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Developing A Supply-Side/
Public-Choice Synthesis
Supply-Side Fundamentals for Tax Reform
By
Lawrence A. Hunter
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CHART 1
Original Laffer Curve
0%
100%
0%
Revenues
TaxRate
A
B
C
D
E
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CHART 2
0%
0% 100%
Tax ate
Output
B
Ym
A
Y+
rmr
+r-
C
Y-
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CHART 3
Rahn Curve
0
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1
0% 100%
Tax Rate
IndexofOutput
Output
T1
YMAX
Output is maximized at Ymax with a tax rate of T1
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EXAMPLE 1Output Maximized @ 13% Tax Rate Tax
Revenues Maximized @ 26% Tax Rate
0
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1
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Tax Rate
IndexofOutput
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90%
100%
RevenueAsPercentOutput
Output Revenues
Maximizing Revenues Reduces Economic Output by 27%
CHART 4
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EXAMPLE 2Output Maximized @ 18% Tax Rate
Revenue Maximized @ 39 % Tax Rate
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1.0
1.1
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Tax Rate
IndexofPotential
Output
0%
10%
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90%
100%
110%
RevenueAsPercen
tOutput
Output Revenues
Output-Maximizing Tax Rate Equals 18%
Revenue-Maximizing Tax Rate Equals 39%
Pure Rent Seeking
between Tax Rates of
18% and 39%
Up to 25% Lost Economic Output Due to Excessive Tax Rates
CHART 5
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CHART 6
Demand For Taxable Output
0%
100%
Taxable Output
TaxRate
Tax RevenueExcess
Burden
T1
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CHART 7
EXAMPLE 3Output Maximized @ 33 Percent Tax Rate
Tax Revenues Maximized @ 60 Percent
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1.0
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IndexofOutput
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RevenueAsPercentO
utput
Output Revenues
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CHART 8
Derived Laffer CurveOutput Maximized @ 33% Tax Rate
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%
Revenues As Percent Output
TaxRate
E = Revenue Maximizing Rate of 60%
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CHART 9
Revenue-Maximizing Tax Rate
Exceeds Output-Maximizing Tax Rate
Even With Output Extremely Sensitive To Tax Rate
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1
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Tax Rate
IndexofOutpu
t
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100%
RevenueAsPercent
Output
Output Revenues
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CHART 10
Revenue-Maximizing Tax Rate Exceeds
Output-Maximizing Tax Rate Even With Output-Maximizing Rate Skewed Unrealistically to Right
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Tax Rate
IndexofOutp
ut
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100%
RevenueAsPercen
tOutput
Output Revenues
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DIAGRAM 1
OUTPUT CURVE
0%
0% 100%
Out
ut
A
Y+
rr
+r-
CY
-
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(1) By Conjecture: Rm > R' R' { Rm
(2) For all r-, the Conjecture clearly is true since by definition (rm) > (r
-) and
(Ym) > (Y-), which implies (rm)(Ym) > (r
-)(Y
-), proving that Rm > R
-, r-. This fact is
easily seen in Diagram 1. As r-increases above 0, Y
-also increases but still remains
smaller than Ym,, and the rectangle representing revenues, Y-Cr
-0, remains contained
within YmA rm0, the rectangle representing revenues at rm,
(3) For all r +, it is not readily discernable from Diagram 1 whether the Conjecture is
true since it is not obvious whether the increase in revenues due to an increase in the taxraterepresented by the area of XBr
+rmexceeds the loss of revenues due to the
decrease in output (tax base)represented by the area ofYmA XY+. Therefore, it is
necessary to derive the conditions, if any, under which the conjecture holds. To explorewhether such conditions exist, and if so what they are, rewrite expression (1) for R
+as:
(4) (rm)(Ym) "(r+)(Y
+)
(5) Rearranging terms
" YY
m
r
rm
(6) Recalling that Ym = 1
" Y
rrm which establishes the condition for
the Conjecture to hold:
Condition: Y+