Effects of Taxation on Advertising in Two-sided Markets (Matthew Ce Shi)

Introduction Monopoly Benchmark Extensions Discussion
Eﬀects of Taxation of Advertising in Two-sided
Markets Under Imperfect Competition
C. Matthew Shi
Department of Economics
The Chinese University of Hong Kong
FSR C&M, CMPF, FCP Annual Scientiﬁc Seminar
March 23, 2018

Taxation of Advertising
Debates on taxation of advertising services.
• Florida, US: 1987, removed soon afterward.

• Increasingly popular in developed economies:

• E.g., Austria, Hungary: all media.

• New Zealand: 2000, TV ads.

• Proposals in US: Michigan; Ohio, Minnesota (2013); West
Virginia (2017).

Virginia (2017).
• US tax reform: Deductibility of advertising expenses.

Virginia (2017).
• Taxation of online platforms.

Virginia (2017).
• Taxation of online platforms.
• Unclear about of what would happen due to market
“two-sidedness”.

Terminology
• Two-sided Markets: markets in which two groups of
agents/users interact via intermediaries or platforms.

Terminology
• As applied to media markets:

Terminology
• Two sides: media consumers & advertisers;

Terminology
• Platforms: TV networks, print media, websites, etc.

Terminology
• Cross-group externality/indirect network eﬀects: each side’s
demand & welfare depends on (1) own price, (2) other side’s
participation.

Terminology
participation.
• Ex ante, diﬃcult for welfare analysis.

Terminology
participation.
• Ex ante, diﬃcult for welfare analysis.
• Other two-sided markets: credit cards, night clubs, etc.

Externalities in Two-sided Markets
• Cross-group externalities in two-sided markets make pricing
structure convoluted and welfare analysis diﬃcult.
Platform
Side 1 Side 2
p1 p2
N1(p1, N2)
Surplus1(p1, N2)
N2(p2, N1)
Surplus1(p2, N1)

Externalities in Two-sided Markets
• Cross-group externalities in two-sided markets make pricing
structure convoluted and welfare analysis diﬃcult.
Platform
Side 1 Side 2
p1 p2
N1(p1, N2)
Surplus1(p1, N2)
N2(p2, N1)
Surplus1(p2, N1)
• This paper uses a framework so that the analysis becomes
transparent & plausible in many diﬀerent situations.

Contribution
• Conventional wisdom: tax corrects negative externality
problem

Contribution
problem
• More recently, Kind, Koethenbuerger, & Schjelderup (KKS,
2008); Bourreau, Caillaud, & De Nijs (2016): Tax on ads may
hurt social and/or consumer welfare

Contribution
problem
• Focus on monopoly platform.

Contribution
problem
• Innovation: framework to deliver sets of theoretical results in
media markets.

Contribution
problem
media markets.
• Many market structures: monopoly, oligopoly w/ symmetry

Contribution
problem
media markets.
• Various business models: partial & pure advertising ﬁnance.

Contribution
problem
media markets.
• Eﬀects on (endogenous) proﬁt splits

Contribution
problem
media markets.
• Ad-averse vs. ad-loving consumers

Contribution
problem
media markets.
• Ad-averse vs. ad-loving consumers
• Anderson & Shi (2017): demand shocks, asymmetric ﬁrms w/
empirics from US magazines

Overview
• Road map

Overview
• Road map
• Benchmark: two-sided monopoly

Overview
• Road map
• Extention: symmetric Bertrand w/ mixed ﬁnance

Overview
• Road map
• Pure-ad ﬁnance

Overview
• Road map
• Ad-loving consumers

Overview
• Road map
• Central ideas:

Overview
• Road map
• Central ideas:
• (1). Platforms internalize externalities (to some extent)

Overview
• Road map
• Central ideas:
• (2). Have Incentive to lower prices to engage subscribers

Overview
• Road map
• Central ideas:
• While taxation does not change (1), it hurts (2).

Overview
• Road map
• Central ideas:
• While taxation does not change (1), it hurts (2).
• May break down w/ pure ad-ﬁnance or ad-loving consumers.

Model Set-up
• Benchmark model: two-sided pricing monopoly platform

Model Set-up
• Anderson & Jullien (2016): adding mixed ﬁnance, new results

Model Set-up
• Supply side: monopoly platform.

Model Set-up
• Consumer choice:

Model Set-up
• face ps
, subscription price;

Model Set-up
• face ps
• observe a, advertising level.

Model Set-up
• face ps
• Advertiser decision:

Model Set-up
• face ps
• face Pa
, unit advertising rate;

Model Set-up
• face ps
• face Pa
• observe N, number of consumers/subscribers.

Model Set-up
• face ps
• face Pa
• observe N, number of consumers/subscribers.
• Assumptions in media economics.

Model Set-up: Media Consumers
Assumption 1 (Additive Ad Nuisance)
Consumers have an ad nuisance cost function, γ(a), with γ > 0
and γ ≡ dγ/da > 0, which is additively separable from the
subscription price. So, the full consumer price from joining a
platform is deﬁned as f = ps + γ(a).

• Consumers have the same distaste for ads, which can be
monetized into $.

• Consumers have the same distaste for ads, which can be
monetized into $.
• Consumer decision based on f : N(f ), with N ≡ dN
df < 0.

Model Set-up: Advertisers
Assumption 2
The value to an advertiser from joining a platform is
(i) proportional to the number of consumers that can be reached
(ii) independent of other advertisers on the same platform;
(iii) the platform charges a per-user ad rate; i.e., Pa = paN.

Assumption 2
• Motivated by pricing practice like CPM.

Assumption 2
• Resulted (inverse) ad demand function: pa(a), w/ dpa
da < 0;

Assumption 2
da < 0;
• Unit ad rate: Pa(a, N) = pa(a)N.

Assumption 2
da < 0;
• Unit ad rate: Pa(a, N) = pa(a)N.
• Weyl & White (15): platform insulation; Anderson & Jullien
(16): a possible equilibrium w/ two-part tariﬀ.

Model Set-up: Platform
Platform’s profit (before tax):
max
ps ,a
π = (ps
− cs
)N(f )
πs :subscription profit
+ (pa
(a)N(f ) − ca
N(f ))a
πa:advertising profit
= (ps
− cs
)N(f ) + (R(a) − ca
a)N(f )
= (ps
− cs
+ R(a) − ca
a)N(f ),

Model Set-up: Platform (continued)
• An ad valorem tax on advertising, t;

• Platform (producer) price of ads: pa
1+t , or (1 − τ)pa, where
τ ≡ t
1+t .

• Platform (producer) price of ads: pa
1+t , or (1 − τ)pa, where
τ ≡ t
1+t .
• Platform’s proﬁt (after tax):
π = (ps
− cs
+ (1 − τ)R(a) − ca
a)N(f ).

Characterization of Equilibrium
• The monopoly platform sets ps and a simultaneously.

• Anderson & Coate (2005): ﬁx f , hence ¯N = N(¯f ), ﬁnd the
optimal combination (pa∗, a∗);

•
a∗
= arg max
¯f ≥a≥o
(¯f − γ(a) − cs
+ (1 − τ)R(a) − ca
a) ¯N.

•
a∗
= arg max
¯f ≥a≥o
(¯f − γ(a) − cs
+ (1 − τ)R(a) − ca
a) ¯N.
• FOC implies
(1 − τ)R (a∗
) = γ (a∗
) + ca
.

Characterization of Equilibrium: Discussion
FOC implies
(1 − τ)R (a∗
) = γ (a∗
) + ca
.
• Perceived marginal cost: γ (a∗) + ca;

FOC implies
(1 − τ)R (a∗
) = γ (a∗
) + ca
.
• Perceived marginal cost: γ (a∗) + ca;
• Platform does consider/internalize some negative externalities
on consumers.

• Assume (1 − τ)R (0) > γ (0) + ca:

• Assume (1 − τ)R (0) > γ (0) + ca:
• No corner solution - subscription-only business model.

• Assume (1 − τ)R (0) > γ (0) + ca:
• However, ¯f = γ(a∗), when (1 − τ)R (a∗) > γ (a∗) + ca for all
a.

• Assume (1 − τ)R (0) > γ (0) + ca:
a.
• Endogenous pure ad-ﬁnance when ad demand is strong and/or
the ad cost is low.

• Assume (1 − τ)R (0) > γ (0) + ca:
a.
• Endogenous pure ad-ﬁnance when ad demand is strong and/or
the ad cost is low.
• Diﬀerent analytics; to be discussed.

Given a∗, we solve for f :
• FOC implies
N(f )+(f −γ(a∗
)−cs
)N (f )+((1−τ)R(a∗
)−ca
a∗
)N (f ) = 0.

• FOC implies
N(f )+(f −γ(a∗
)−cs
)N (f )+((1−τ)R(a∗
)−ca
a∗
)N (f ) = 0.
• Reﬂects market ”two-sidedness”.

• FOC implies
N(f )+(f −γ(a∗
)−cs
)N (f )+((1−τ)R(a∗
)−ca
a∗
)N (f ) = 0.
• Deﬁne eﬀective MC: ˜c = cs + γ(a∗) − (1 − τ)R(a∗) + caa∗.

• FOC implies
N(f )+(f −γ(a∗
)−cs
)N (f )+((1−τ)R(a∗
)−ca
a∗
)N (f ) = 0.
• Deﬁne eﬀective MC: ˜c = cs + γ(a∗) − (1 − τ)R(a∗) + caa∗.
• ps∗ = f ∗ − γ(a∗).

Incidence in Ad Market
Lemma 1
d ˜c/dτ = R(a∗).

Lemma 1
d ˜c/dτ = R(a∗).
• Application of the envelope theorem

Lemma 1
d ˜c/dτ = R(a∗).
• Transforming a two-side market problem to an usual
price-setting problem.

Lemma 1
d ˜c/dτ = R(a∗).
• Transforming a two-side market problem to an usual
price-setting problem.
• Holds for any monopoly ad market, regardless of the structure
of consumer market.

Result 1
In a monopoly advertising market, an increase in the ad valorem
tax on advertising reduces the number of ads and raises the
advertiser price of ads.

Result 1
• Proof.
da
dτ
=
R
(1 − τ)R − γ
< 0,
dpa
dτ
=
dpa
da
da
dτ
> 0.

Result 1
• Proof.
da
dτ
=
R
(1 − τ)R − γ
< 0,
dpa
dτ
=
dpa
da
da
dτ
> 0.
• Standard analysis applies;

Result 1
• Proof.
da
dτ
=
R
(1 − τ)R − γ
< 0,
dpa
dτ
=
dpa
da
da
dτ
> 0.
• Standard analysis applies;
• Holds for any monopoly ad market, regardless of the structure
of consumer market.

Incidence in Consumer Market
Result 2
In a two-sided monopoly platform, both the consumer subscription
price and the full price rise with the ad valorem tax on advertising.
Thus, the subscription level decreases with the tax.

Result 2
• Proof.
df ∗
dτ
=
−∂(f −˜c)
∂τ N
Φ
=
RN
Φ
> 0

Result 2
• Proof.
df ∗
dτ
=
−∂(f −˜c)
∂τ N
Φ
=
RN
Φ
> 0
• Apply Lemma 1.

Welfare Analysis
• Consumer surplus: CS(ps, a) = CS(f ) =
∞
f N(x)dx.

Welfare Analysis
∞
f N(x)dx.
• Advertiser surplus: AS(pa(a), N) = N· ¯AS(a), where
¯AS(a) =
a
0 (pa(x) − pa(a))dx.

Welfare Analysis
∞
f N(x)dx.
¯AS(a) =
a
• Tax revenue: T = τR(a)N(f ).

Welfare Analysis
∞
f N(x)dx.
¯AS(a) =
a
• Tax revenue: T = τR(a)N(f ).
• Social surplus SS = CS + AS + π + T.

Welfare Analysis
• On consumer surplus:
dCS
dτ
= −N
df
dτ
< 0;

Welfare Analysis
• On consumer surplus:
dCS
dτ
= −N
df
dτ
< 0;
• On advertiser surplus:
dAS
dτ
= N
d ¯AS
da
da
dτ
+
dN
dτ
¯AS < 0.

Welfare Analysis
• On platform proﬁt:
dπ∗
dτ
=
∂π
∂τ
= −RN < 0
.

Welfare Analysis
dπ∗
dτ
=
∂π
∂τ
= −RN < 0
.
• On social surplus:
dSS
dτ
=
dCS
dτ
+
dAS
dτ
+
dπ
dτ
+
dT
dτ
< 0

Welfare Analysis
dπ∗
dτ
=
∂π
∂τ
= −RN < 0
.
• On social surplus:
dSS
dτ
=
dCS
dτ
+
dAS
dτ
+
dπ
dτ
+
dT
dτ
< 0
• Result 3: tax on ads hurts all parties and the society as whole.

Welfare Analysis: Discussion
• Although less ad nuisance, consumers face higher full price.

• Reason: monopolist internalizes (some) externalities, and a
tax reduces its incentive to engage more consumers.

• Whether consumers dislike ads acts like a cost-shifter, and is
not crucial.

not crucial.
• Same idea for a unit-tax.

not crucial.
• However, γ(a) matters for the business model (source of
revenues).

not crucial.
• However, γ(a) matters for the business model (source of
revenues).
• Result 4: ad proﬁt decreases, subscription proﬁt increases (!)

Tax Eﬀects in One Graph
fB
N(f0)

f*
cs
N(fB)
N(f)
N(f*
)
MR
Subscription profit (before tax
change)
Total Profit (before tax change)
Subscription profit (after tax
change)
Total Profit (after tax change)
∆
p0 = f0
ps
B
ps
*

Extension: Competitive Bottlenecks
Competitive Bottlenecks: most important market structure for
two-sided markets.
• I platforms: diﬀerentiated products to consumers.

two-sided markets.
• Consumers: discrete-choice, pick one (”single-homing”).

two-sided markets.
• Consumer demand: N(fi ; f−i ) with ∂N
∂fi
< 0, ∂N
∂f−i
> 0.

two-sided markets.
∂fi
< 0, ∂N
∂f−i
> 0.
• Advertisers: independent decision to join each, can join many
(”multi-homing”).

two-sided markets.
∂fi
< 0, ∂N
∂f−i
> 0.
• Each platform still a monopolist to advertisers.

two-sided markets.
∂fi
< 0, ∂N
∂f−i
> 0.
• Examples: TV channels (at a moment), etc.

Consumer demand incorporates many standard models:
• Spatial competition models:

• Hotelling duopoly.

• Salop’s circular city.

• CES-logit models:

• Anderson, de Palma, & Thisse (1992).

• Logit is the powerhouse of empirical I.O.

• Linear demands:

• Linear demands:
• Armstrong & Vickers (2015): linear demands can have a
discrete-choice foundation.

Incidence in Ad Markets
• A consumer can be reached only on one platform.

• Result 1 applies in this case.

• Result 1 applies in this case.
• Tax on ads: ad price ↑, ad level ↓.

Incidence in Consumer Markets
• FOC implies
fi − γ(ai ) − cs
+ (1 − τ)R(ai ) − ca
ai +
N
∂N/∂fi
= 0

• FOC implies
+ (1 − τ)R(ai ) − ca
ai +
N
∂N/∂fi
= 0
• Familiar symmetric Bertrand model with MC
cs + γ(a∗) − (1 − τ)R(a∗) + caa∗.

• FOC implies
+ (1 − τ)R(ai ) − ca
ai +
N
∂N/∂fi
= 0
• Familiar symmetric Bertrand model with MC
cs + γ(a∗) − (1 − τ)R(a∗) + caa∗.
• Use standard symmetric oligopoly analysis.

Result 5
In competitive bottlenecks, both the consumer subscription price
and the full price rise with the ad valorem tax on advertising.

Result 5
• Proof.
dfi
dτ
=
R
Ψ
> 0

Result 5
• Proof.
dfi
dτ
=
R
Ψ
> 0
• Analogous situation to our monopoly case.

Result 5
• Proof.
dfi
dτ
=
R
Ψ
> 0
• Analogous situation to our monopoly case.
• Possibility of increased proﬁts (!)

Extension: Pure Ad-ﬁnance
Pure Ad-Finance: endogenously arises in the benchmark model.
• Platform: two-sided monopoly, free to consumers.

• Same characterization of consumers & advertisers.

• Same characterization of consumers & advertisers.
• Examples: websites, radio networks, free print media, etc.

Platform’s proﬁt (after tax):
max
a
π = ((1 − τ)R(a) − ca
a)N(γ(a))
• FOC implies
(1 − τ)R − ca
(1 − τ)R − caa
= −γ
N
N
.

Platform’s proﬁt (after tax):
max
a
π = ((1 − τ)R(a) − ca
a)N(γ(a))
• FOC implies
(1 − τ)R − ca
(1 − τ)R − caa
= −γ
N
N
.
• Whether consumers dislike ads matters.

Tax Incidence
Result 6
advertiser price of ads. Thus, the subscription level also increases
with the tax.

Tax Incidence
Result 6
with the tax.
• Full price (ad nuisance cost) ↓: consumer surplus ↑.

Tax Incidence
Result 6
with the tax.
• Full price (ad nuisance cost) ↓: consumer surplus ↑.
• Ad rate ↑, no. consumers ↑: ex ante, unclear eﬀect on
advertiser welfare.

Welfare Eﬀects
Result 7
If pa(a) is log-concave, advertiser surplus decreases.

Welfare Eﬀects
Result 7
• When ad demand is not ”too convex,” advertisers and the
platform have their interest aligned.

Welfare Eﬀects
Result 7
• Parallel to media see-saw principle (Anderson & Peitz, 2015)

Welfare Eﬀects
Result 7
• Parallel to media see-saw principle (Anderson & Peitz, 2015)
• In this case, tax on ads hurts advertisers and the platform but
beneﬁts consumers.

Extension: Ad-loving Consumers
• W/ ad-loving consumers & a unit-tax, results largely
unchanged.

unchanged.
• For ad-valorem tax, possible to have higher ad level, less ad
price, which may beneﬁt advertisers.

unchanged.
• For ad-valorem tax, possible to have higher ad level, less ad
price, which may beneﬁt advertisers.
• Interesting interaction between tax instrument & consumer
ad-preference.

Taxing Negative Externalities in Two-sided Markets
• Our motivation comes from ad tax policies in real worlds.

• However, our analysis applies to similar situations:

• Market places with pollution: consumers & ﬁsher sellers or
loud salespersons in Sam’s club.

• Market places with pollution: consumers & ﬁsher sellers or
loud salespersons in Sam’s club.
• Decentralized governments with economic incentives: local
polluters to ﬁnance public-good provision.

Possible Extension/Application
• Two-sided multi-homing: nascent literature.

• Theory: Ambrus, Calvano, Reisinger (2016); Anderson, Foros,
& Kind (2017).

& Kind (2017).
• Empirical: Shi (2016) on magazine markets.

& Kind (2017).
• Theory and empirics on other policies:

& Kind (2017).
• Caps on advertising level in many countries.

& Kind (2017).
• Caps on advertising level in many countries.
• Ad-avoidance technology, pay-to-avoid option.

Thank you for your presence.
• Email: shice@cuhk.edu.hk.

Thank you for your presence.
• Email: shice@cuhk.edu.hk.
• Comments & suggestions are appreciated.

Effects of Taxation on Advertising in Two-sided Markets (Matthew Ce Shi)

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