Plots of wages and production

wK

Figure 1 for paper

Because of the need to use FindRoot for 3 factor case, we must first create a table to plot

Now the correct figures start.

Color Figure 1 for Economics Letters is the line below.

Show[Plot[{wK1f[K0 (10^12),labor,AF,a,c],wK2crf[K0 (10^12),labor,AF,a,c,223859.3251`,700000]},{K0,Khat/(10^12),6 Khat/(10^12)},PlotStyle->{ {Blue},{Green}},AxesOrigin->{10,0},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"K ($ trillions)","wK"},LabelStyle-> Directive[18]],ListLinePlot[Table[{(1+i .1) Khat/(10^12),wK3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,58}],PlotStyle->Red],Plot[.04,{K0,0,6 Khat/(10^12)},PlotStyle->Dashed]]

Plot of wK vs K: blue is without robots, red is 3 factor,green is 2 factor

B&W Figure 1 for Economics Letters is the line below.

Show[Plot[{wK1f[K0 (10^12),labor,AF,a,c],wK2crf[K0 (10^12),labor,AF,a,c,223859.3251`,700000]},{K0,Khat/(10^12),6 Khat/(10^12)},PlotStyle->{ {Black},{Black,Dashed}},AxesOrigin->{10,0},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"K ($ trillions)","wK"},LabelStyle-> Directive[18]],ListLinePlot[Table[{(1+i .1) Khat/(10^12),wK3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,58}],PlotStyle->{Black,Dotted}],Plot[.04,{K0,0,6 Khat/(10^12)},PlotStyle->DotDashed]]

Effect of changing the number of goods

Repeat of Fig. 1 with 300000 instead of 700000 goods

wK3crtp=Table[{(1+i .1) Khat/(10^12),wK3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{i,0,58}];

Show[Plot[{wK1f[K0 (10^12),labor,AF,a,c],wK2crf[K0 (10^12),labor,AF,a,c,223859.3251`,300000]},{K0,Khat/(10^12),6 Khat/(10^12)},PlotStyle->{ {Blue},{Green}},AxesOrigin->{10,0},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"K ($ trillions)","wK"},LabelStyle-> Directive[18]],ListLinePlot[Table[{(1+i .1) Khat/(10^12),wK3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{i,0,50}],PlotStyle->Red],Plot[.04,{K0,0,6 Khat/(10^12)},PlotStyle->Dashed]]

Ignore problem with red line

Create plots of dependence of wK upon CRmx

Choose K=3 Khat

The answer is complex for CRmx less than about 273509

wK3crff[3 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,273508]

wK3crff[3 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,273509]

wK3crtpp=Table[{(1+i .1) 280000,wK3crff[3 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,(1+i .1)280000]},{i,0,20}];

Try 6 Khat

wK3crff[6 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,273509]

wK3crtpp=Table[{(1+i .1) 280000,wK3crff[4 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,(1+i .1)280000]},{i,0,19}];

ListLinePlot[wK3crtpp,AxesOrigin-> {200000,0}, PlotRange->All]

The dependence upon the number of goods is not striking as long a solution exists.

Plot[wK2crf[4 Khat,labor,AF,a,c,223859.3251`,CRmx],{CRmx,230000,800000},AxesOrigin->{230000,0},PlotRange->All]

Show[Plot[wK2crf[4 Khat,labor,AF,a,c,223859.3251`,CRmx],{CRmx,230000,800000},PlotStyle-> Red,AxesOrigin->{230000,0},PlotRange->All,Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"K ($ trillions)","wK"},LabelStyle-> Directive[18]],ListLinePlot[wK3crtpp]]

2 factor is red, 3 factor is blue

Show[Plot[wK2crf[4 Khat,labor,AF,a,c,223859.3251`,CRmx],{CRmx,230000,800000},PlotStyle-> {Black},AxesOrigin->{230000,0},PlotRange->All,Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"K ($ trillions)","wK"},LabelStyle-> Directive[18]],ListLinePlot[wK3crtpp,PlotStyle->{Black,Thick}]]

wB

wB3crt=Table[{(1+i .1) Khat/(10^12),wB3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,58}];

Show[Plot[{wL1f[(10^12)K0,labor,AF,a,c],wL2crf[(10^12) K0,labor,AF,a,c,223859.3251`,700000]},{K0,Khat/(10^12),3 Khat/(10^12)},PlotStyle->{ {Blue},{Green}},AxesOrigin->{10,0},AxesLabel->{"K","wB"}],ListLinePlot[wB3crt,PlotStyle->Red]]

Type B wages vs K: Blue is no robots, green is 2 factor, red is 3 factor
The 3 factor curve does not meet the other two because Type A labor sucks away income from Type B labor even without robots.

wA 3 factor case only

wA3crt=Table[{(1+i .1) Khat/(10^12),wA3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,24}];

wB3crt=Table[{(1+i .1) Khat/(10^12),wB3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,24}];

Color Figure 2 for Economics Letters is the line below.

Show[ListLinePlot[Table[{(1+i .1) Khat/(10^12),wA3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,60}],AxesOrigin->{10,0},PlotRange-> {{10,70},{0,210000}},Frame->True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","Wages"},LabelStyle-> Directive[18]],ListLinePlot[Table[{(1+i .1) Khat/(10^12),wB3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,60}],PlotStyle->Red]]

Type A blue, Type B red

B&W Figure 2 for Economics Letters is the line below.

Show[ListLinePlot[Table[{(1+i .1) Khat/(10^12),wA3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,60}],AxesOrigin->{10,0},PlotRange-> {{10,70},{0,220000}},PlotStyle-> Black, Frame->True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","Wages"},LabelStyle-> Directive[18]],ListLinePlot[Table[{(1+i .1) Khat/(10^12),wB3crff[(1+i .1) Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,0,60}],PlotStyle->{Black,Thick}]]

Type B wages thick, Type A wages thin

Plots of Capital’s share

Assume that only Kt0 is changing. Create a function for capital’s share.

Kshare3f[3 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]

LAshare3f[3 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]

LBshare3f[3 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]

tres2f[Khat,labor,AF,a,c,223859.32510687847`,700000]

tres2f[3 Khat,labor,AF,a,c,223859.32510687847`,700000]

Show[Plot[Kshare2f[K ,labor,AF,a,c,223859.32510687847`,700000],{K, Khat,10 Khat},AxesOrigin->{0,0}],ListLinePlot[Table[{Khat i,Kshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1,10,.2}],PlotStyle-> {Red}]]

Blue 2 factor; Red 2 factor

Plots of three factor all shares

Color Figure 4 for Economics Letters is the line below.

Show[ListLinePlot[Table[{Khat i/(10^12),Kshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1,6,.1}],PlotRange->{{10,70.},{0,.5}},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","Share"},LabelStyle-> Directive[18]],ListLinePlot[Table[{Khat i/(10^12),LAshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1,6,.1}],PlotStyle->Red],
ListLinePlot[Table[{Khat i/(10^12),LBshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1,6,.1}],PlotStyle->Green]]

Blue is capital’s share, Red is Type A’s share, Green is Type B’s share.

B&W Figure 4 for Economics Letters is the line below.

Show[ListLinePlot[Table[{Khat i/(10^12),Kshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1,6,.1}],PlotRange->{{10,70.},{0,.5}},PlotStyle->Black,Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","Share"},LabelStyle-> Directive[18]],ListLinePlot[Table[{Khat i/(10^12),LAshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1,6,.1}],PlotStyle->{Black,Dotted}],
ListLinePlot[Table[{Khat i/(10^12),LBshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1,6,.1}],PlotStyle->{Black,Dashed}]]

Solid line Capital’s share, dashed line Type B labor’s share, dotted line Type A labor’s share

Three factor ratio of type A to type B

Color Figure 3 for Economics Letters is the line below.

ListLinePlot[Table[{Khat i/(10^12),(LAshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]/LBshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000])},{i,1,6,.1}],PlotRange->{{10,70.},{0,2.1}},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","(LA share)/(LB share)"},LabelStyle-> Directive[20]]

B&W Figure 3 for Economics Letters is the line below.

ListLinePlot[Table[{Khat i/(10^12),(LAshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]/LBshare3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000])},{i,1,6,.1}],PlotRange->{{10,70.},{0,2.1}},PlotStyle->Black,  Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","(LA share)/(LB share)"},LabelStyle-> Directive[20]]

Considering the dependence of fraction of robots & wages upon CRmx

We have used CRmx+CR0-CRcr as the number of human goods.  The total number of goods  is CRmx-CR0 making the number of robot goods CRcr-CR0. Thus the fraction of robots is (CRcr-CR0)/(CRmx-CR0)

Take the 2 factor case first

Show[ListLinePlot[Table[{Khat i/(10^12),100 fr2Rf[Khat i,labor,AF,a,c,223859.3251,700000]},{i,1.,3.5,.1}],PlotRange->{{10,35.},{0,50}},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","%Robot"},LabelStyle-> Directive[18]],ListLinePlot[Table[{Khat i/(10^12),100 fr2Rf[Khat i,labor,AF,a,c,223859.3251 ,300000]},{i,1.,3.5,.1}],PlotStyle-> Red]]

Plot[{100 fr2Rf[K0 (10^12),labor,AF,a,c,223859.3251,700000],100 fr2Rf[K0  (10^12),labor,AF,a,c,223859.3251 ,240000]},{K0,Khat/(10^12),20 Khat/(10^12)},AxesOrigin-> {0,0},PlotRange->{{10,200.},{0,100}},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","%Robot"},LabelStyle-> Directive[18]]

Plot[{100 fr2Rf[K0 (10^12),labor,AF,a,c,223859.3251,700000],100 fr2Rf[K0  (10^12),labor,AF,a,c,223859.3251 ,240000]},{K0,Khat/(10^12),20 Khat/(10^12)},AxesOrigin-> {0,0},PlotRange->{{10,200.},{0,100}},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","%Robot"},LabelStyle-> Directive[18]]

Plot[{wK2crf[K0 (10^12),labor,AF,a,c,223859.3251,700000],wK2crf[K0  (10^12),labor,AF,a,c,223859.3251 ,240000]},{K0,Khat/(10^12),20 Khat/(10^12)},AxesOrigin-> {0,0},PlotRange->{{10,200.},{0,.1}},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","%Robot"},LabelStyle-> Directive[18]]

Plot[{wK2crf[K0 (10^12),labor,AF,a,c,223859.3251,700000],wK2crf[K0  (10^12),labor,AF,a,c,223859.3251 ,240000]},{K0,Khat/(10^12),20 Khat/(10^12)},AxesOrigin-> {0,0},PlotRange->{{10,200.},{0,.1}},PlotLegends->Placed[{"CRmx=700000","CRmx=240000"},{.3,.25}],Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","wK"},LabelStyle-> Directive[18]]

Plot[{wL2crf[K0 (10^12),labor,AF,a,c,223859.3251,700000],wL2crf[K0  (10^12),labor,AF,a,c,223859.3251 ,240000]},{K0,Khat/(10^12),20 Khat/(10^12)},AxesOrigin-> {0,0},PlotRange->{{10,200.},{0,30000}},PlotLegends->Placed[{"CRmx=700000","CRmx=240000"},Bottom],Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","wL"},LabelStyle-> Directive[18]]

Switch to 3 factor fraction of goods robotized

Show[ListLinePlot[Table[{Khat i/(10^12),100 fr3R[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1.,3.5,.1}],PlotRange->{{10,35.},{0,30}},Frame-> True,PlotLegends->Placed[{"CRmx=700000"},{.7,.25}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","%Robot"},LabelStyle-> Directive[18]],ListLinePlot[Table[{Khat i/(10^12),100 fr3R[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{i,1.,3.5,.1}],PlotStyle-> Red,LabelStyle-> Directive[18],PlotLegends->Placed[{"CRmx=240000"},{.7,.15}]]]

Show[ListLinePlot[Table[{Khat i/(10^12),wK3crff[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1.,7,.2}],AxesOrigin-> {0,0},Frame-> True,PlotLegends->Placed[{"CRmx=700000"},{Left,.3}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","wK"},LabelStyle-> Directive[18]],ListLinePlot[Table[{Khat i/(10^12),1wK3crff[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{i,1.,7,.2}],PlotStyle-> Red,LabelStyle-> Directive[18],PlotLegends->Placed[{"CRmx=240000"},{Left,0.2}]]]

Show[ListLinePlot[Table[{Khat i/(10^12),wA3crff[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1.,7,.2}],AxesOrigin-> {0,0},PlotRange->{{10,70.},{0,300000}},Frame-> True,PlotLegends->Placed[{"CRmx=700000"},{.6,.2}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","wA"},LabelStyle-> Directive[18]],ListLinePlot[Table[{Khat i/(10^12),wA3crff[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{i,1.,7,.2}],PlotStyle-> Red,LabelStyle-> Directive[18],PlotLegends->Placed[{"CRmx=240000"},{.6,.3}]]]

Show[ListLinePlot[Table[{Khat i/(10^12),wB3crff[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{i,1.,7,.2}],AxesOrigin-> {0,0},PlotRange->{{10,70.},{0,20000}},Frame-> True,PlotLegends->Placed[{"CRmx=700000"},{.3,.2}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","wB"},LabelStyle-> Directive[16]],ListLinePlot[Table[{Khat i/(10^12),wB3crff[Khat i,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{i,1.,7,.2}],PlotStyle-> Red,LabelStyle-> Directive[16],PlotLegends->Placed[{"CRmx=240000"},{.7,.2}]]]

Plots of lai, kti, and yi vs CR for different CRmx

2 factor

lai is irrelevant to 2 factor system and kti is constant leaving only yi to be plotted

yi2f[224000.,70 Khat,labor,AF,a,c,223859.3251,700000]

Show[Plot[yi2f[CRi,70 Khat,labor,AF,a,c,223859.3251,700000],{CRi,223870., CRcr2f[70 Khat,labor,a,c,223859.3251,700000.]},AxesOrigin->{223870,700000},Frame-> True,PlotLegends->Placed[{"K=70 Khat"},{.25,.35}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"CRi","yi"},LabelStyle-> Directive[18],PlotLabel->"Robot y2 vs CR to CRcr"],Plot[yi2f[CRi,10 Khat,labor,AF,a,c,223859.3251,700000],{CRi,223870., CRcr2f[10 Khat,labor,a,c,223859.3251,700000.]},PlotStyle-> Red,LabelStyle-> Directive[18],PlotLegends->Placed[{"K=10 Khat"},{.7,.35}]]]

3 factor

Show[ListLinePlot[Table[{CRi,lai3f[CRi,70 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{CRi,165821.72231850054`,300000,1000}],PlotRange-> {{161000,700000},{0,80}},Frame-> True,PlotLegends->Placed[{"CRmx=300000"},{.3,.1}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"CRi","lai"},LabelStyle-> Directive[12],PlotLabel->"Robot lai vs CR to CRcr"],ListLinePlot[Table[{CRi,lai3f[CRi,70 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{CRi,165821.72231850054`,700000,1000}],PlotStyle->{Red},PlotLegends->Placed[{"CRmx=700000"},{.70,.1}]]]

Show[ListLinePlot[Table[{CRi,kti3f[CRi,70 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{CRi,165821.72231850054`,300000,1000}], PlotRange-> {{161000,700000},{0,(10^10)}},Frame-> True,PlotLegends->Placed[{"CRmx=300000"},{.25,.35}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","kti"},LabelStyle-> Directive[12],LabelStyle-> Directive[12],PlotLabel->"Robot kt3i vs CR to CRcr"],ListLinePlot[Table[{CRi,kti3f[CRi,70 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{CRi,165821.72231850054`,700000,1000}],PlotStyle->{Red},PlotLegends->Placed[{"CRmx=700000"},{.7,.35}]]]

tyi300000=Table[{CRi,yi3f[CRi,70 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,300000]},{CRi,165821.72231850054`,300000,1000}];

tyi700000=Table[{CRi,yi3f[CRi,70 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,700000]},{CRi,165821.72231850054`,700000,1000}];

Show[ListLinePlot[tyi300000, PlotRange-> {{161000,700000},{0,8.5 (10^7)}},Frame-> True,PlotLegends->Placed[{"CRmx=300000"},{.3,.35}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"CR","yi"},LabelStyle-> Directive[12],PlotLabel->"Robot ty3i vs CR to CRcr"],ListLinePlot[tyi700000,PlotStyle->{Red},PlotLegends->Placed[{"CRmx=700000"},{.7,.35}]]]

Plots of CRcr vs CRmx

2 factor

Plot[{CRcr2f[70 Khat,labor,a,c,223859.3251299757`,CRmx]/CRmx,CRcr2f[10 Khat,labor,a,c,223859.3251299757`,CRmx]/CRmx},{CRmx,223859.3251299757`,700000},AxesOrigin-> {223859.3251299757`,0},PlotRange->{{223859.3251299757,700000},{0,1}},Frame-> True,PlotLegends->Placed[{"K=70 Khat","K=10 Khat",Red},{.80,.15}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"CRmx","CRcr/CRmx"},PlotLabel->"2 factor CRcr vs CRmx",LabelStyle-> Directive[Black,16]]

3 factor

tCRcr310Khat=Table[{CRmx,CRcr3f[CRmx,10 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`]/CRmx},{CRmx,165825`,700000,1000}];

tCRcr370Khat=Table[{CRmx,CRcr3f[CRmx,70 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`]/CRmx},{CRmx,165825,700000,1000}];

Show[ListLinePlot[tCRcr370Khat,AxesOrigin-> {165821.72231850054`,0},PlotRange->{{165821.72231850054`,700000},{0,1}},Frame-> True,PlotLegends->Placed[{"K=70 Khat"},{.3,.35}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"CRmx","CRcr/CRmx"},LabelStyle-> Directive[18],PlotLabel->"3 factor CRcr vs CRmx"],ListLinePlot[tCRcr310Khat,PlotStyle->{Red},PlotLegends->Placed[{"K=10 Khat"},{.7,.35}]]]

2 factor and 3 factor dependences of CRcr upon CRmx are remarkably similar.

Plots of total value versus CRmx

2 factors

Plot[{value2f[70 Khat,labor,AF,a,c,223859.3251299757`,CRmx]/(10^12),value2f[10 Khat,labor,AF,a,c,223859.3251299757`,CRmx]/(10^12)},{CRmx,225000,700000},AxesOrigin-> {200000,0},PlotRange->{{200000,700000},{0,70}},Frame-> True,PlotLegends->Placed[{"K=70 Khat","K=10 Khat",Red},{.50,.35}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"CRmx","value (T$)"},PlotLabel->"2 factor value vs CRmx",LabelStyle-> Directive[18]]

3 factors

tvalue310Khat=Table[{CRmx,value3f[10 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,CRmx]/(10^12)},{CRmx,165825`,700000,1000}];

tvalue370Khat=Table[{CRmx,value3f[70 Khat,LAI,LBI,AF3,a3,b3,c3,165821.72231850054`,CRmx]/(10^12)},{CRmx,165825,700000,1000}];

Show[ListLinePlot[tvalue370Khat,AxesOrigin-> {165821.72231850054`,0},PlotRange->{{165821.72231850054`,700000},{0,11.5 }},Frame-> True,PlotLegends->Placed[{"K=70 Khat"},{.8,.1}],FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"CRmx","value ($T)"},LabelStyle-> 12,PlotLabel->"3 factor value vs CRmx"],ListLinePlot[tvalue310Khat,PlotStyle->{Red,Thick},PlotLegends->Placed[{"K=10 Khat"},{.5,.1}]],Plot[2.78,{CRmx,165825`,700000},PlotStyle->{Black,Dashed,Thick},PlotLegends->Placed[{"K= Khat"},{.2,.1}]]]

Welfare total & welfare LB

Plot welfare total vs Kv

2 factor

value2f[Khat,labor,AF,a,c,223859.3251,700000]

(476140.6749` YH2f[KH2f[CRcr2f[1.1152`*^13,9.9634`*^7,0.9999821319548539`,0.00001786804514619618`,223859.3251`,700000],9.9634`*^7,0.9999821319548539`,0.00001786804514619618`],9.9634`*^7,0.7499865989661404`,0.9999821319548539`,0.00001786804514619618`])/(700000-CRcr2f[1.1152`*^13,9.9634`*^7,0.9999821319548539`,0.00001786804514619618`,223859.3251`,700000])

Plot[value2f[Kv,labor,AF,a,c,223859.3251,700000],{Kv,Khat, 5 Khat}]

ListLinePlot[Table[{Khat i/(10^12),welfareB3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165820.63591815968`,700000]},{i,1.,5,.1}]]

Show[ListLinePlot[Table[{Khat i/(10^12),welfareB2f[Khat i,labor,AF,a,c,223859.3251,700000]},{i,1.,5,.1}],PlotRange->{{10,35.},{0,50}},Frame-> True,FrameStyle-> Directive[Thickness[.0032],12], FrameLabel->{"Capital ($T)","%Robot"},LabelStyle-> Directive[18]],ListLinePlot[Table[{Khat i/(10^12),100 fr2Rf[Khat i,labor,AF,a,c,223859.3251 ,300000]},{i,1.,3.5,.1}],PlotStyle-> Red]]

ListLinePlot[Table[{Khat i/(10^12),welfareB3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165820.63591815968`,700000]},{i,1.,20,.1}]]

ListLinePlot[Table[{Khat i/(10^12),welfaretot3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165820.63591815968`,700000]},{i,1.,20,.1}]]

ListLinePlot[Table[{Khat i/(10^12),welfareA3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165820.63591815968`,700000]},{i,1.,20,.1}]]

ListLinePlot[Table[{Khat i/(10^12),welfareK3f[Khat i,LAI,LBI,AF3,a3,b3,c3,165820.63591815968`,700000]},{i,1.,20,.1}]]