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Pissarides, "Equilibrium Unemployment Theory", Chapter 1

The graphs below implement the model for any combination of parameters (with a Cobb-Douglas matching function with elasticity η). Note that p is set to be the upper bound for z, so a solution will always exist.
For comparative statics, check "Fixed frame". To ensure that the solution is visible for any combination of parameters, uncheck "Fixed frame".
Notable fact: even a tiny β gives an equilibrium wage well above z, due to the search cost.

With[{vBC=(((mm λλ))^(1/(1-ηη)))((#)^(-((ηη)/(1-ηη))))(((1-#))^(1/(1-ηη)))&,
wJC=pp-((pp cc(rr+λλ))/(mm ((#)^(-ηη))))&,
wWC=(1-ββ)zz+ββ(pp+pp cc #)&},
Manipulate[With[{params={mm->m,λλ->λ,ηη->η,pp->p,cc->c,zz->z,ββ->β,rr->r}},
With[{θstar=θ/.FindRoot[(wJC[θ]==wWC[θ])/.params,{θ,1}]},With[{ustar=u/.FindRoot[(vBC[u]==θstar u)/.params,{u,0.1}]},GraphicsGrid[{
{Plot[
{z,p,wJC[θ]/.params,wWC[θ]/.params},{θ,0,If[fix,0.91,2θstar]},PlotRange->{If[fix,4,0.8z],If[fix,12,1.2p]},
AxesOrigin->{0,If[fix,4,0.8z]},
Frame->{{True,False},{True,False}},FrameLabel->{"Tightness (θ)","Wage (w)"},
PlotLabel->Style["JC (light blue) and WC (dark blue); z and p dotted\n",FontSize->14],PlotStyle->{{Black,Dotted},{Black,Dotted},RGBColor[.4,.4,1],RGBColor[.1,0,.6]},
BaseStyle->{FontFamily->"Helvetica",FontSize->14},ImageSize->400,AspectRatio->.71,
Epilog->{RGBColor[.6,.4,.1],Dashed,Line[{{θstar,If[fix,4,0.8z]},{θstar,wWC[θstar]/.params}}]}
],
Plot[
{vBC[u]/.params,u θstar},{u,0,.2},PlotRange->{0,If[fix,0.0622,vBC[.02]/.params]},Frame->{{True,False},{True,False}},FrameLabel->{"Unemployment (u)","Vacancies (v)"},PlotLabel->Style["Beveridge Curve and (SuperStar[θ])="<>ToString[SetPrecision[θstar,2]]<>"\n",FontSize->14],PlotStyle->{RGBColor[.7,.1,.1],RGBColor[.6,.4,.1]},
BaseStyle->{FontFamily->"Helvetica",FontSize->14},ImageSize->400,AspectRatio->.71,Epilog->{{RGBColor[.3,.5,.2],Dotted,Line[{{0,vBC[ustar]},{ustar,vBC[ustar]}}/.params]},{RGBColor[.3,.5,.2],Dotted,Line[{{ustar,0},{ustar,vBC[ustar]/.params}}]}}
]}},Spacings->0]]]],
Grid[{{Control[{{fix,True,"Fixed frame"},{True,False}}],""},{Control[{{r,0.01,"Time discount rate (r)"}}],Control[{{p,10,"Job productivity (p)"},0,20}]},{Control[{{λ,0.03,"Matching rate (λ)"}}],Control[{{c,1,"Vacancy cost (c)"},0,2}]},{Control[{{η,0.5,"Matching elasticity (η)"}}],Control[{{z,0.5p,"Worker outside option (z)"},0,p}]},{Control[{{m,1.2,"Matching efficiency (m)"}}],Control[{{β,0.5,"Bargaining power (β)"},0,1}]}
},Alignment->Right,Spacings->{{3,{2},3}},Frame->True,FrameStyle->Opacity[0]],
FrameLabel->{{None,None},{Style["\n(CC BY\[Hyphen]NC\[Hyphen]SA 3.0)  -  Lucas Herrenbrueck, 2011  -  herrenbrueck@ucdavis.edu",FontSize->12],Style["The Basic Mortensen\[Hyphen]Pissarides Model\n",Bold,FontSize->24,FontFamily->"Helvetica"]}},
LabelStyle->{FontSize->14,FontFamily->"Helvetica"},BaselinePosition->Bottom,ControlPlacement->Top,ContentSize->840,SaveDefinitions->False]]