+vB)))=0: > focB:=(1-psi(lBL)*(yBL-yBH)-Sigma-gamma0/(1-eta)*(3*vB*lBL-(1-eta)*(1+vB/(vA+vB))))=0: > focvA:=yAH-g(lAH)*(yAH-yAL)-g(lAH+lAL)*yAL+gamma0*vA*lAH^2/eta+gamma0*vA*lAL^2/(1-eta)-cA=0: > focvB:=yBL-g(lBH)*(yBL-yBH)-g(lBL+lBH)*yBH+gamma0*vB*lBL^2/(1-eta)+gamma0*vB*lBH^2/(1-eta)-cB=0: > sys:={focA,focB,focvA,focvB}: > fsolve(sys,{vA,vB,lAH,lBL},{vA=0..VVAA,vB=0..VVBB,lAH=0..2,lBL=0..2}); > end proc: > > lAHstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),lAH); > lBLstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),lBL); > vAstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),vA); > vBstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),vB); The procedure is only to define my system and the key comand is fsolve. I'm interested in plotting the four functions defined below the procedure, or in plotting each of the four procedure outputs for different values of the parameters. Thanks in advance for your support Lorenzo Rocco, Ph.D. School of Economics University of Padova Italy

This is the code: restart; > numsol:=proc(eta,tau,lambda,beta,gamma0,cA,cB,VVAA,VVBB) > local lambda_H, lambda_L, yAH, yAL, yBL, yBH, psi, g, Sigma, focA, focB, focvA, focvB, sys: > global vA,vB,lAH,lBL,lAL,lBH: > lambda_H:=1+lambda+beta*(1-eta): > lambda_L:=1+lambda+beta*eta: > yAH:=1+(lambda_H-1)*tau: > yAL:=1-tau: > yBL:=1+(lambda_L-1)*tau: > yBH:=1-tau: > lBH:=(eta-vA*lAH)/vB: > lAL:=(1-eta-vB*lBL)/vA: > psi:=x->1-exp(-x): > g:=x->(1+x)*exp(-x): > Sigma:=(1-psi(lAH))*(1-psi(lAL))*yAL-(1-psi(lBL))*(1-psi(lBH))*yBH: > focA:=(1-psi(lAH))*(yAH-yAL)+Sigma-gamma0/eta*(3*vA*lAH-eta*(1+vA/(vA+vB)))=0: > focB:=(1-psi(lBL)*(yBL-yBH)-Sigma-gamma0/(1-eta)*(3*vB*lBL-(1-eta)*(1+vB/(vA+vB))))=0: > focvA:=yAH-g(lAH)*(yAH-yAL)-g(lAH+lAL)*yAL+gamma0*vA*lAH^2/eta+gamma0*vA*lAL^2/(1-eta)-cA=0: > focvB:=yBL-g(lBH)*(yBL-yBH)-g(lBL+lBH)*yBH+gamma0*vB*lBL^2/(1-eta)+gamma0*vB*lBH^2/(1-eta)-cB=0: > sys:={focA,focB,focvA,focvB}: > fsolve(sys,{vA,vB,lAH,lBL},{vA=0..VVAA,vB=0..VVBB,lAH=0..2,lBL=0..2}); > end proc: > > lAHstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),lAH); > lBLstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),lBL); > vAstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),vA); > vBstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),vB); The procedure is only to define my system and the key comand is fsolve. I'm interested in plotting the four functions defined below the procedure, or in plotting each of the four procedure outputs for different values of the parameters. Thanks in advance for your support Lorenzo Rocco, Ph.D. School of Economics University of Padova Italy