UNLEASHING LEVIATHAN: PUBLIC GOODS UNDER INVOLUNTARY
TAXATION
Johnnie B. Linn IIIConcord UniversityAthens, WV 24712
This Model
• Many competing firms, each in its own arena, facing “outliers” who use force only.
• Ratio Rule• Government enters arenas.• Government is viable if individuals are better
off with government than in anarchistic arenas.
Outliers
• Outliers are force-using individuals who do not act collectively on the margin (they are like an open-access fishery).
• In short run, number of outliers is an environmental variable, like a price.
• In long run, per-capita winnings of outliers is comparable to the wage they would have earned if employed as workers or guards.
Government
• Tax collectors receive residual they extract from firms beyond amount they are required to forward to government.
• Tax collectors act on the margin at the direction of government.
• Government force is a public good.• Individuals have recourse to government force
in private disputes; and government against firms, but not firms against government.
The Force Ratio Rule
(1)
Input Elasticities
(4)
(5)
Government Force Input Elasticity
(6)
Tax on Outlier Income
• Tax is defined on range [0, ]
(7)
Competitive Equilibrium
(13)
Range of Share-of-Winnings Function
0 1
I II III
0 1
1
Range of the Competitive Equilibrium
0
1
1
Q
Outliers’ Share of Income
(14)
Tax on Firm Income
(7’)
Competitive Equilibrium
(13’)
(14’)
Firm’s First-Order Conditions
(8’)
(9’’)
Estimators of Firm Parameters
(17)
(18)
Government Budget Condition
(15)
Use of the Surplus
Public GoodTax Collectors
TB
TC
Surplus
Gross Winnings
Non-Public-Goods Outlays
Government Winnings under Exponential Force Function
(19)
Estimator of Government Parameters
(16)
Government Superior to Anarchy
(21)
Results
CATEGORY SOURCE 2002 2008 DESIGNATORAfter-Taxes Tax Rate OECD 0.36 0.37 t
Tax Collector IncomeOES Sector 99 (13-2081)
$3.2 billion $3.5 billion wT
Tax CollectorsOES Sector 99 (13-2081)
69,320 66,030 T
Law Enforcement IncomeOES Sector 99 (33-0000)
$73.4 billion $91.1 billion
Non-Public-Good Gov’t Worker Income
OES Sector 99 (00-0000 less 33-0000)
$340.70 billion $378.3 billion wT0
Non-Public-Good Gov’t Capital Outlay
U.S. Census Bureau
$96.1 billion* $105.9 billion* wK0
Outlier Income FBI $17.1 billion $17.8 billion wUGuard Income OES 33-9032 $20.6 billion $27.0 billion wGGuards OES 33-9032 977,650 1,046,070 GGov’t Surplus Multiplier 3.31 3.99 bTax Collector Advantage 6.43 8.83 c
Worker IncomeOES 00-0000 (less sector 99) less OES 33-9032
$4045.2 billion $5,204.4 billion wL
Statistic for 196.37 192.76
Statistic for 1.20 1.52
Threshold before-tax rate for government viability
0.108 0.093
*Inferred from ratio of capital outlays to employee compensation in 1992.
