Robots Are Us - Some Economics of Human Replacement (Tables)

Table 1 Parameters for Immiserating Growth Model Parameter Role Value εs Elasticity in Service Sector ∞ εy Elasticity in Good Sector 1 γ Service High-Tech Input Share Param. 0.5 α Good Capital Input Share Param. 0.5 δ Code Retention Rate 0 shocked to 0.7 φ Saving Rate 0.2 H High-Tech Worker Quantity 1 G Low-Tech Worker Quantity 1 κ Service Consumption Share 0.5 z Code Writing Productivity 1 Dy TFP in Goods 1 Ds TFP in Services 1 Table 1: This table gives parameter values for the first illustration of the effects of a one-time, permanent increase in the depreciation rate, δ, from zero to .7. We take the intermediate value of .5 for κ, α, and γ. The productivity terms z, DY , and DS , are set to one. σ takes its CD value of zero, ρ, the CES substitution parameter, takes on the perfect-substitute value of 1. φ is the saving rate. In this and all subsequent simulations invoking an elasticity of 1 (except for the endogenous technology extension) the true elasticity is actually 1.0001 Figure 1 Immiserating Growth Good#Output# 160# 130# Service#Output# NaQonal#Income# 140# 120# 110# 100# 100# 80# 90# 60# 80# 20# 60# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# p# r# q# 120# Indexed#Value# Indexed#Value# # 110# Wage#Low(Tech#Workers# 90# 80# 70# 60# 50# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 20# Labor#Share#of#total#Income# 15# 10# Percentage# 75# Percentage# Total#Wage#High(Tech#Workers# 100# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 80# K# 40# 70# 220# 200# 180# 160# 140# 120# 100# 80# 60# 40# A# 120# Indexed#Value# # Indexed#Value# 140# 70# 65# 60# 5# CompensaQng#DifferenQal#High(Tech# Workers# CompensaQng#DifferenQal#Low(Tech# Workers# 0# (5# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# (10# 55# (15# 50# (20# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# Period# Figure 1: Transition paths based on table 1. “Compensating Differential” references the percentage change in initial steady-state consumption that would be needed for the utility levels of workers to equal their respective transition utility levels. Service output is raw indexed output, not market value. Period 1 non-indexed prices are r = 1.737, q = .349, and p = .043. 24 Figure 2 Felicitous Growth (higher saving rate, φ = .95) Good#Output# 220# Service#Output# 200# NaQonal#Income# 180# Indexed#Value# # Indexed#Value# # 160# 150# 140# 130# 120# 110# 100# 90# 80# 70# 60# 140# 120# 100# 60# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# p# r# q# 170# 180# 150# Wage#Low(Tech#Workers# 130# 140# 110# 120# 90# 100# 70# 80# 50# 60# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# Labor#Share#of#total#Income# Percentage# 75# Percentage# Total#Wage#High(Tech#Workers# Indexed#Value# # Indexed#Value# # 160# 80# K# 80# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 200# A# 160# 70# 65# 60# 55# 50# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 40# 35# 30# 25# 20# 15# 10# 5# 0# (5# (10# (15# CompensaQng#DifferenQal#High( Tech#Workers# CompensaQng#DifferenQal#Low( Tech#Workers# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# Figure 2: Transition paths based on table 1, with the exception of a higher saving rate (φ = .95). “Compensating Differential” references the percentage change in initial steady-state consumption that would be needed for the utility levels of workers to equal their respective transition utility levels. Service output is raw indexed output, not market value. Period 1 non-indexed prices are r = .454, q = 2.204, and p = .631. 25 Figure 3 The First Will Be Last 150# 140# Good#Output# 240# Service#Output# 220# NaQonal#Income# Indexed#Value# Indexed#Value# 130# 120# 110# 100# 200# 160# 140# 120# 100# 90# 80# K# 60# 80# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 200# A# 180# 150# Total#Wage#High(Tech#Workers# 180# 140# Wage#Low(Tech#Workers# 160# 130# r# q# Indexed#Value# # Indexed#Value# # p# 140# 120# 120# 110# 100# 100# 80# 90# 60# 80# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 80# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 50# Labor#Share#of#total#Income# 40# Percentage# Percentage# 75# 70# 65# 60# 30# CompensaQng#DifferenQal#High(Tech# Workers# 20# CompensaQng#DifferenQal#Low(Tech# Workers# 10# 55# 0# 50# (10# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# (# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# Figure 3: Transition paths based on table 2. “Compensating Differential” references the percentage change in initial steady-state consumption that would be needed for the utility levels of workers to equal their respective transition utility levels. Service output is raw indexed output, not market value. Period 1 non-indexed prices are r = .529, q = 1.317, and p = .398. 26 Figure 4 Better Tasting Goods 140" 120" Good"Output" 400" Service"Output" 350" NaSonal"Income" Indexed"Value" " Indexed"Value" " 300" 100" 200" 80" 150" 60" 100" 40" 50" 20" r" q" 120" Total"Wage"High(Tech"Workers" 100" Wage"Low(Tech"Workers" Indexed"Value" " Indexed"Value" " p" (" 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10"11"12"13"14"15"16"17" Periods" 80" 60" 40" 20" 0" (" 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10"11"12"13"14"15"16"17" Period" 80" Labor"Share"of"total"Income" 60" %"of"High(Tech"Workers"Coding" Percentage" Percentage" (" 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10"11"12"13"14"15"16"17" Period" 80" 75" 70" 65" 60" 55" 50" 45" 40" 35" 30" K" 0" (" 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10"11"12"13"14"15"16"17" Periods" 500" 450" 400" 350" 300" 250" 200" 150" 100" 50" 0" A" 250" 40" 20" 0" (20" (40" (" 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10"11"12"13"14"15"16"17" Period" CompensaSng"DifferenSal"High(Tech" Workers" CompensaSng"DifferenSal"Low(Tech" Workers" (" 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10"11"12"13"14"15"16"17" Period" Figure 4: Transtion paths based on table 2, except in addition to the δ shock, κ is simultaneously shocked from .5 to .25. “Compensating Differential” references the percentage change in initial steady-state consumption that would be needed for the utility levels of workers to equal their respective transition utility levels. Service output is raw indexed output, not market value. Period 1 non-indexed prices in terms of the good are r = .587, q = .784, and p = .200. 27 Table 2 Parameters for The First Will Be Last Model Parameter Role Value εs Elasticity in Service Sector 1 εy Elasticity in Good Sector 1 γ Service High-Tech Input Share Param. 0.5 α Good Capital Input Share Param. 0.5 δ Code-Retention Rate 0 shocked to 0.7 φ Saving Rate 0.7 H High-Tech Worker Quantity 2 G Low-Tech Worker Quantity 1 κ Service Consumption Share 0.5 z Code Writing Productivity 1 Dy TFP in Goods 1 Ds TFP in Services 1 28 Table 3: Sensitivity Analysis Baseline Period Initial.Steady.State 1 2 3 4 10 Steady.State εs εy 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 δ φ Labor.High; Tech. Labor.Low; Tech κ γ z 0.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Nat.Income Good.Output 100 121 118 114 112 107 107 100.0 117.5 116.0 113.2 111.0 107.0 106.7 Service.Output K A p q r 100.0 106.4 109.1 109.6 109.7 109.6 109.5 100.0 100.0 96.6 88.3 82.1 71.9 71.1 100.0 112.6 143.0 152.4 156.0 159.8 160.0 ; 100.0 89.6 83.6 80.0 74.2 73.8 100.0 116.3 116.2 110.6 106.0 98.0 97.4 100.0 106.1 121.7 131.4 137.8 149.1 150.0 Wage.High; Wage.Low; Tech.Workers Tech.Workers Labor.Share 50.0 54.4 61.9 60.3 58.1 53.7 53.4 100.0 124.4 109.2 101.3 96.7 89.5 88.9 75.0 66.8 65.6 65.6 64.8 62.7 62.5 %.High;Tech. Workers.Coding 50.0 56.3 43.4 40.5 39.9 40.0 40.0 Compensating. Differential.High; Tech.Workers 0.0 20.3 8.9 4.5 2.3 ;1.0 ;1.2 Compensating. Differential.Low; Tech.Workers ;49.9 ;47.4 ;38.3 ;37.7 ;38.5 ;40.5 ;40.7 Compensating. Differential.High; Tech.Workers 0.0 20.3 8.9 4.5 2.3 ;1.0 ;1.2 Compensating. Differential.Low; Tech.Workers ;49.8 ;47.3 ;38.2 ;37.6 ;38.4 ;40.4 ;40.6 Compensating. Differential.High; Tech.Workers 0.0 22.3 ;4.5 ;18.2 ;25.7 ;34.9 ;35.2 Compensating. Differential.Low; Tech.Workers ;49.9 ;68.9 ;68.2 ;71.0 ;73.2 ;76.5 ;76.6 Compensating. Differential.High; Tech.Workers 0.0 6.8 ;9.3 ;15.9 ;19.0 ;22.3 ;22.4 Compensating. Differential.Low; Tech.Workers ;50.0 ;47.9 ;44.6 ;46.2 ;47.6 ;49.6 ;49.6 Compensating. Differential.High; Tech.Workers 0.0 25.0 16.4 13.7 12.4 11.7 10.5 10.3 Compensating. Differential.Low; Tech.Workers ;49.9 ;50.9 ;38.0 ;35.7 ;35.5 ;35.8 ;36.7 ;36.9 Service/Taste/Shock//κ Jumps/from/0.5/to/0.75 Period Initial.Steady.State 1 2 3 4 10 Steady.State εs εy 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 δ φ Labor.High; Tech. Labor.Low; Tech κ γ z 0.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5 0.75 0.75 0.75 0.75 0.75 0.75 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Nat.Income Good.Output 100 203 231 251 266 305 313 100.0 117.2 129.2 136.7 142.0 154.1 156.5 Service.Output K A p q r 100.0 120.6 123.6 124.4 124.8 125.6 125.8 100.0 100.0 140.0 173.0 200.0 275.8 293.4 100.0 87.1 98.2 96.4 93.4 85.2 83.5 ; 100.0 116.7 130.9 142.3 172.2 178.7 100.0 178.9 230.1 264.4 290.4 358.3 373.3 100.0 93.4 83.7 74.7 68.4 55.6 53.4 Wage.High; Wage.Low; Tech.Workers Tech.Workers Labor.Share 50.0 95.0 138.8 163.3 180.6 225.0 234.8 100.0 168.4 190.8 214.0 233.3 285.3 296.7 75.0 58.4 67.2 72.0 74.6 80.2 81.3 %.High;Tech. Workers.Coding 50.0 43.6 27.3 23.7 22.6 21.2 20.9 Good/Taste/Shock//κ/Jumps/from/0.5/to/0.25 Period 29 Initial.Steady.State 1 2 3 4 10 Steady.State εs εy 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 δ φ Labor.High; Tech. Labor.Low; Tech κ γ z 0.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5 0.25 0.25 0.25 0.25 0.25 0.25 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Nat.Income Good.Output 100 78 67 60 56 51 51 100.0 117.2 102.4 91.9 85.4 76.7 76.3 Service.Output K A p q r 100.0 81.6 84.1 84.8 85.0 84.9 84.9 100.0 100.0 66.0 44.9 34.4 23.1 22.7 100.0 149.3 208.1 233.3 244.7 255.6 255.9 ; 100.0 67.6 52.4 44.8 36.1 35.7 100.0 69.2 54.4 43.7 37.7 30.2 30.0 100.0 122.2 177.6 227.9 266.5 332.7 335.6 Service.Output K A p q r 100.0 110.5 113.1 113.8 113.9 114.0 114.0 100.0 100.0 78.8 63.7 55.8 47.8 46.9 100.0 102.3 129.1 136.6 138.9 140.3 140.4 ; 100.0 78.5 68.6 63.6 57.9 57.9 100.0 105.6 93.3 83.4 77.9 71.6 71.5 100.0 101.2 128.1 146.6 158.0 172.3 172.6 Service.Output K A p q r 100.0 103.2 106.3 107.0 107.2 107.1 107.0 106.9 100.0 100.0 104.4 102.0 99.2 97.1 92.7 91.8 100.0 121.5 154.4 164.1 167.5 168.9 170.9 171.3 ; 100.0 95.0 92.1 90.3 89.1 86.8 86.3 100.0 117.7 126.1 125.2 123.2 121.5 118.0 117.2 100.0 110.2 121.6 126.8 129.9 131.9 135.8 136.5 Wage.High; Wage.Low; Tech.Workers Tech.Workers Labor.Share 50.0 24.6 22.2 18.4 16.0 12.8 12.7 100.0 97.1 66.7 51.9 44.4 35.6 35.3 75.0 70.5 56.4 52.3 49.0 44.0 43.8 %.High;Tech. Workers.Coding 50.0 74.7 66.8 64.6 64.1 64.0 64.0 Low/Saving/Rate φ/=/0.1 Period Initial.Steady.State 1 2 3 4 10 Steady.State εs εy 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 δ φ Labor.High; Tech. Labor.Low; Tech κ γ z 0.0 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Nat.Income Good.Output 100 100 92 88 85 82 81 100.0 100.8 93.2 88.1 85.0 81.6 81.4 Wage.High; Wage.Low; Tech.Workers Tech.Workers Labor.Share 49.9 52.2 51.5 47.2 44.2 40.8 40.7 100.0 106.8 84.4 73.8 68.5 62.8 62.6 75.1 77.5 70.0 67.4 65.3 62.6 62.5 %.High;Tech. Workers.Coding 50.1 51.2 39.0 36.1 35.4 35.1 35.1 High/Saving/Rate φ/=/0.9 Period Initial.Steady.State 1 2 3 4 5 10 Steady.State εs εy 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 δ φ Labor.High; Tech. Labor.Low; Tech κ γ z 0.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Nat.Income Good.Output 100 131 132 130 129 128 126 125 100.0 126.9 129.4 128.9 128.0 127.3 125.7 125.4 Wage.High; Wage.Low; Tech.Workers Tech.Workers Labor.Share 50.0 52.2 65.1 66.6 66.0 65.1 63.1 62.7 100.0 132.9 122.3 117.7 115.1 113.4 110.3 109.6 75.0 60.9 62.3 63.7 63.6 63.4 62.7 62.5 %.High;Tech. Workers.Coding 50.0 60.8 46.8 43.5 42.7 42.6 42.8 42.8 In all examples, the δ is shocked from 0 in the initial steady state to .5. Simulations subsequent to the baseline have one (highlighted) parameter changed. Endogenous variables are indexed. Service output is in market value terms. Table 3 Continued 30 In all examples δ is shocked from 0 in the initial steady state to .5. Simulations subsequent to the baseline have one (highlighted) parameter changed. Endogenous variables are indexed. Service output is in market value terms. Figure 5 Comparing Four Case Studies National(Income 140( The(First(Will(Be(Last( Felicitous(Growth( ImmiseraMng(Growth( BeOer(TasMng(Goods( 120( 100( Indexed(Value( 160( Indexed(Value( Capital The(First(Will(Be(Last( Felicitous(Growth( ImmiseraMng(Growth( BeOer(TasMng(Goods( 180( 120( 100( 80( 80( 60( 40( 20( 60( 40( ?( 0( 1( 2( 3( 4( 5( Period( 6( 7( 8( 0( 9( 10( ?( 0( 1( 2( Code Indexed(Value( Indexed(Value( 250( 200( The(First(Will(Be(Last( Felicitous(Growth( ImmiseraMng(Growth( BeOer(TasMng(Goods( 100( 50( 0( ?( 0( 1( 2( 3( 4( 5( Period( 6( 7( 8( 100( 80( 0( ?( Percentage( The(First(Will(Be(Last( Felicitous(Growth( ImmiseraMng(Growth( BeOer(TasMng(Goods( 230( 180( 130( 80( ?( 0( 1( 2( 3( 4( 5( Period( 9( 10( 40( 9( 10( 430( 280( 8( 20( 480( 330( 7( 60( 0( 1( 2( Intrest(Rate 380( 6( The(First(Will(Be(Last( Felicitous(Growth( ImmiseraMng(Growth( BeOer(TasMng(Goods( 120( 300( 150( 4( 5( Period( Price(of(Code 140( 350( Indexed(Value( 3( 6( 7( 8( 9( 10( 3( 4( 5( Period( Labor(Share 6( 7( 8( 9( 10( The(First(Will(Be(Last( Felicitous(Growth( ImmiseraMng(Growth( BeOer(TasMng(Goods( 80( 75( 70( 65( 60( 55( 50( 45( 40( 35( 30( ?( 0( 1( 2( 3( 4( 5( Period( 6( 7( 8( 9( 10( Figure 5: Transition paths from the first 4 cases presented (immiserating growth, etc.) superimposed. 31 Figure 6 Comparing National Incomes In Sensitivity Analysis 500# 450# Indexed#Value# 400# 350# 300# Baseline# kappa#to#0.75# kappa#to#0.25# phi#0.1# phi#0.9# z#to#1.5# Subs#Service# Com#Service# Subs#Good# Com#Good# 250# 200# 150# 100# 50# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17#18# Period# Figure 6: Illustration of the 10 sensitivity analysis cases superimposed. ‘Subs’ refer to cases in which the production technology of a sector is more substitutable. ‘Com’ refer to cases in which the production technology is more complimentary. Table 4 Parameters for Institutional Simulations Model Parameter Role Value εs Elasticity in Service Sector 1 εy Elasticity in Good Sector 1 γ Service High-Tech Input Share Param. 0.5 α Good Capital Input Share Param. 0.5 δ Code Retention Rate 0 shocked to 0.25 φ Saving Rate 0.5 H High-Tech Worker Quantity 1 G Low-Tech Worker Quantity 1 κ Service Consumption Share 0.5 z Code Writing Productivity 1 Dy TFP in Good Sector 1 Ds TFP in Service Sector 1 C Firm Setup cost .055 A Exogenous Free Code .25 Table 4: This table gives parameter values for illustrations of the effects of a onetime, permanent increase in the depreciation rate, δ, from zero to .25 given different institutional settings. 32 Figure 7 Long-Run National Income Impact of Alternative Saving and Code-Retention and Productivity Shocks Figure 7: Long-run national income (NI) indexed by pre-shock steady state NI. Parameters not on axes are given in table 1. X’s denote parameter combinations with transition paths discussed in the text. 33 Figure 8 Long-Run National Income Impact of Alternative Saving, Elasticity of Substitution, and Taste Shocks Figure 8: Long-run national income (NI) indexed by pre-shock steady state NI. Parameters not on axes are given in table 2. X’s denote parameter combinations with transition paths discussed in the text. 34 116# 114# 112# 110# 108# 106# 104# 102# 100# 98# 96# 140# 135# 130# 125# 120# 115# 110# 105# 100# 95# 90# Indexed#Value# # Indexed#Value# Figure 9 Rival, Excludable (Private) Code Good#Output#(Net)# Service#Units#of#Output# NaWonal#Income# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 115# 113# 111# 109# 107# 105# 103# 101# 99# 97# 95# q# Indexed#Value# # Indexed#Value# # 110# 105# 100# 95# 90# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# Wage#Low)Tech#Workers# 8# Percentage# Percentage# Total#Wage#High)Tech#Workers# 10# 55# 45# Publicly#Available#A# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 60# 50# K# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 115# r# A# Labor#Share#of#total#Income# %#of#High)Tech#Workers# Coding# 6# 4# 2# 0# 40# CompensaWng#DifferenWal#High)Tech# Workers# CompensaWng#DifferenWal#Low)Tech# Workers# )2# 35# )4# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 105# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 0.25# Indexed#Value# 100# 95# 90# Number#of#Firms#Producing#Goods# 0.20# 0.15# 85# 80# K/A#RaWo#Within#a#Firm# 0.10# 75# 70# 0.05# 65# 60# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Periods# 0.00# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Periods# Figure 9: Transition paths based on Table 4. “Compensating Differential” references the percentage change in initial steady-state consumption that would be needed for the utility levels of workers to equal their respective transition utility levels. Service output is raw indexed output, not market value. Period 1 non-indexed prices in terms of the good are r = 1.136, q = .382, and p = .117. 35 Figure 10 Non-Rival, Non-Excludable (Public) Code Good#Output#(Net)# 115# 130# NaWonal#Income# Indexed#Value# # Indexed#Value# 140# Service#Units#of#Output# 110# 120# 105# 110# 100# 100# 95# 90# 80# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# r# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 120# q# 130# Indexed#Value# # Indexed#Value# # 100# 120# 80# 110# 60# 100# 40# 90# 20# 80# Labor#Share#of#total#Income# %#of#High)Tech#Workers#Coding# 40# 30# 20# 10# 0# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# Indexed#Value# 25# 20# 15# 10# 5# 0# )5# )10# )15# )20# )25# CompensaWng#DifferenWal#High)Tech# Workers# CompensaWng#DifferenWal#Low)Tech# Workers# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 220# 200# Wage#Low)Tech#Workers# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# Percentage# Percentage# 50# Total#Wage#High)Tech#Workers# 0# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 60# Publicly#Available#A# 90# 85# 140# K# 0.20# 0.19# 0.18# 0.17# 0.16# 0.15# 0.14# 0.13# 0.12# 0.11# 0.10# Number#of#Firms#Producing#Goods# 180# 160# 140# 120# 100# 80# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Periods# K/A#RaWo#Within#a#Firm# )# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Periods# Figure 10: Transition paths based on Table 4. All parameters are identical to Figure 10 except equations are modified as detailed in the text. “Compensating Differential” references the percentage change in initial steady-state consumption that would be needed for the utility levels of workers to equal their respective transition utility levels. Service output is raw indexed output, not market value. Period 1 non-indexed prices in terms of the good are r = 1.136, q = .353, and p = N A. 36 Figure 11 Non-Rival, Excludable (Private) Code 170# 126# 160# 150# Indexed#Value# # Indexed#Value# 121# 116# Good#Output#(Net)# 111# 110# 100# 96# 90# +# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# +# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 130# 130# 125# 125# r# q# 120# Indexed#Value# # Indexed#Value# # 115# 115# 110# 105# 100# 95# 110# Total#Wage#High+Tech#Workers# 105# Wage#Low+Tech#Workers# 100# 90# 95# +# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# +# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 14# 65# 12# 50# 45# 10# Percentage# Percentage# 60# 55# Publicly#Available#A# 120# NaWonal#Income# 101# 120# K# 130# Service#Units#of#Output# 106# A# 140# Labor#Share#of#total#Income# %#of#High+Tech#Workers# Coding# 8# 6# 4# 2# 0# 40# CompensaWng#DifferenWal#High+Tech# Workers# CompensaWng#DifferenWal#Low+Tech# Workers# +2# 35# +4# +# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# +# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Period# 105# 0.25# Indexed#Value# 100# 95# 90# 0.20# Number#of#Firms#Producing#Goods# 0.15# 85# 80# K/A#RaWo#Within#a#Firm# 0.10# 75# 70# 0.05# 65# 60# 0.00# +# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Periods# +# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10#11#12#13#14#15#16#17# Periods# Figure 11: Transition paths based on Table 4. All parameters are identical to Figure 10 except equations are modified as detailed in the text. “Compensating Differential” references the percentage change in initial steady-state consumption that would be needed for the utility levels of workers to equal their respective transition utility levels. Service output is raw indexed output, not market value. Period 1 non-indexed prices in terms of the good are r = 1.136, q = .393, and p = .164. 37 Table 5 Parameters for the Endogenous Technology Extension Model Parameter Role Value γ Service High-Tech Input Share Param. 0.5 α Good Capital Input Share Param. [0.3, 0.5] δ Code-Retention Rate 0 shocked to 0.6 φ Saving Rate 0.9 H High-Tech Worker Quantity 1 G Low-Tech Worker Quantity 10 κ Service Consumption Share 0.5 z Code Writing Productivity 1 Dy TFP in Goods 1 Ds TFP in Services 1 Figure 12 Endogenous α 160$ Good$Output$ Service$Output$ 1.6$ NaSonal$Income$ 150$ Indexed$Value$ $ 140$ Units$ 1.0$ 120$ 0.8$ 110$ 0.6$ 100$ 90$ 0.4$ )$ 0$ 1$ 2$ 3$ 4$ 5$ 6$ 7$ 8$ 9$ 10$11$12$13$14$15$16$17$ Period$ P$ r$ )$ 0$ 1$ 2$ 3$ 4$ 5$ 6$ 7$ 8$ 9$ 10$11$12$13$14$15$16$17$ Period$ 120$ q$ Indexed$Value$ Indexed$Value$ 100$ 80$ 60$ 40$ 0$ Labor$Share$of$total$Income$ %$of$High)Tech$Workers$Coding$(right$axis)$ Percentage$ 85$ 80$ 75$ 70$ 65$ 60$ )$ 0$ 1$ 2$ 3$ 4$ 5$ 6$ 7$ 8$ 9$ 10$11$12$13$14$15$16$17$ Period$ CompensaSng$DifferenSal$High)Tech$Workers$ 70$ 65$ 60$ 55$ 50$ 45$ 40$ 35$ 30$ 25$ 20$ )$ 0$ 1$ 2$ 3$ 4$ 5$ 6$ 7$ 8$ 9$ 10$11$12$13$14$15$16$17$ Period$ CompensaSng$DifferenSal$Low)Tech$Workers$ Percentage$ 90$ Total$Wage$High)Tech$Workers$ Wage$Low)Tech$Workers$ 20$ )$ 0$ 1$ 2$ 3$ 4$ 5$ 6$ 7$ 8$ 9$ 10$11$12$13$14$15$16$17$ Period$ 95$ K$ 1.2$ 130$ 150$ 140$ 130$ 120$ 110$ 100$ 90$ 80$ 70$ 60$ 50$ A$ 1.4$ 70$ 60$ 50$ 40$ 30$ 20$ 10$ 0$ )10$ )20$ )30$ )$ 0$ 1$ 2$ 3$ 4$ 5$ 6$ 7$ 8$ 9$ 10$11$12$13$14$15$16$17$ Period$ Figure 12: Transition paths based on table 3.“Compensating Differential” references the percentage change in initial steady-state consumption that would be needed for the utility levels of workers to equal their respective transition utility levels. Service output is raw indexed output, not market value. Wage of low-tech workers is indexed to the initial steady state wage of high-tech workers. 38