Tourism Economics, 2014, 20 (1), 107–122 doi: 10.5367/te.2013.0265

Specific or ad valorem? A theory of
casino taxation
KAHLIL S. PHILANDER

University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas,
NV 89154–6107, USA. E-mail: kahlil.philander@unlv.edu.
This paper explores the effects of excise taxation in markets containing
two consumer groups with distinct differences in demand elasticity.
A model of second degree price discrimination is employed with an
endogenously funded public good to represent a protected casino
market with two distinct consumer groups, problem gamblers and
recreational gamblers. The paper finds that, when quantity is used
as the endogenous product variable, consumers tend to obtain a
higher provision of the public good with specific taxes than with ad
valorem taxes. The model also provides evidence that the casino
gambling industry may not be a good candidate for a Pigovian tax
due to the behaviour of a small group that produces negative
externalities (problem gamblers) but that also tends to be more priceinsensitive than the rest of the population.
Keywords: casino tax; tax theory; commodity; addiction; inelastic
demand

Throughout the world, casino style gambling tends to be a heavily taxed
industry (Eadington, 1996, 1998). However, the way gaming taxes are
structured varies significantly from one jurisdiction to another, and even tends
to differ substantially within the same country (Anderson, 2005). Although
some variation is sensible, since each jurisdiction has a different market
structure, the different tax policy decisions frequently seem to be made on an
ad hoc basis, without full consideration to the efficiency of those decisions
(Anderson, 2005). This study puts forth a theoretical analysis that seeks to
provide more clarity on one aspect of casino tax design, choosing between
specific or ad valorem taxes.

Casino market structure
A common delineation of casino patrons is between players characterized as
pathological (or problem) gamblers and non-problem (or recreational) gamblers.
These two groups in particular can also be classified as those which have a weak

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sensitivity to price (relatively inelastic problem gamblers) and a strong sensitivity to price (relatively elastic recreational gamblers).1 Problem gamblers have
been clinically described as characterized by a need to continue to increase the
amount of money spent gambling to receive the same excitement, and a need
to continue to gamble once they have lost (American Psychiatric Association,
2000). In its comprehensive review of the gaming industry, the Australian
Productivity Commission (1999) modelled problem gamblers as having a more
inelastic demand curve than non-problem gamblers, reflecting a lower
sensitivity to price changes. A similar view on the reduced sensitivity of
problem gamblers to price has been expressed by several authors, including
Quiggin (2000), Clarke (2008), Paldam (2008) and Forrest (2008).
Since tax policy is often used as an instrument to regulate the gaming
industry, examining how taxes affect each of these groups – either directly, or
indirectly through an increase in gaming operators’ costs – seems to be an
important policy consideration. The potential for policy decisions that lead to
the opposite of the intended outcomes is noted by Forrest (2010, p 15):
‘Advocates of restrictive regulation have proposed that high prices should be
retained in a gambling market in order not to encourage over-consumption
by existing and potential problem gamblers. For this to be an effective policy,
it would have to be the case that any fall in price would raise losses among
dysfunctional players. Whether or not this or the contrary occurs depends
on whether demand from this pool of players is ‘elastic’ or ‘inelastic’. Inherent
problems exist in designing an experiment to settle this issue and, to date,
no relevant scientific evidence is available.’
From a fairness perspective, it may be sensible for casino taxes and fees to be
as high as they are currently. Casinos have many infrastructure requirements,
including the creation of an entire regulatory body to monitor the industry,
ensure the fairness of the games, evaluate license holders, and so forth – and
the majority of these services are directly provided by government entities.
There are also many negative externalities caused by casino gambling (Eadington,
1996, 2003; Collins and Lapsley, 2003; Walker, 2007), therefore there may be
a Pigovian justification for high effective tax rates (Pigou, 1920). In line with
this ‘fairness’ perspective, this paper analyses a partial equilibrium framework,
where all public goods must be endogenously funded.
The combination of high effective tax rates and industry price discrimination
creates a compelling motive to examine the effect of excise taxes on overall
efficiency and cross-subsidization between the consumer price groups. There is
also an added interest in studying this model within the field of casino
gambling. The analysis will help reveal the policies under which the public
good is more highly funded by people whose behaviour can be described as
addictive. Put simply, does tax revenue generated from gambling tend to come
disproportionately from problem gamblers because of the choice of taxation
method?

Excise tax theory
The literature examining the efficiency effects of ad valorem and specific taxation

A theory of casino taxation

is quite developed. In the case of perfect competition, the two commodity taxes
are widely cited as being equivalent, but perfect competition tends to be quite
rare in the casino gaming industry.2 The original findings on this topic can be
found in Cournot (1960) and Suits and Musgrave (1953).
Diamond and Mirrlees (1971a, 1971b) make a widely cited contribution,
finding that it may be appropriate not to tax any intermediate good. However,
this finding relies on a perfectly competitive market (their model also assumes
that firms are characterized by constant returns to scale and zero externalities),
which is not applicable in general to the gaming industry. Accordingly, there
still may be efficiency gains by taxing casino providers, such as slot
manufacturers. For an overview of key results in the commodity tax literature,
Keen (1998) provides a very useful survey of the literature that arises under
conventional market structures. Delipalla and Keen (2006) extends the results
of optimal commodity taxation in a model of endogenous product quality. In
a limited empirical analysis of gaming excise taxes, Paton et al (2001) find that
ad valorem taxation of net revenue is an alternative that is at least as efficient
as a commodity-based tax on gross stakes.

Overview
This paper explores a model of excise taxation to fund a public good in a market
with second degree price discrimination. In particular, the paper attempts to
provide an insight into who are the winners and losers when ad valorem versus
specific taxes are imposed in a monopoly casino market. Following this
introduction an outline of the structure of the model is provided, along with
the key results. The next section discusses the findings, highlighting potential
limitations and opportunities for future research. Full derivations of the results
shown can be found in the appendices.

Model
The structure of this second degree price discrimination model is adapted from
the ‘two-type/nonlinear pricing’ case by Tirole (1988).3,4 The monopolist
(casino) produces in a market serving two consumer groups; low-value
consumers (recreational gamblers) and high-value consumers (problem
gamblers). There are no substitutes for the good provided by the casino –
although this can be considered a simplification for ease of calculation, if we
set the value of utility from the numeraire good to be zero, we can achieve the
same results.

Consumers
Suppose consumers preferences for casino gaming are defined by a utility curve
such that they receive no utility if they do not buy any quantity (that is, they
do not gamble), and receive net benefits of some utility function less the
price paid if they do gamble; this could be defined by the following utility
function:

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 i
 θ V(yj) – qj
U (yj) = 
 0


if consumer i purchases bundle j

i

if they do not buy

i ∈ {R,P} and j ∈ {1,2},
where yj denotes the quantity purchased and qj denotes the after tax price. The
yj value could be characterized as the identification of whether the gambler is
playing a higher denomination slot machine versus a lower denomination slot
machine, whether they play for a long period versus a short period, or the
combination of these two variables. The player increases his coin-in (consumes
a higher quantity) given higher values of yj.
The typical assumption that utility is concave in yj is made, such that there
is diminishing marginal utility in consumption of gambling – for example, the
first $100 of coin-in produces higher utility to the player than the last $100:
Vy > 0 and Vyy < 0.
To illustrate the general effects of excise taxation, we restrict the theoretical
market to contain two utility maximizing consumer group types, problem
gamblers (P) and recreational gamblers (R). Each has a distinct taste parameter
for casino gaming:
θ P = Problem Gambler Value of Gaming,
θ R = Recreational Gambler Value of Gaming

where we assume that:
0 < θ R < θ P.
This reflects the phenomenon that problem gamblers have a higher valuation
of consumption – that is, they value gambling more. Consumers in each group
are assumed to be homogeneous.

Firm
The market is served by a monopolist, which is aware of the existence of these
two (problem gambler and non-problem gambler) groups, but is unable to
distinguish directly between the two. Therefore, the monopolist must choose
a pricing mechanism that maximizes profit, without directly restricting
consumption to either consumer type. The bundles provided by the monopolist
can be generally categorized as (y1, p1) intended for recreational gamblers in
proportion β and (y2, p2) intended for problem gamblers in proportion (1 – β),
where the sum of these two proportions represents the population of potential
gamblers, β∈[0,1].5 The pre-tax price of good yj is noted by pj. The cost of
production of the good is a constant value equal to c. As in Tirole (1988), it
is assumed that the monopolist serves both types of consumers – which will

A theory of casino taxation

occur if the share of the lower valued recreational consumer group (β) is
sufficiently large.
The profit maximizing monopolist therefore behaves in a way that solves the
following equation:
MaxΠ = β(p1 – cy1) + (1 – β)(p2 – cy2)
s.t.

(1)

(1) UR(y1) ≥ 0, and
(2) UP(y2) ≥ UP(y1).
Profit, defined as the sum of revenue less costs from problem gamblers plus
the revenue less costs from recreational gamblers, is maximized subject to two
constraints. Constraint (1) is an incentive compatibility constraint, which
requires a non-negative return for recreational gamblers to purchase any
gambling activity. That is, recreational gamblers must at least receive utility
greater than or equal to the utility of zero that they could receive from not
consuming any amount of gambling. Constraint (2) is an individual rationality
constraint needed for problem gamblers to reveal themselves as the higher
valued group. That is, they must yield higher utility from consuming the
bundle (y2, p2) than they would from consuming (y1, p1), since they could receive
a given positive return by purchasing the bundle intended for recreational
gamblers.

Government
Much in the way that tax revenue from casinos are used to fund public works
projects, or generally support government budget, a planner is introduced that
can provide a public good (x), and tax purchases of casino activity (y). For
simplicity, both consumer groups are assumed to value the public good equally;
the value of the public good can therefore be expressed by:
–

–

–

βV(x) + (1 – β)V(x) = V(x).

(2)

Again, a typical assumption about the concavity of consumption is made that
represents diminishing marginal utility:
–
–
Vx(x) > 0 and Vxx(x) < 0.
Under the constraints of this model, the government seeks to raise revenue to
fund provision of the public good by imposing an excise tax on casino revenue.
The government sets either an ad valorem tax (t) on the value of consumption
or a specific tax (T) on the incidence of consumption to raise this revenue.
Consumer prices are therefore:
qjs = pj + T
v
j

q = pj(1 + t)

under specific taxation, and
under ad valorem taxation.

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The planner seeks to maximize consumer welfare – defined as the sum of utility
from problem gamblers consumption of gambling, recreational gamblers
consumption of gambling, and both consumers utility from the public good.6
Under specific taxation, the government planner’s optimization equation can
be represented by the following function:
–
Max
W(T) = β[θ RV(y1) – (p1+T)] + (1–β)[θ PV(y2) – (p2+T)] + V(x)
T
s.t. x = β•T + (1–β)•T = T.
Under ad valorem taxation, the government planner’s optimization equation
can be represented by the following function:
–
Max
W(t) = β[θ RV(y1) – p1(1+t)] + (1–β)[θ PV(y2) – p2(1+t)] + V(x)
t
s.t. x = t•[βp1 + (1–β)p2].

Results of Model
No Taxation
The baseline – zero taxation – result for the problem outlined above is identical
to the two consumer, second degree price discrimination problem outlined by
Tirole (1988). The planner has no means of affecting the market to increase
consumer welfare. The monopolist’s first order conditions are therefore:

(θ R – θ P)
(1 – β) 
dV(y1)
y1: θ R ––––– = c / 1 + ––––––––
• ––––––– 
R
dy

θ
β


(3)

dV(y2)
y2: θ P ––––– = c.
dy

(4)

Worth noting is the result of Equation (4) where the welfare optimal condition
for problem gamblers is reached. There, the marginal benefit of additional
quantity equals its marginal cost. Also of interest is that there will be under
provision of quantity to recreational gamblers since:
(1 – β) 

(θ R – θ P)
c / 1 + ––––––––
• –––––––  > c.
R

θ
β

That is, the marginal benefit of additional quantity,
dV(y1)

θ R –––––,

dy

A theory of casino taxation

is larger than the marginal cost, c. These would be equal under an efficient
solution.

Specific taxation7
Since the monopolist’s profit function under specific taxation is:
MaxΠ = β(θ RV(y1) – T – cy1) + (1–β)(θ PV(y2) – (θ P–θ R)V(y1) – T – cy2).
y1,y2

The level of tax T does not enter the first order conditions, and (ignoring
participation constraints) the monopolist will operate in an identical manner
(in terms of providing pricing and quantity bundles) as it would in the zero
taxation environment:

(θ R – θ P)
(1 – β) 
dV(y1)
y1: θ R ––––– = c / 1 + ––––––––
• ––––––– 
dy

θR
β

dV(y2)
y2: θ P ––––– = c.
dy
The choice of tax level by the government planner does not affect any marginal
decisions by the monopolist, therefore it continues to offer bundles (y1, p1)
intended for recreational gamblers and (y2, p2) intended for problem gamblers
that reaches the typical monopolist equilibrium. Again, the problem gamblers
reach their efficient solution, but there is an under-provision of quantity to
recreational gamblers.
The final result of this tax structure is that the planner will use the specific
tax to capture the entire monopoly surplus and use this revenue to fund the
public good. Effectively, the economic rents from the provision of gambling in
a market characterized by a single firm have been entirely transferred to the
government planner, who then redistributes the rents in the form of a public
good. The planner’s first order condition is constant:
_
dV
––– = 1.
dT

(5)

Ad valorem taxation
Under ad valorem taxation, the tax rate enters the marginal decisions made by
the monopolist, leading to different outcomes for all stakeholders. The
monopolist’s profit function can be represented by the following optimization
equation in the presence of an ad valorem tax:

θ PV(y2) – (θ P – θ R)V(y1)

 θ RV(y1)
MaxΠ = β ––––––– – cy1  + (1 – β)–––––––––––––––––– – cy2 .
y1,y2
 1 + t


1 + t


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The solution of the above equation yields the following first order conditions:

θP

dV(y1)
y1: θ R ––––– = c•(1+t) / 1 – –––
• (1 – β) 
dy

θR


(6)

dV(y2)
y2: θ P ––––– = c•(1+t).
dy

(7)

In Equation (7) the marginal benefit of additional quantity for problem gamblers equals the after tax marginal cost, as opposed to strictly the marginal cost
under the no taxation or specific taxation environments. The ad valorem tax
distorts consumption by problem gamblers below the efficient level. As seen
in Equation (6), the change in marginal quantity is less clear for recreational
gamblers. The (1 + t) term affects recreational gamblers in the same way as
it affects problem gamblers, but the net change in consumption differs appreciably from the no taxation or specific taxation result, due to the denominator
on the right hand side of Equation (6). Comparing this term to the right hand
side denominator from Equation (3), we have:
θP
(θ R – θ P) (1 – β)
1 – ––R • (1 – β) ≠ 1 + –––––––
• –––––– .
R
θ

θ

β

This inequality can be simplified to show that if
θP – θR
β > –––––––,
θP

then the effect of (1 + t) will be magnified to create an even larger distortion
from the no tax/specific tax result, and if
θP – θR
β < –––––––,
θP

then the impact of (1 + t) will be abated, reducing the level of distortion. Note
that if
θP – θR
β > –––––––,
θP

then recreational gamblers consumption levels will be distorted even more than
problem gamblers consumption levels have been distorted, which is important
if taxes are being used by policy makers to discourage problem gambling; this
result would imply that recreational gamblers’ consumption would be more

A theory of casino taxation

affected by the tax than problem gamblers’ consumption, and public revenue
generated from the tax would tend to come in greater proportion from problem
gamblers, as compared to a specific tax.
The planner’s first order condition with respect to the ad valorem tax is:
–
dV
 dV ∂y   βθ R + (1 – β)θ P 
––– = 1 – ––– • –––  • ––––––––––––––  .
 dy
∂t   βp1 + (1 – β)p2 
dt

(8)

This equation implies that
–
dV
––– > 1.
dt
Since we know that
–
dV
––– = 1
dT
from Equation 5 we can combine these results to show that:
–
–
dV
dV
––– > ––– .
dt
dT
That is, there is a higher provision of the public good (to both consumers) when
a specific taxation mechanism is used instead of ad valorem taxation mechanism.

Results
In the confines of this model, a few noteworthy results arise. The first is that
both consumers generally prefer specific taxation while the monopolist prefers
ad valorem taxation. Under specific taxation, the planner is essentially employing
a lump-sum tax on the producer that will be equal to his entire monopoly
profits. With this mechanism, consumers obtain a higher provision of the public
good than under ad valorem taxes, and the equivalent level of consumption as
under no taxation. Effectively, government planners are capturing all of the
economic rents from the casino gambling market, and redistributing these rents
in the form of a public good for all consumers.
These findings provide some support for altering the method in which excise
(or retail) taxes are levied on the gaming industry. Currently, the most popular
taxes (in terms of generating the most public revenue) are ad valorem taxes on
gross gaming revenue (Anderson, 2005). The above finding suggests that
maximization of consumer welfare may be better served by expanding the use
of specific taxes, such as admission fees or fixed transaction fees on wagers.
Currently, these tend to be used only in limited capacity.8

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A second point of interest occurs when ad valorem taxes are employed. As
seen in Equation (7), the marginal benefit of higher consumption now equals
the after tax marginal cost (as opposed to strictly the marginal cost under a
no taxation environment), creating distortions to the efficient consumption level
of problem gamblers. Distortions are also expected to occur to recreational
gamblers, as the marginal benefit of higher consumption equals the after tax
marginal cost, and another term shown in Equation (6). By comparing Equation
(6) with Equation (3), we can interpret which consumer group has had their
consumption distorted more by the ad valorem tax. The reduction in marginal
quantity is either greater for recreational gamblers if
θP – θR
β > –––––––,
θP

or less severe if the inequality is reversed. This implies that the larger the
market for recreational gamblers, the more recreational gamblers will have their
(no taxation) consumption levels distorted from the imposition of an ad valorem
tax. That is, recreational gamblers consumption levels will be reduced (at a
higher rate relative to problem gamblers), leaving a higher share of problem
gamblers in the market to fund the tax.
Another implication of the inequality is that if problem gamblers have only
moderately higher values of gambling, then the population proportion effects
described above may not be offset. For example, if problem gamblers value of
gambling (θ P) is twice as large as recreational gamblers value of gambling (θ R),
then recreational gamblers consisting of over half the population (β > 0.5)
would lead to them having their consumption distorted more than problem
gamblers.
Empirically, the proportion of problem gamblers in the general population
has been cited as being fairly small, roughly 1–6% in national studies (Williams
et al, 2012). At even a 10% problem gambling prevalence rate, problem
gamblers value of gambling would have to be ten times as large as recreational
gamblers value of gambling in order to lead to equal distortions in consumption. Combining the theoretical findings from this study with those simple
empirical results suggests that recreational gamblers, who face no health issues
from addiction and create minimal negative externalities, are the same gamblers
whose consumption is being reduced most from the distortive ad valorem tax.
An increased reliance on ad valorem taxes to generate revenue from the gaming
industry will tend to lead disproportionately to more public revenue from
problem gamblers, since those gamblers continue to consume higher relative
levels of casino gambling, in spite of the imposition of the tax.
This is an unfortunate side-effect if policy makers are attempting to force
problem gamblers to internalize the externalities caused by their consumption
– healthy gamblers who are not expected to create externalities are having their
consumption reduced due to the blunt imposition of the tax on all consumer
types. The casino gambling industry may therefore not be a good candidate for
a Pigovian tax since negative externalities occur from only a small group (of
problem gamblers) in the population and this group is generally found to be
much more price insensitive than the rest of the population.

A theory of casino taxation

Conclusion
Both the demand for casino gaming and the theory of excise taxation have been
studied thoroughly, but very little has been done to study the interaction
between these two topics. In particular, there are few studies that focus on the
theoretical issues relevant to casino taxation and fewer still that model these
formally. High levels of taxation in the casino industry imply that the welfare
effects from an efficient tax schedule will be quite substantial, and is most
certainly worth further research. The US commercial casino industry alone
contributed US$7.59 billion in tax revenue to state and local governments in
the USA during 2010 (American Gaming Association, 2011). The framework
for studying the gaming industry is also quite unique, as it is characterized by
two very different consumers. One is consuming a standard good with no
externalities as a by-product of consumption, while the other (much smaller)
consumer is characterized by addiction/inelasticity, and produces negative
externalities. This study revealed that such subtleties of the industry can lead
to important policy differences, even for straightforward topics such as the
choice between an ad valorem or specific commodity tax.

Limitations and future research
This study provided some guidance on only one aspect of the issues facing
gaming policy makers, and is far from a complete perspective on the issues
raised. Significantly more thought is needed to explore how different taxes affect
this very unique industry. This model relied on comparative statics, but a more
general equilibrium framework may reveal other findings. For example,
applications of the double-dividend results by Tullock (1967) and Sandmo
(1975) may be appropriate, as increasing gaming taxes beyond those necessary
to internalize any negative externalities could theoretically reduce more
distortive taxes elsewhere in the economy. Non-excise taxes may also be more
appropriate mechanisms worth exploring as means for generating public
revenues (such as licence auctions). Furthermore, the findings in this study rely
heavily on a single period model of consumer utility. Using a forward looking
model of addiction where consumption decisions are maximized over multiple
time periods, such as that prescribed by Becker and Murphy’s model of rational
addiction (1988), may yield different outcomes.
Endnote
1. Although high elasticity consumers and low elasticity consumers cannot be perfectly divided
into these respective recreational and problem gambler categories, these groups appear to display
sufficient differences in their demand to create these groupings for theoretical discussion.
Alternative modeling of gamblers into (relatively) inelastic and elastic groups may be
appropriate, such as between high rollers and non-high rollers.
2. The closest jurisdiction whose market resembles perfect competition in casino gaming is Nevada,
which does not restrict the quantity of casino licences issued.
3. This article continues to use quantity as an endogenous good, but similar arguments could be
made with quality that would have relevance to the casino gaming industry.
4. For generalization of second degree price discrimination past the two-type case, see Maskin and
Riley (1984)
5. Bundles need not differ.

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6. Although this specification departs from some commodity taxation literature in that monopolist
profits do not appear in the welfare maximization equation, this specification likely better
reflects the positivist reasons for decision making in terms of casino adoption. There is much
evidence that gaming policy has been shaped by the desire to raise (and perhaps maximize) public
revenues (Eadington, 1996, 1998; Chapman et al, 1997; Adam Rose and Associates, 1998;
Smith, 1998; Paldam, 2008).
7. See Appendix A for full derivation of results.
8. This finding could also be extended to other markets with dichotomically divided consumer
groups, such as business and leisure tourists in the wider tourism industry.

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A theory of casino taxation

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Appendix A – specific taxation
Monopolist problem
The profit maximizing monopolist seeks to solve:

MaxΠ = β(p1 – cy1) + (1 – β)(p2 – cy2)
s.t.

(9)

(1) UR(y1) ≥ 0, and
(2) UP(y2) ≥ UP(y1).
The constraints can be rewritten as:

(1) θ RV(y1) – (p1 + T) ≥ 0

or p1 ≤ θ RV(y1) – T

(10)

(2) θ PV(y2) – (p2 + T) ≥ θ PV(y1)–(p1 + T) or p2 ≤ θ PV(y2) – θ PV(y1) + p1
At the optimum the inequalities becomes equalities. Substituting Equation (10–1)
into (10–2) we have:

p2 = θ PV(y2) – (θ P – θ R)•V(y1) – T.
The monopolist problem can therefore be simplified:

MaxΠ = β(θ RV(y1) – T – cy1) + (1–β)(θ PV(y2) – (θ P–θ R)•V(y1) – T – cy2).
y1,y2

TOURISM ECONOMICS

First order conditions:


(θ R – θ P)
(1 – β) 
dV(y1)
y1: θ R ––––– = c / 1 + ––––––––
• ––––––– 
R
dy

θ
β

dV(y2)
y2: θ P ––––– = c.
dy

Government problem
The government seeks to maximize
– welfare defined as the sum of consumer surpluses
and value from a public good, V(x).

–
Max
W(T) = β[θ RV(y1) – (p1+T)] + (1–β)[θ PV(y2) – (p2+T)] + V(x)
T
s.t. x = β•T + (1–β)•T = T.

(11)

First order condition:

–
dW

dV ∂y1


dV ∂y2
 dV
––– = β θ R• ––– • ––– – 1  + (1–β) θ P• –– • ––– – 1  + –– = 0.

dy1 ∂t


dy2 ∂T
 dT
dT
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This can be rearranged to produce Equation (13):

–
dV
∂yi
––– = 1, since ––– = 0, i∈{1,2}.
∂T
dT

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Appendix B – ad valorem taxation
Monopolist problem
As in the case of specific taxation, the profit maximizing monopolist seeks to solve:

MaxΠ = β(p1 – cy1) + (1 – β)(p2 – cy2)
s.t.
(1) UR(y1) ≥ 0, and
(2) UP(y2) ≥ UP(y1).

(14)

A theory of casino taxation

The constraints can be rewritten as:

(1) θ RV(y1) – (p1 + t) ≥ 0

or

p1 ≤ θ RV(y1)/1 + t

(15)

(2) θ PV(y2) – p2 (1 + t) ≥ θ PV(y1) – p1 (1 + t)
θ PV(y2) – θ PV(y1)

or p2 ≤ ––––––––––––––+ p1.
1 + t
At the optimum the inequalities becomes equalities. Substituting Equation (14) into
(15) we have:
θ PV(y2) – (θ P – θ R)•V(y1)

p2 = ––––––––––––––––––––.
1 + t
The monopolist problem can therefore be simplified:

 θ RV(y1)

θ PV(y2) – (θ P – θ R)V(y1)

MaxΠ = β ––––––– – cy1  + (1 – β)–––––––––––––––––– – cy2 .
y1,y2
 1 + t


1 + t

First order conditions:


θP

dV(y1)
y1: θ R ––––– = c•(1+t) / 1 – –––
• (1 – β) 
R
dy

θ

dV(y2)
y2: θ P ––––– = c•(1+t).
dy

Government problem
The government seeks to maximize
– welfare defined as the sum of consumer surpluses
and value from a public good, V(x).

–
Max
W(t) = β[θ RV(y1) – p1(1+t)] + (1–β)[θ PV(y2) – p2(1+t)] + V(x)
t
s.t. x = t•[βp1 + (1 – β)p2].

(16)

First order condition

–
dW
 R dV ∂y1

 P dV ∂y2
 dV
––– = β θ • ––– • ––– – p1 + (1–β) θ • –– • ––– – p2  + ––

dy1 ∂t


dy2 ∂T
 dT
dt
• β 1

[ p + (1 – β)p2] = 0.

(17)

TOURISM ECONOMICS

Rearrange:

–
dV
β(p2 – p1) – p2 + βV′(θ R – θ P) + θ PV′
––– = –––––––––––––––––––––––––––––
β(p2 – p1) – p2
dt

(18)

–
dV
βV′(θ R – θ P) + θ PV′
––– = 1 + –––––––––––––––.
β(p2 – p1) – p2
dt
–
dV
 dV ∂y  βθ R + (1 – β)θ P 
––– = 1 – ––– • –––  • –––––––––––––  > 1.
 dy1 ∂t  βp1 + (1 – β)p2 
dt
Since from Equation (5):

–
dV
––– = 1, then
dT
–
–
dV
dV
––– > ––– .
dt
dT

(19)