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.