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using NLsolve
using PyPlot



    











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# model parameters
Cv=.2;
psi1=1.05;
alpha=0.1;
epsilon=1.0;
hbar=1.0;
gamma=.85;
mu=0.9;



    











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function h(ps::Float64,c::Float64,q)
    hfunc=(((1+ps)/ps)*(c./q)).^(1/(1+ps))
end



    


















    
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h (generic function with 1 method)

















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function nflex(eps,aa::Float64,ps::Float64,c::Float64,q)
    nfunc=(eps*aa).^(1/(1-aa)).*((1+1/ps)*(c./q)).^(-(1-aa+ps)/((1-aa)*(1+ps)))
end



    


















    
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nflex (generic function with 1 method)

















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function nfix(eps,aa::Float64,ps::Float64,c::Float64,q,hb::Float64)
    nfunc=(eps*aa*hb^aa).^(1/(1-aa)).*(((hb^(1+ps))/(1+ps))+(c./q)).^(1/(aa-1))
end



    


















    
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nfix (generic function with 1 method)

















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function q(mm::Float64,gg::Float64,n)
    (mm*((1-n)./n).^gg).^(1/(1-gg))
end



    


















    
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q (generic function with 1 method)

















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function g!(x,fvec)
    # x[1]=h; x[2]=n; x[3]=q; 
    fvec[1]=x[1]-h(psi1,Cv,x[3])
    fvec[2]=x[2]-nflex(epsilon,alpha,psi1,Cv,x[3])
    fvec[3]=x[3]-q(mu,gamma,x[2])
end


function g2!(x2,g2vec)
    # x[1]=h1; x[2]=h2; x[3]=n1; x[4]=n2; x[5]=q;
    g2vec[1]=x2[1]-h(psi1,Cv,x2[5])
    g2vec[2]=x2[2]-h(psi1,Cv,x2[5])
    g2vec[3]=x2[3]-nflex(epsilon,alpha,psi1,Cv,x2[5])
    g2vec[4]=x2[4]-nflex(1,alpha,psi1,Cv,x2[5])
    g2vec[5]=x2[5]-q(mu,gamma,x2[3]+x2[4])
end

function g2fix!(x2fix,g2fixvec)
    # x[1]=n1; x[2]=n2; x[3]=q; 
    g2fixvec[1]=x2fix[1]-nfix(epsilon,alpha,psi1,Cv,x2fix[3],hvec1[end])
    g2fixvec[2]=x2fix[2]-nfix(1,alpha,psi1,Cv,x2fix[3],hvec1[end])
    g2fixvec[3]=x2fix[3]-q(mu,gamma,x2fix[1]+x2fix[2])
end



    


















    
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g2fix! (generic function with 1 method)

















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hvec1=Array{Float64,1}(0)
hvec2=Array{Float64,1}(0)
nvec1=Array{Float64,1}(0)
nvec2=Array{Float64,1}(0)
qvec=Array{Float64,1}(0)

for eps=.1:.01:1
    epsilon=eps;
    r=nlsolve(g2!, [ 1.0; 1.0; .1; .1; .1])
    push!(hvec1,r.zero[1])
    push!(hvec2,r.zero[2])
    push!(nvec1,r.zero[3])
    push!(nvec2,r.zero[4])
    push!(qvec,r.zero[5])
end


hvecfix1=Array{Float64,1}(0)
hvecfix2=Array{Float64,1}(0)
nvecfix1=Array{Float64,1}(0)
nvecfix2=Array{Float64,1}(0)
qvecfix=Array{Float64,1}(0)

for eps=.1:.01:1
    epsilon=eps;
    rfix=nlsolve(g2fix!, [.1; .1; .05])
    push!(hvecfix1,hvec1[end])
    push!(hvecfix2,hvec2[end])
    push!(nvecfix1,rfix.zero[1])
    push!(nvecfix2,rfix.zero[2])
    push!(qvecfix,rfix.zero[3])
end



    











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function eqfixedhours!(var,residuals)
    # x[1]=n1; x[2]=n2; x[3]=q; 
    residuals[1]=alpha*hbar*epsilon*(var[1]*hbar)^(alpha-1)-(1/(1+psi1))*hbar^(1+psi1)-Cv/var[3]
    residuals[2]=alpha*hbar*1*(var[2]*hbar)^(alpha-1)-(1/(1+psi1))*hbar^(1+psi1)-Cv/var[3]
    residuals[3]=var[3]-q(mu,gamma,var[1]+var[2])
end

function eqflexiblehours!(var,residuals)
    # x[1]=n1; x[2]=n2; x[3]=h1; x[4]=h2; x[5]=q
    residuals[1]=alpha*var[3]*epsilon*(var[1]*var[3])^(alpha-1)-(1/(1+psi1))*var[3]^(1+psi1)-Cv/var[5]
    residuals[2]=alpha*var[4]*1*(var[2]*var[4])^(alpha-1)-(1/(1+psi1))*var[4]^(1+psi1)-Cv/var[5]
    residuals[3]=alpha*epsilon*(var[1]*var[3])^(alpha-1)-var[3]^psi1
    residuals[4]=alpha*1*(var[2]*var[4])^(alpha-1)-var[4]^psi1
    residuals[5]=var[5]-q(mu,gamma,var[1]+var[2])
end



    


















    
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eqflexiblehours! (generic function with 1 method)

















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hvec1flexible=Array{Float64,1}(0)
hvec2flexible=Array{Float64,1}(0)
nvec1flexible=Array{Float64,1}(0)
nvec2flexible=Array{Float64,1}(0)
qvecflexible=Array{Float64,1}(0)

for eps=.5:.01:1
    epsilon=eps;
    r=nlsolve(eqflexiblehours!, [ .1; .1; 1; 1; .05])
    push!(nvec1flexible,r.zero[1])
    push!(nvec2flexible,r.zero[2])
    push!(hvec1flexible,r.zero[3])
    push!(hvec2flexible,r.zero[4])
    push!(qvecflexible,r.zero[5])
end


nvec1fixed=Array{Float64,1}(0)
nvec2fixed=Array{Float64,1}(0)
qvecfixed=Array{Float64,1}(0)

for eps=.5:.01:1
    epsilon=eps;
    hbar=hvec1flexible[end];
    r=nlsolve(eqfixedhours!, [ .1; .1; .05])
    push!(nvec1fixed,r.zero[1])
    push!(nvec2fixed,r.zero[2])
    push!(qvecfixed,r.zero[3])
end



    











In [11]:



    


fig, ax = subplots()
ax[:plot](.5:.01:1,nvec1flexible./nvec1flexible[end], linewidth=2, color="red", alpha=0.9, label="Sector 1, flexible hours")
ax[:plot](.5:.01:1,nvec2flexible./nvec2flexible[end], linewidth=2, color="blue", alpha=0.9, label="Sector 2, flexible hours")
ax[:legend](loc="lower right")
ax[:set_title]("Employment by sector")



    


















    

















    
Out[11]:








PyObject <matplotlib.text.Text object at 0x14fa3f790>

















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fig, ax = subplots()
ax[:plot](.5:.01:1,(nvec1flexible+nvec2flexible)./(nvec1flexible[end]+nvec2flexible[end]), linewidth=2, color="black", alpha=0.9, label="E, flexible hours")
ax[:legend](loc="lower right")
ax[:set_title]("Employment")



    


















    

















    
Out[12]:








PyObject <matplotlib.text.Text object at 0x14fbad6d0>

















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fig, ax = subplots()
ax[:plot](.5:.01:1,hvec1flexible./hvec1flexible[end], linewidth=2, color="red", alpha=0.9, label="Sector 1, flexible hours")
ax[:plot](.5:.01:1,hvec2flexible./hvec2flexible[end], linewidth=2, color="blue", alpha=0.9, label="Sector 2, flexible hours")
ax[:legend](loc="lower right")
ax[:set_title]("Average Hours by sector")



    


















    

















    
Out[13]:








PyObject <matplotlib.text.Text object at 0x1452bf5d0>

















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fig, ax = subplots()
ax[:plot](.5:.01:1,(Cv./qvecflexible)./(Cv./qvecflexible[end]), linewidth=2, color="black", alpha=0.9, label="vacancy costs")
ax[:legend](loc="lower right")
ax[:set_title]("Vacancy costs, flexible hours")



    


















    

















    
Out[14]:








PyObject <matplotlib.text.Text object at 0x153569f10>

















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fig, ax = subplots()
ax[:plot](.5:.01:1,nvec1flexible./nvec1flexible[end], linewidth=2, color="red", alpha=0.9, label="Sector 1, flex hours")
ax[:plot](.5:.01:1,nvec2flexible./nvec2flexible[end], linewidth=2, color="blue", alpha=0.9, label="Sector 2, flex hours")
ax[:plot](.5:.01:1,nvec1fixed./nvec1fixed[end], linewidth=2, color="red", alpha=.3, label="Sector 1")
ax[:plot](.5:.01:1,nvec2fixed./nvec2fixed[end], linewidth=2, color="blue", alpha=0.3, label="Sector 2")
ax[:legend](loc="lower right")
ax[:set_title]("Employment by sector")



    


















    

















    
Out[22]:








PyObject <matplotlib.text.Text object at 0x154454150>

















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fig, ax = subplots()
ax[:plot](.5:.01:1,(nvec1flexible+nvec2flexible)./(nvec1flexible[end]+nvec2flexible[end]), linewidth=2, color="red", alpha=0.9, label="flexible hours")
ax[:plot](.5:.01:1,(nvec1fixed+nvec2fixed)./(nvec1fixed[end]+nvec2fixed[end]), linewidth=2, color="blue", alpha=0.9, label="fixed hours")
ax[:legend](loc="lower right")
ax[:set_title]("Employment")



    


















    

















    
Out[16]:








PyObject <matplotlib.text.Text object at 0x1535d1a90>

















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fig, ax = subplots()
ax[:plot](.1:.01:1,Cv./qvec, linewidth=2, color="black", alpha=0.9, label="flexible hours")
ax[:plot](.1:.01:1,Cv./qvecfix, linewidth=2, color="black", alpha=0.3, label="fixed hours")
ax[:legend](loc="lower right")
ax[:set_title]("hiring costs")
ax[:set_xticks]([.1, .5, 1])
#ax[:set_yticks]([0, .007, .015])



    


















    

















    
Out[17]:








3-element Array{PyCall.PyObject,1}:
 PyObject <matplotlib.axis.XTick object at 0x153722290>
 PyObject <matplotlib.axis.XTick object at 0x153ef94d0>
 PyObject <matplotlib.axis.XTick object at 0x15407be50>

















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outputflexible=collect(.5:.01:1).*(nvec1flexible.*hvec1flexible).^alpha + 
        1*(nvec2flexible.*hvec2flexible).^alpha;

outputfixed=collect(.5:.01:1).*(nvec1fixed.*hbar).^alpha + 
        1*(nvec2fixed.*hbar).^alpha;

fig, ax = subplots()
ax[:plot](.5:.01:1,log.(outputflexible./outputflexible[end]), linewidth=2, color="red", alpha=0.9, label="flexible hours")
ax[:plot](.5:.01:1,log.(outputfixed./outputfixed[end]), linewidth=2, color="blue", alpha=0.9, label="fixed hours")
ax[:legend](loc="lower right")
ax[:set_title]("Output")



    


















    

















    
Out[18]:








PyObject <matplotlib.text.Text object at 0x1540c89d0>

















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fig, ax = subplots()
ax[:plot](.5:.01:1,hvec1flexible./hvec1flexible[end], linewidth=2, color="red", alpha=0.9, label="Sector 1, flexible hours")
ax[:plot](.5:.01:1,hvec2flexible./hvec2flexible[end], linewidth=2, color="blue", alpha=0.9, label="Sector 2, flexible hours")
ax[:legend](loc="lower right")
ax[:set_title]("Hours by sector")



    


















    

















    
Out[19]:








PyObject <matplotlib.text.Text object at 0x15437dbd0>

















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hvec1flexible[1]



    


















    
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0.5275337353607061

















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nvec2flexible[1]



    


















    
Out[21]:








0.3095138166741908

















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Content source: jbrogueira/jbrogueira.github.io

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