In a tax-evasion model with profit tax, we reexamine and clarify the issues of neutrality and separability with imperfect detection of tax fraud. With this more realistic setting, we show that the profit tax is not necessarily neutral and the separability conclusion may not hold. Furthermore, the property of non-neutrality may coexist with that of separability or inseparability. However, in contrast to the traditional conclusion, raising the audit probability may reduce the tax compliance when the property of inseparability is present.

Chiaen J. Wu

K. L. Glen Ueng

English

Research Papers in Economics

     
 
 
  
  
Volume 29, Issue 1 
  
A note on the neutrality of profit taxes and tax compliance with imperfect 
detection 
  
 
 
K. L. Glen Ueng  
Department of Public Finance, National Chengchi 
University 
Chiaen J. Wu  
Department of Public Finance, National Chengchi 
University
Abstract 
In a tax-evasion model with profit tax, we reexamine and clarify the issues of neutrality and separability with imperfect 
detection of tax fraud. With this more realistic setting, we show that the profit tax is not necessarily neutral and the 
separability conclusion may not hold. Furthermore, the property of non-neutrality may coexist with that of separability 
or inseparability. However, in contrast to the traditional conclusion, raising the audit probability may reduce the tax 
compliance when the property of inseparability is present.
 
Citation: K. L. Glen Ueng and Chiaen J. Wu, (2009) ''A note on the neutrality of profit taxes and tax compliance with imperfect detection'', 
Economics Bulletin, Vol. 29 no.1 pp. 312-318. 
Submitted: Oct 14 2008.   Published: March 11, 2009. 
 
     1
1. Introduction
The conventional view that the profit tax has no influence on the monopolist’s production
decision is well known. However, much of the literature on profit taxation (e.g., Marrelli
1984, Kreutzer and Lee 1986 and 1988, Wang and Conant 1988, Wang 1990, Yaniv 1995 and
1996, Lee 1998) has incorporated tax evasion into the analysis of tax neutrality and, therefore,
the issue of separability between production and evasion decisions has become a focus of
research. In most models the neutrality of profit taxes and the separability of decisions are
still robust under a fixed audit rate.
However, the possibility of an uncertain audit  outcome has been neglected in these
models.
1 In the real world, taxpayers often complain about significant changes in the tax law,
difficulties in interpreting  the existing  tax laws (Alm  1988, Beck and Jung 1989, Alm
Cronshaw and McKee 1993) and the high cost of tax compliance (Scotchmer and Slemrod
1989). In practice, production costs or sales revenues are difficult to measure with a high
degree of precision. In view of uncertain audit outcomes, taxpayers may overstate costs even
though the tax-evading monopolist will be audited. The purpose of this note is to investigate
non-neutrality and inseparability under a formulation of uncertain detection of tax fraud.
With this more realistic setting, the analysis shows that the profit tax is not necessarily
neutral and the separability conclusion may not hold. However, non-neutrality can not imply
inseparability. This is different from the view of Lee (1998) who did not distinguish
inseparability from non-neutrality. Furthermore, when the evasion and output decisions are
inseparable, there exist not only direct but also indirect effects of raising the audit probability
on tax compliance. Thus, raising the audit probability may encourage tax evasion if the
indirect effect outweighs the direct effect. To the best of our knowledge, there are few studies
that are concerned with this possibility.
2
2. The Model
Following Wang and Conant, consider a monopolistic monopolist facing a proportional tax
rate, t with0 t 1. Denote the monopolist’s output level as q and true total costs as
C(q) which is not known to the tax collector. Suppose that the monopolist can evade a profit
tax liability by overstating its production costs by a positive fraction (referred to as the
declaration factor), which are either audited with probability p , or remain unaudited with
probability 1 p . He/she may either be audited with probability p , or unaudited with
1 Those studies mentioned above have implicitlyassumed that the tax authority can perfectly discover the fraud
reports when the tax returns are audited.
2 It is worth noting that the possibility that a very high penalty will be counterproductive in deterring crimes has
been explored in several papers (Malik 1990, Andreoni 1991, Chang et al. 2000, Ueng and Yang 2006).
However, the result that an increase in the audit probability will enhance compliance is rather robust.2
probability 1 p . When audited, the tax authority does not detect evasion precisely, for the
reasons mentioned above. Thus the monopolist, in addition to being audited or not being
audited, faces another kind of uncertainty regarding the audit outcome. The authorized costs
will become(1 x)C(q), where xis the difference ratio between the authorized costs and the
true production costs. The actual profit of a monopolist is
where Rdenotes total revenues.
(q)  R(q) C(q ) ,
Let the authorization factor x be a random variable with distribution F(x) that is
continuously distributed throughout the population with x
L  x  x
H .
3 The uncertain
(certain) detection is defined by a non-degenerate (degenerate)F(x). The penalty rates(1) is
applied as the declared costs exceed the authorized costs. Thus, if tax evasion is not audited,
the monopolist’s net profit will be
A  ( 1 t)  tC . (1)
However, if the monopolist is audited, then there exist three
cases:   x
L, x
L    x
H,and  x
H . Case 1 can be ignored since it is irrational for the
evading taxpayer to report a lower production cost. In case 2, the monopolist will pay the tax
due plus a fine on the unreported profit if he is assessed as having lower production costs
than those declared. However, if the monopolist is assessed as having higher production costs
than those declared, he receives a rebate for the overpaid tax, but does not receive a rebate for
the reward at the fine rate s. In case 3, the evader will always pay the tax plus a fine if he is
audited. Therefore, the random audited profit becomes
B  A st(  x)C, (2)
where s 1 if   x and s 1 if 

x . Since we focus on the issues of the neutrality and
separability of the profit tax, and case 2 offers no further insight in this respect, we only
discuss case 3 where  x
H for easy analysis.
Suppose that the monopolist’s preference function is given by a von
Neumann-Morgenstern utility function U() withU()  0andU()  0 , which implies
that the monopolist is risk-averse. The monopolist’s problem is to chooseqand to maximize
its expected utility,
Max E[U()  ]  (1 p) U(A)
x
H
p U(B  )d  F(x)  (1 p)U(A) pE[U(B)]. (3)
q, x
L
The first-order conditions for an interior maximum of expected utility are
(1 p)AqU(A) pE[BqU(B)]  0 (4)
and
(1 p)U(A) p(s 1)E[U(B)]  0, (5)
where the subscript indicates a partial derivative. Equation (4) represents the optimal level of
production. Another characterization of the optimal evading condition is obtained by
3 Our model will reduce to Wang and Conant (1988) if x
L  x
H x  0 .3
rewriting (5) as U(A)/ E[U(B)]  p(s 1)/(1 p)and demonstrates that the optimal internal
rate of overstated costs requires that the marginal rate of substitution (between unaudited
profit and expected profit detected) be equal to the real price of evasion.
To more easily demonstrate the focus and the comparative statics of this paper in what
follows, we substitute (5) into (4) to reveal that at the optimum
(1t)E[U(B)]tCE[U(B)x] 0. (6)
Furthermore, to provide important insights into the issues of the neutrality of profit taxes
and the separability of decisions in the tax-evasion model, we re-write Equation (6) as
   tC E[U(B)x]
. (7)
(1t) E[U(B)]
Obviously, the profit tax is non-neutral (  0) if E[U(B)x] 0, and the separability
of decisions is not preserved if the RHS of  (7) depends on  . In general, these two
conditions hold, and hence we have the following proposition:
Proposition 1: With uncertain detection the profit tax can affect the profit-maximizing
output, and the monopolist’s output and tax evasion decisions are inseparable; that is,
the neutrality and separability results can not be preserved in general.
As we argued in the Introduction, this is quite different from the conventional results
indicated in the previous literature (e.g., Wang and Conant 1988, Yaniv 1995 and 1996). It is
worthwhile mentioning that Lee (1998) obtained similar results to these by formulating an
endogenous audit rate rather than an uncertain audit outcome. Note that if
E[U(B)x] E[U(B)] is a function of  , then E[U(B)x] 0; that is, inseparability implies
non-neutrality. However, the reverse is not true. To see this, we know thatE[U(B)x] 0(i.e.,
  0 ) may not imply that E[U(B)x] E[U(B)] depends on  . For example, if
F(x) degenerates to a non-zero constant x , then E[U(B)x] xE[U(B)] 0 and
E[U(B)x] E[U(B)] x, which is independent of  . That is, non-neutrality may not imply
inseparability. This result does not arise in Lee's model (1998) and has been neglected in the
literature.
4
3. Raising the Audit Probability may Reduce Compliance
Now we turn to investigate the comparative statics of how raising the audit probability affects
tax compliance. Totally differentiating equations (5) and (6) given the penalty and tax rate
4Lee (1998, L.1-25, P.335) argued that: “Thus, it must be that  0 , meaning that the tax evasion decision has
no effect on the output decision, and profit taxes are neutral even in the presence of tax evasion.  . As a
consequence,   0 , . Hence, the neutralityresult above may not hold, and the tax evasion decision may
affect the output decision (Actually, it is the property of inseparability in the previous literature).” Therefore, Lee
considered the two properties to be equivalent and did not distinguish inseparabilityfrom non-neutrality.4
q  p

p
1 2


leads to the following equations:
5
J
1dq J
1d  J
1dp (8)
and
J
2d q  J
2d  0 (9) q 

where
J
1  (  1 p)AU(A  ) p( s 1)E[B U(B)] q q q
J
1 tC(1  p)U(A)  p(s 1  )
2E[U(B)]  0
J
2  E [(1  t)

 tCx]B U(B)  E[(1  t)  tCx]U(B)]

(10) q q
J
2  E[(1  t)  tCx]B U(B)
 
J
1 U(A) (s1)E [U(B)] 0 .
By Cramer’s rule, we obtain the comparative statics
 J pJq 
p J
1J
2  J
1J
2 . (11)
q   q
It is worth noticing that the monopolist’s output and evasion decision are separable with
certain detection outcomes.  In this case, J
2equals zero via  condition (6), and  we obtain
 /p  J
1 / J
1 0   which is consistent with the conventional result. However, if the p 


monopolist’s output and evasion decisions are inseparable, then J
2 may not equal zero. This
may make the sign of /pin equation (11) ambiguous. To demonstrate the underlying
economic intuition, we substitute dq  (  J
2 / J
2)d from (9) into (8) to decompose these  q
effects of raising the audit rate, which leads to
[J
1 / J
1  J
1J
2 /(J
1J
2)]d  dp. (12)  p q  p q
The first term in the brackets on the LHS of (12)  represents the direct effect of changing the
audit rate on tax evasion, while the second term denotes the indirect effect (via changing the
level of output) due to inseparability. When these two effects have opposite impacts on  ,
and the indirect effect outweighs the direct effect, increasing the audit probability may reduce
tax compliance.
5 The comparative statics of  p with (4) and (5) is equivalent to that with (5) and (6). However, it is much
easier to show the focus of this note using the latter. The fuller derivation can be obtained via an email
(klueng@nccu.edu.tw) to Glen Ueng.5
Proposition 2: Under uncertain detection with inseparability, raising  the  audit
probability may encourage rather than discourage tax evasion.
4. Conclusions
It is conventionally believed that profit taxes are neutral, and the monopolist’s output and tax
evasion decisions are separable under a fixed audit probability. However, re-examining
neutrality and inseparability by the formulation of uncertain audit outcomes leads to different
results. First, with uncertain detection, the neutrality and separability results cannot be
preserved in general. Second, non-neutrality and inseparability are not equivalent since
inseparability implies non-neutrality but not vice versa. This result cannot be obtained in Lee
(1998) and has been neglected in the literature. Finally, under an uncertain detection outcome
with inseparability, raising the audit probability may encourage rather than discourage tax
evasion. Therefore, as for the policy implications, controlling assessment outcomes may be
significantly relevant for tax compliance purposes.
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Income Tax Evasion: ATheoretical Analysis”

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Tax Evasion and Output Decisions”

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Tax Evasion: AModel”

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Uncertainty about Income Tax Policies,

A note on the neutrality of profit taxes and tax compliance with imperfect detection

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A note on the neutrality of profit taxes and tax compliance with imperfect detection

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