ISSN (Print) 0473-453X

Discussion Paper No. 1182

ISSN (Online) 2435-0982

SHOULD PRODUCT-SPECIFIC
ADVERTISEMENT BE REGULATEDIN PHARMACEUTICAL MARKETS?

Junichiro Ishida
Tsuyoshi Takahara

July 2022

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Should Product-Specific Advertisement be
Regulated in Pharmaceutical Markets?∗
Junichiro Ishida†
Tsuyoshi Takahara‡
July 27, 2022

Abstract
This paper examines the optimal content regulation of DTCA by comparing two
forms of DTCA—product-specific and category-specific—and identifies a key tradeoff
which underlies this policy debate. Our analysis suggests that the optimal form of
DTCA depends crucially on the cost effectiveness of DTCA and the market-size distortion induced by DTCA. When the cost of advertisement is high, there often exists a
Pareto-improving policy choice: category-specific DTCA is preferred when the marketsize distortion is more severe while produce DTCA is preferred when it is less so. As
the cost decreases, however, a conflict emerges between pharmaceutical firms andpatients: firms are worse off under product-specific DTCA while patients are better
off. We also find that the physician’s reluctance to persuade misinformed patients canactually alleviate the market-size distortion and hence be welfare-enhancing.

JEL Classification Code: M37, I11, I18
Keywords: category-specific DTCA, product-specific DTCA, advertisement regulation, prescription decision, pharmaceutical market∗

The first author acknowledges financial support from JSPS KAKENHI (18H03640, 19H01468,
20H05631, 21H04398), and the Joint Usage/Research Center for Behavioral Economics at ISER and Osaka University for its International Joint Research Promotion Program.
†
Institute of Social and Economic Research, Osaka University. E-Mail: jishida@iser.osaka-u.ac.jp‡
School of Economics, University of Toyama. E-Mail: takahara@a0.rusk.to1.

Introduction

Marketing activities, such as TV advertisement, play a major role in the pharmaceuticalindustry. According to Sufrin and Ross (2008), Pfizer, Merck, and Bristol-Meyer-Squibb—
the three biggest pharmaceutical firms in the US—spend a greater share of expenditure on
marketing than on R&D activities in 2005. Although a large fraction of advertisement isdirected at physicians (prescribers), pharmaceutical firms are increasingly more involved
in direct-to-consumer advertisement (DTCA), especially after the deregulation of DTCA
of prescription drugs by the US Food and Drug Administration (FDA) in 1997. Owing tosome unique features of the industry, however, many experts and practitioners suspect theeffectiveness of DTCA in pharmaceutical markets by noting that it may distort prescription
decisions in some ways. There is now a heated debate about whether DTCA should be
regulated, and if so, in what ways (Ventola, 2011; Parekh and Shrank, 2018; Jacob, 2018).
A body of evidence suggests that DTCA in the pharmaceutical industry can in fact be adouble-edged sword. As proponents of DTCA insist, it could serve an educational purpose
by informing patients of particular medical conditions and potential treatments, thereby
encouraging them to contact a health care provider at an opportune time. Opponents ofDTCA argue, however, that it often misinforms patients, by selectively omitting risk factors
or causes of the condition and overemphasizing drug benefits (see Section 2.6 for morediscussion on this).1 Among those, Ventola (2011) notes:
If a patient’s request for an advertised drug is clinically inappropriate and thehealth care provider is unable or unwilling to correct the patient’s perceptionthat it is a good choice, this situation may lead to unnecessary or harmfulprescribing. An additional problem mentioned by critics is that patients may
withhold information to fit a particular profile that they saw in DTC ads in an
attempt to get the doctor to prescribe a drug they want but that might not beappropriate for them.
To sum up, giving information to patients is beneficial to the extent that it brings them
to clinics in search of medical treatment, but anything above that could just disturb thephysician-patient relationship and cause unnecessary complications.
1

The most notable example may be the case of Rofecoxib which is a nonsteroidal anti-inflammatory drug
marketed by Merck. While approved in 1999, it was later withdrawn over safety concerns after disclosuresthat Merck withheld information about the drug’s risks from physicians and patients for over five years.

2

Although the concern expressed by Ventola (2011) and others seems to reflect the general perception of the medical community and policymakers, it is not necessarily straightforward to understand this assertion in light of economic reasoning. Even if a patient withsome symptoms is misinformed about a particular product, it is always the physician who
can make the final prescription decision. As long as the physician can correct and educate any misinformed patient, the outcome should be the same regardless of the patient’s
prior knowledge: the physician diagnoses and prescribes the best available alternative nomatter what the patient knows beforehand. To the extent that this argument holds true,
therefore, the problem simply disappears and the current debate loses its ground. It is presumably for this reason that this issue has attracted only sparse attention from economic
theorists, despite the heated debate among practitioners and policymakers.
A close look at reality reveals, however, that the issue is not that simple. There isabundance of evidence to show that giving information directly to patients can result in
substantial prescription distortions (see section 2.6 for more detail). Our stance is thatto understand and analyze this current debate in the right frame, we need to look at thehuman side of the physician-patient relationship and consider some psychological or behavioral factors that could potentially harm prescription decisions. More precisely, we
focus on two psychological factors that are particularly eminent in this problem:• Informed patients may develop a biased preference for a particular product, depending on the extent of exposure to DTCA. Given this biased attachment, some patients
may obstinately ask for a specific brand which may not be the best alternative.
• Persuasion is costly under any circumstance, and this is especially so for physicians
who tend to have a high opportunity cost. The cost is even higher when the patientis ill-informed to begin with and has developed a biased attachment.
Under these conditions, we may in fact have a situation where DTCA can be “too informative,” and there may arise a scope for welfare improvement by regulating the content
of DTCA. One way to achieve this is to require that DTCA only describe the presence of adisease and its typical symptoms and treatments but without providing any information
about particular brand names or products; throughout the analysis, we refer to this type ofadvertisement as category-specific. This is precisely what has been done in many countries
outside of the US where DTCA is permitted only if it is category-specific in nature.2
2

Outside of the US, New Zealand is the only OECD country which allows DTCA that includes product3

At a glance, category-specific DTCA can be an effective remedy for the distortion caused
by DTCA in pharmaceutical markets because it only provides minimal information to patients while still serving the educational purpose. However, the welfare impact of such aregulation is not necessarily so straightforward, especially in pharmaceutical markets thatare typically oligopolistic and dominated by a few major firms, as it alters the strategic
nature of market competition. In particular, under category-specific DTCA, advertisement
effectively becomes a public good, which diminishes each firm’s incentive to engage in marketing activities. This can be welfare-reducing as it may leave a large fraction of potential
patients uninformed and receiving no treatment at all in the end.
In this paper, we investigate how the content regulation of DTCA (hereafter, simply
the content regulation) affects pharmaceutical firms’ expenditures on advertisement andwelfare to contribute to the current debate surrounding the pharmaceutical industry. To
this end, we analyze a market of prescription-only drugs for a particular disease with two
horizontally differentiated firms (pharmaceutical suppliers). The two firms decide howmuch to advertise to reach out potential patients who are initially unaware of the disease
and need to be informed via advertisement to receive any medical treatment before it
becomes too serious. Within this framework, we consider two DTCA regulation policies:
in one case, the firms are allowed to promote their own specific brand names (productspecific DTCA); in the other, they can only provide general information about a disease andits typical symptoms without specifying their own brand names (category-specific DTCA).
The difference in the nature of DTCA gives different incentives to the pharmaceuticalfirms and induces different responses from potential patients. Under category-specific
DCTA, no specific information about a particular product is available, and all informed
patients are largely neutral with respect to the two available products. Under productspecific DTCA, on the other hand, informed patients may develop a biased attachment toa particular product when exposed to DTCA. Borrowing from Brekke and Kuhn (2006),
we call those patients selective and captive throughout the analysis: patients are called
selective when they are exposed to both firms’ products and captive when exposed only
to one of them. In either case, patients are informed and hence visit a (representative)
physician in search of medical treatment, which captures the demand-expansion effect of
DTCA (Grossman and Shapiro, 1984). We assume, however, that only selective patients
can ask the physician to compare the two products and be prescribed a suitable drug whilenames. In other countries, there are some regulations on the extent that a firm can promote its own brands
or products, virtually prohibiting product-specific DTCA.

4

captive patients, with a biased attachment, insist on the product they have in mind andneeds to be persuaded if an alternative measure is to be taken.
Faced with a captive patient, the physician needs to persuade him but as noted above,
this persuasion process is, broadly speaking, costly for the physician. The presence of
captive patients may then create a welfare loss by leading to inappropriate prescribing if
the physician deems the persuasion cost too much to bear. A subtle point to note is that thepresence of the persuasion cost, which imposes an extra burden on the physician, creates
two forms of market distortion under product-specific DTCA: on one hand, a fraction of
captive patients may receive a suboptimal outside treatment; on the other hand, they may
also be prescribed the suboptimal product. To make clear distinction between them, we
refer to the former, which limits the equilibrium industry demand below its efficient level,
the market-size distortion, and to the latter as the prescription distortion. These two formsof distortion depend on various parameters in a somewhat complicated way and play amajor role in our welfare analysis.
Main results: We obtain several results regarding the costs and benefits of productspecific DTCA vis-a-vis category-specific DTCA. Our argument centers around the interactions between the two forms of market distortion mentioned above and the strategic
investment incentives that are crucially shaped by the context regulation in effect.
First, it is intuitively clear that the firms invest more in advertisement under productspecific DTCA than under category-specific DTCA. In fact, the advertisement competitionis excessively strong under product-specific DTCA because of the potential of businessstealing, as a consequence of which the firms overinvest in advertisement compared to theefficient level. Under category-specific DTCA, on the other hand, the incentives to informpatients via advertisement are substantially weaker due to its public-good nature, and thefirms indeed underinvest compared to the efficient level. Despite the apparent distortion inprescription decisions induced by product-specific DTCA, the welfare effect of the content
regulation is thus ambiguous because the stronger, though excessive, incentives to invest inadvertisement reduce the number of uninformed patients, ultimately helping them receive
treatment in time.
With this result as a building block, we proceed to characterize the welfare impactof the content regulation. When the cost of advertisement is relatively high, the interests of the firms and potential patients are better aligned, and there often exists a Paretoimproving policy choice. The optimal policy in this case is largely determined by the extent
5

of the market-size distortion induced by product-specific DTCA: category-specific DTCA ispreferred when the market-size distortion is more severe while product-specific DTCA ispreferred when it is less so. As the cost of advertisement decreases, however, the overinvestment problem becomes more of a factor, and a serious conflict arises between thefirms and potential patients as a consequence: while the overinvestment problem is purely
detrimental to the firms, it is beneficial from the viewpoint of patients as it reduces thelikelihood of being left out and helps them seek treatment in time. In general, patients are
made better off under product-specific DTCA as the cost gets smaller while the firms are
made worse off.
It is also worth emphasizing that although the presence of the persuasion cost is thesource of market distortion in our setup, its welfare impact is not entirely negative. Thisis because an increase in the persuasion cost affects the two forms of distortion in different ways: while it aggravates the prescription distortion, it reduces the market-size
distortion by allowing each firm to capture patients who would otherwise be prescribed
the rival firm’s product. The latter effect provides the firms an extra incentive to invest
in advertisement, which can potentially be welfare-enhancing by reducing the number of
uninformed patients. We find that this “distortions as incentives” mechanism can indeed
be strong enough to compensate for the loss from the prescription distortion and benefit
not only the firms but also patients under some conditions.
Finally, although most of our key insight can be illustrated under the assumption ofregulated prices, we also extend the baseline model to incorporate the firms’ price setting
behavior to evaluate the impact of free market pricing in this context. We find that when
the regulated price is set low enough to begin with, free market pricing not only benefits
the firms but also patients despite the higher equilibrium price. This suggests that thetwo forms of regulation are often complementary to each other in that a less stringent
advertisement regulation (i.e., product-specific DTCA) tends to be compatible with a lessstringent price regulation—the type of policy mix adopted in the US—and hence shouldbe evaluated jointly.
Literature: Our model is most closely related to and draws on Brekke and Kuhn (2006)
who investigate the strategic relationship between DTCA and detailing (marketing to physicians). Their focus is on how much information to disseminate to physicians via detailingwhile their DTCA is category-specific in nature as its only role is to bring them to clin-

6

ics.3 Detailing in their model plays a similar role to product-specific DTCA in that it is
an attempt to affect the market share, but is fundamentally different as it is targeted toa different segment of market participants, i.e., physicians; DTCA and detailing are thus
complementary to each other, with no inherent conflict between them. This draws clear
contrast to our model where product and category-specific DTCA are two alternative waysof reaching out to potential patients. We show that these two forms of DTCA yield different
welfare implications, thereby calling for active policy intervention under some conditions.
There are several studies in the fields of management and marketing which investigate
the issue of product-specific advertisement versus category-specific advertisement. Bala
and Bhardwaj (2010) consider two forms of DTCA, called constructive and combative
advertising, in conjunction with detailing. Combative advertising in their model is similar
to product-specific DTCA although it has no market-expansion effect. In their model, eachfirm mixes two forms of DTCA and examines the optimal share of DTCA. Amaldoss and He(2009) consider a duopoly setting where each firm chooses the brand specificity of DTCA.
They consider an aggregate demand model and conduct comparative statics with respect
to the brand specificity. Both of these studies are entirely positive and provide no welfare
analysis; most importantly, patients are not horizontally differentiated in their settings, sothat there is no explicit measure of product-patient mismatch (and prescription distortion)
which lies at the core of our welfare analysis.
Our work also has an obvious connection to analyses of advertisement in industrialorganization. The effect of brand specificity in DTCA has been examined in various contexts outside of the pharmaceutical industry (Krishnamurthy, 2000; Jørgensen and Sigué,
2015; Amir et al., 2021; Shin and Yu, 2021). In conventional analyses of advertisement,
consumers precisely know their preferences (or payoff functions). Here, the situation wedeal with is somewhat special in that physicians, with their expertise, are better informed
about what patients need than patients themselves: specifically, we assume that patientsare lined up on a Hotelling line without knowing their exact location which only the attending physician can tell. However, even though physicians are informationally superior,
it is still patients who must make an initial move and contact a physician on their own.
This unique industry structure gives rise to the possibility of “misinformation” and a scope
for welfare improvement by policy intervention. Although we cast our analysis in a specificcontext of advertisement competition, we believe that this problem can provide a broader
perspective as it is a realistic and pervasive issue in the medical industry at large to what3

In their model, there are captive and selective physicians, but no such distinction is made for patients.

7extent patients should be informed.

2.

The Model

2.1.

Environment

We consider a market of prescription-only drugs for a particular symptom that comprisesof two pharmaceutical firms, potential patients and a representative physician. In thismarket, potential patients with unit mass are horizontally differentiated and uniformly
distributed on the Hotelling line extended on [0, 1]. Each patient is identified with his
location x which captures his “type” (e.g., disease type and/or physical constitution). The
pharmaceutical products are supplied by the two firms, each indexed by i = 0, 1, wherefirm 0 is located at the left end of the Hotelling line while firm 1 is located at the right end.
The two firms supply pharmaceutical products for the same symptom although their products are horizontally differentiated by their chemical compounds and consequent treatment effects.
As a motivating example of our setting, we take the market of antidepressants which offers a variety of drugs for major depressive disorder (MDD).4 Those drugs are categorized
into several distinct classes such as selective serotonin reuptake inhibitor (SSRI), serotonin norepinephrine reuptake inhibitor (SNRI), and noradrenergic antagonist-specificserotonin antagonist (NaSSA). Drugs from different classes have different mechanismsof action and hence produce different effects, or side effects, on different patients. Moreover, even within the same class, there are some subtle yet notable pharmacological differences. As a consequence, there are no “one-size-fits-all” drugs that are equally effective for
all MDD patients (Santarsieri and Schwartz, 2015). Finding a right drug for each patient
generally requires a high level of expertise, giving rise to a unique feature of the market
where buyers (patients) often do not know the best product for them, and must rely onoutside experts (physicians) to identify what is best suited for them.
2.2.

Pharmaceutical firms

In the first stage of the game, the two firms simultaneously choose the levels of DTCA,
which directly affect each potential patient’s decision of whether or not to seek medical
treatment by visiting a physician. Let θi denote the fraction of patients who are exposed
4

Incidentally, it is also one of the most DTCA-intensive markets. See Rosenthal et al. (2002) and Shapiro(2020).

8

to firm i’s advertisement. The demand for firm i’s product (product i) is assumed to be afunction of (θi , θ−i ), i 6= −i, and denoted as Q i (θi , θ−i ). Firm i’s profit is then given byc
πi = pi Q i (θi , θ−i ) − θi2 ,2where pi denotes the price of product i, and c measures the cost of advertisement. To
focus our attention, we abstract away from detailing and take the intensity of detailing as
exogenous.5
As most of our key insight can be illustrated under regulated prices, we assume for
now that the pharmaceutical prices are fixed exogenously at p = p0 = p1 based on factorsthat are not directly related to the issue at hand. The assumption of regulated prices isa relevant one in most countries outside of the US; we will extend our analysis to allow
the firms to set prices endogenously in section 5. To ensure the existence of an interior
solution, we also assume that c is large relative to p.
Assumption 1. 2c > p.
2.3.

Patients

A patient receives medical treatment when he visits a physician. The utility derived bypatient x from consuming a unit of product i is given byu(x, i) = v − τ|x − i| − λp,where v ∈ (0, ∞) denotes the gross effectiveness of a pharmaceutical product, λ ∈ [0, 1]
the copayment rate, and τ ∈ (0, ∞) the “transport cost.” The transport cost τ measuresthe degree of substitutability between the two products: for instance, τ is larger for two
antidepressants that belong to different classes than for those in the same class. The utilityof patients who receive no treatment is normalized to 0.
The key aspect of our model is that a patient’s type x can be observed only by thephysician but not by the patient himself—a defining characteristic of the pharmaceuticalindustry—as assumed in Brekke and Kuhn (2006). The two products have the same effectiveness but differ in their treatment effects across patients, depending on the specificproduct-patient type match. We assume that each product is effective enough to ensurethat it is beneficial even for the most “distant” patient (at x = 0.5).
5This is by no means to deny the importance of detailing. It is rather the opposite: we look at the casewhere detailing is so pervasive that almost all physicians have already been exposed to the two products (aswe assume here), and detailing can hardly make a difference.

9

Assumption 2. 2(v − λp) > τ.
The assumption suggests that there are some patient types for whom multiple products
are potentially beneficial, as is typically the case. Moreover, it is important to note that the
choice of advertising regulation increasingly becomes both irrelevant and insignificant as
the value of each product, measured by v − λp, gets smaller. For the purpose of this study,
we thus focus on the case where the value is relatively large.
2.4.

Advertising regulation

We consider two regulatory regimes—product-specific and category-specific—on the content of DTCA. Under product-specific DTCA, a pharmaceutical firm is allowed to provide
information about a specific product, including its brand name, usage and safety.6 Then,
when the firms are allowed to engage in product-specific DTCA, patients are classified into
three (publicly observable) informational types, depending on the extent of exposure to
the firms’ DTCA:• A patient is selective if he is exposed to advertisement from both firms, which occurs
with probability θi θ−i .
• A patient is captive of product i if he is exposed to advertisement from only one of
the firms, which occurs with probability θi (1 − θ−i ).
• A patient is uninformed if he is exposed to advertisement from neither, which occurs
with probability (1 − θi )(1 − θ−i ).
In contrast, when the firms are restricted to category-specific DTCA, they can only
provide general information about the presence of a disease and its symptoms without
specifying particular brand names or products. Under category-specific DTCA, therefore,
there are no captive patients. As such, a patient becomes selective with probability θi +
θ−i − θi θ−i and uninformed with (1 − θi )(1 − θ−i ).
6An important premise of our analysis is that product-specific DTCA is effective in raising the demand for

its own product (via business stealing) and indeed generates different effects from category-specific DTCA.
Of course, if product-specific and category-specific DTCA make no difference, the whole debate over DTCA
becomes groundless; the current debate over DTCA reflects physicians’ perception that product-specific DTCA
does make a difference at some level. Although empirical evidence on this issue may not be conclusive, there
is in fact some evidence in support of this claim (Kalyanaram, 2008, 2009; Liu and Gupta, 2011; Dave andSaffer, 2012; Sinkinson and Starc, 2018). Most notably, Sinkinson and Starc (2018) measure the impact of
DTCA by pharmaceutical firms and find substantial evidence of business stealing.

10

2.5.

PhysicianWe assume that there is a representative physician to whom all potential patients visit
when they become informed. The physician can prescribe either product 0 or product 1,
or else can choose to provide an “outside treatment,” which invariably provides a utility of
0 for all patient types.7 Given our focus on DTCA, we interpret that products 0 and 1 referto drugs that are relatively new to the market (and hence need to be advertised) while anoutside treatment refers to an aggregate category of “everything else,” including all otherconventionally accepted drugs and medical practices: in the case of MDD, for instance,
they include older brand-name drugs,8 psychotherapy and various lifestyle changes (suchas eating right, getting enough sleep, doing regular exercise, etc). The physician is partly
altruistic in that she cares about the welfare of patients net of the persuasion cost. The
utility of the physician depends on the patient’s informational type.
First, if a patient is selective, he is neutral and simply accepts the physician’s advice as
it is. In this case, the physician incurs no persuasion cost and her utility from prescribing
product i is given by u(x, i). The physician thus simply prescribes the more suitable productfor the patient.9
Second, if a patient is captive, he has developed a biased preference in favor of the
product he has been exposed to and makes a specific request for it. We assume in this casethat the physician either prescribes the product as requested or provides an outside treatment. If the physician takes the option of outside treatment, she must incur a persuasion
cost d which includes time, effort, and psychological discomfort of persuading a patient,
as well as the risk of disrupting the future relationship. As such, the physician prescribes
the requested product i if and only if u(x, i) ≥ −d.
The assumption that the physician provides an outside treatment, rather than the otherproduct, when the persuasion cost is small enough merits a further remark. This specification effectively implies that under product-specific DTCA, patients who are captive of
7

More precisely, the utility gain of an outside treatment is independent of the patient type which is definedwith respect to the relative effectiveness of the two products in question.
8
What constitutes an outside treatment obviously depends on the context. For instance, since promotional
activities typically decrease after generic entry (Huskamp et al., 2008), we can take brand-name drugs with
expired patents as “outside of our model.” Therefore, if we look at the market of antidepressants in the last
decade or so, brand-name drugs such as Prozac, Zoloft, Paxil and Celexa—drugs that had seen generic entry
by the early 2000s—can be regarded as constituting part of an outside treatment.
9
Under Assumption 2, it is never optimal to provide an outside treatment in this case.

11

i can only be prescribed product i, suggesting that product-specific DTCA generates nospillover benefits to the rival firm. Note, however, that it is not our intention to argue
that product-specific DTCA generates no spillovers;10 what is essential in this specification
is rather that product-specific DTCA generates less spillovers than category-specific DTCA.
Here, we focus on an extreme case where product-specific DTCA generates no spillovers
in order to capture this aspect in the simplest manner.
2.6.

On prescription distortion

The key premise of our analysis is that product-specific DTCA may disturb the physicianpatient relationship and distort prescription decisions to some extent. We believe, at some
intuitive level, that this is not only possible but also almost inevitable. On the one hand,
it is hardly surprising that patients sometimes develop a biased preference for a particular
product: first, it is very difficult, if not impossible, for patients to understand all the possible
consequences of prescription drugs; at the same time, health-related problems are always
emotionally arousing, and it is very difficult to stay perfectly calm and rational throughout
the decision process. On the other hand, physicians are also humans with limited resources
and persuasion is never free. A combination of these two factors necessarily gives rise tosome distortion in prescription decisions.
To motivate our analysis further, there is also ample evidence which suggests that giving
detailed information to patients via product-specific DTCA creates seemingly unnecessary
complications and psychological pressures to physicians. Murray et al. (2003) report thatmany physicians feel that DTCA worsens the time efficiency of the visit and have a negative response to the recent increase in DTCA. Similarly, Robinson et al. (2004) report that“few (physicians) believe that these advertisements are a positive trend in health care.”Moreover, it is well documented that many physicians have prescribed inappropriate drugs
which are requested by patients.11 Kravitz et al. (2005) also report that patients’ requests
10

This may or may not be true and is purely a matter of empirical investigation. For instance, Shapiro(2020) finds a spillover effect of brand-specific advertisement on other products. However, given that aphysician has a wealth of alternative options when faced with a captive patient, it is natural to assume thatshe provides an outside treatment, which includes “everything other than the rival product,” at least on someoccasions. This naturally limits the extent of spillovers compared to category-specific DTCA. It is of course
straightforward to extend our setting to incorporate some spillovers of product-specific DTCA, at the expenseof an extra notation.
11
See Frosch et al. (2010) and Ventola (2011) for surveys on the effect of DTCA on the physicians’ prescription decision. Frosch et al. (2010) argue that the request for the advertised product by the patients increases

12have a profound effect on prescription decisions in major depression and adjustment disorder. These results lend support for the view that physicians do indeed face some persuasion
costs when patients are exposed to product-specific DTCA. Additionally, the magnitude of
the persuasion cost seems to differ across symptoms. For instance, Kravitz et al. (2005)
find that the influence of patients, especially brand-specific requests, on the prescription ofantidepressants is higher for adjustment disorder than for major depression and argue that
DTCA may stimulate prescribing more for questionable than for clear indications. This lineof argument is again consistent with the existence of persuasion costs because it is natural to think that persuasion is more costly in the absence of clear and verifiable scientificevidence.

3.

Analysis

3.1.

Prescription decisions

We solve the model backward, starting with the final stage where the representative physician decides whether to prescribe a drug and, if so, which one. Given that a patient visits
the physician, he must be either selective or captive. The physician’s prescription decision
clearly depends on the patient’s informational type as we describe below.
Suppose first that a patient is selective (exposed to both products). Under Assumption
2, the physician recommends product 0 (product 1) if x ≤ 0.5 (x > 0.5) and the patient
simply accepts the advice. As such, the two firms split the market evenly in this contingency. Since the two firms compete for selective patients, this is the competitive segmentof the market.
If a patient is captive (exposed only to one of the products), on the other hand, thephysician chooses either to prescribe the product he requests or to provide an outsidetreatment. The market is now monopolized by one firm, i.e., this is the monopolistic
segment of the market. The physician prescribes a requested product if and only if thebenefit exceeds the persuasion cost, i.e.,v − λp − τ|x − i| ≥ −d.
both appropriate and inappropriate prescribing, though it is unclear which effect is greater. Weissman et al.
(2004) show that physicians who consider DTCA positively prescribe more DTCA drug than those who consider DTCA negatively. Dai et al. (2005) also argue that the marketing activities by Merck had contributed
to the widespread use of Vioxx, which was discontinued due to fatal side effects.

13

The demand for each product in the monopolistic segment is then given by§ªv − λp + d
M := min,1 .
τ
By Assumption 2, M > 0.5, so that each firm can capture a larger market share.
Note that the presence of the persuasion cost generates two forms of distortion inprescription decisions. First, there is a fraction of captive patients who end up receiving
an outside treatment. For the sake of exposition, we call this the market-size distortion,
the size of which is captured by M , as it limits the industry demand below its efficientlevel. We say that the market-size distortion is more severe when M is small and close
to 0.5, while it is less so when M is large and close to 1. Second, there is also a fractionof captive patients who are prescribed the suboptimal product. This form of distortionis called the prescription distortion, which we will discuss in depth when we analyze thewelfare of patients in section 4.3.
3.2.

Advertisement expenditures

Each firm decides how much to invest in advertisement, taking the other firm’s choice asgiven. First, under product-specific DTCA, a patient is selective with probability θi θ−i andcaptive of i with probability θi (1 − θ−i ). The demand for product i under product-specific
DTCA is then obtained as
Q Pi =

θi θ−i+ θi (1 − θ−i )M ,2

where the superscript P stands for product-specific DTCA. It follows from this that firm i’s
problem under product-specific DTCA can be written asθi θ−icc 2
Pmax pQ i − θi = p+ θi (1 − θ−i )M − θi2 .
θi ∈[0,1]
2
2
2
The best-response function is given byθi =p[2M − θ−i (2M − 1)] .
2c

Solving this, the equilibrium expenditure, denoted by θ P , can be obtained as
θP =

2M p
.
2c + p(2M − 1)Note that θ P < 1 by Assumption 1.
14

Second, there are no captive patients under category-specific DTCA. The demand undercategory-specific DTCA is hence given by
Q Ei =

θi + θ−i − θi θ−i,2where, as above, the superscript E stands for category-specific DTCA.12 As such, firm i’s
problem under category-specific DTCA can be written as
θi + θ−i − θi θ−i c 2c− θi .
max pQ Ei − θi2 = p
θi ∈[0,1]
2
2
2
We can then obtain the best-response function asθi =p(1 − θ−i ).
2c

It follows from this that the equilibrium expenditure, denoted by θiE , can be obtained as
θE =

p
.
2c + p

It is intuitively clear that the firms have more incentive to invest in advertisement when
they are allowed to engage in product-specific DTCA. To see this, observe that
θP > θE ⇔

2M p
p
>
.
2c + p(2M − 1) 2c + p

This is further reduced to
2M (2c + p) > 2c + p(2M − 1),which holds for any M ∈ (0.5, 1]. In words, there is a private gain from DTCA when thefirms are allowed to promote their own products, giving them more incentive to invest inadvertisement. Moreover, we can show that the difference in the advertisement expenditures widens as c gets smaller.
We summarize these findings below. Throughout the analysis, all the proofs are relegated to the Appendix unless otherwise noted.
12Here, the demand size for each firm is simply one half of all informed patients because of Assumption
2. If this assumption fails and M < 0.5, on the other hand, the demand size becomes M (θi + θ−i − θi θ−i ).
This means that the optimal investment under either regime tends to 0 as M → 0. When M is relatively
small, therefore, the comparison of regulatory regimes becomes increasingly irrelevant and also insignificant
in absolute terms.

15

Proposition 1. The advertisement expenditure is higher under product-specific DTCA thanunder category-specific DTCA. Moreover, the difference between θ P and θ E is strictly decreasing in c.
Given our incentive structure, it is intuitively clear that the firms invest more in advertisement under product-specific DTCA than under category-specific DTCA; in fact, similar
results have been obtained in the literature (Brekke and Kuhn, 2006; Bala and Bhardwaj,2010). In this paper, we use this fact as a building block and investigate how this incentive
structure interacts with the two forms of market distortion—market-size distortion andprescription distortion—induced by the physician’s persuasion cost and affects welfare.
3.3.

Equilibrium market demand

The effect of the content regulation on the demand for each product is ambiguous with
two opposing forces at work: although product-specific DTCA expands the potential market size due to higher advertisement expenditures, prescription decisions are necessarily
distorted. To see this, observe that
∆Q := Q P − Q E =θ P [θ P + 2(1 − θ P )M ] θ E (2 − θ E )−.
2
2This shows that for any M ∈ (0.5, 1] and θ P = θ E , ∆Q < 0, i.e., if the equilibrium advertisement expenditures are the same between the two regimes, the demand for each productis higher under category-specific DTCA. A necessary condition for ∆Q > 0 is hence that θ P
is sufficiently larger than θ E , although this happens for a wide range of parameter values
as we will see below.
To conduct comparative statics on ∆Q, we first obtain∆Q =4M 2 cpp(4c + p)−.
2[2c + p(2M − 1)]2(2c + p)2

From this, ∆Q > 0 if and only if
2c + p(2M − 1) 2
8M 2 c>.
4c + p2c + p(1)

Two facts are worth noting here. First, ∆Q naturally converges to 0 as c tends to infinity,
because the advertisement expenditures converge to zero under both regimes. Second,observe also that (1) always holds at c = 0.5p, regardless of M , since the difference in16the advertisement expenditures widens as c gets smaller. Aside from these properties,
the exact shape of ∆Q depends crucially on the value of M , as the next proposition fully
characterizes.
Proposition 2. ∆Q > 0 for all c ∈ [0.5p, ∞) if M ≥pp
0.5. For M ∈ [0.5, 0.5), there

exists an interior threshold cQ (v, d) ∈ (0.5p, ∞) such that ∆Q > 0 if and only if cQ (v, d) > c.
Moreover, cQ (v, d) is increasing in both v and d.
[Figure 1 about here]
3.4.

Efficient advertisement

The content regulation influences the equilibrium advertisement expenditure by changing
the nature of competition between the two firms. To illustrate this point, it is instructive toderive the efficient level of advertisement expenditures, defined as the one that maximizes
the joint profit of the two firms, and compare it to the equilibrium level.
The efficient level under product-specific DTCA can be obtained by solving the following problem:

θ2
c
max p
+ θ (1 − θ )M − θ 2θ ∈[0,1]
2
2
Let θ P∗ denote the efficient level under product-specific DTCA, which is given byθ P∗ =

Mp.
c + p(2M − 1)

It is clear that θ P > θ P∗ , i.e., the firms overinvest in advertisement under product DCTA.
This is due to the business-stealing effect of advertisement: a firm can “steal” a fraction of
captive patients by reaching out to them and transforming them into selective.
Similarly, the problem under category-specific DTCA is defined aspc(2θ − θ 2 ) − θ 2θ ∈[0,1] 2
2max

As above, let θ E∗ denote the efficient level under category-specific DTCA, which is givenbyθ E∗ =

p
.
c+p

17

It follows from this that θ E∗ > θ E , i.e., the firms underinvest in advertisement undercategory-specific DTCA. Aside from the fact that there is no business-stealing effect, thisis due to the fact that advertisement under category-specific DTCA is a public good which
also increases the demand for the rival product as well.
We summarize these findings as follows (the proof omitted).
Proposition 3. The firms overinvest in advertisement under product-specific DTCA and underinvest under category-specific DTCA.

4.

Optimal content regulation of DTCA

4.1.

Welfare measures

Denote by πk the equilibrium profit under regime k = P, E. Similarly, we denote by PS kwhat we call the patient surplus (to be defined more precisely below). We consider aregulatory authority with the objective function given by
W k = ωπk + (1 − ω)PS k , k = P, E,
where the parameter ω ∈ [0, 1] reflects the authority’s policy stance where it is more“pro-business” when ω is close to 1 while it is “pro-patient” when ω is close to 0.13
4.2.

Firm profit

We first examine how the content regulation affects the firms’ equilibrium profit. Letting22∆π := π P − π E , ∆θ := θ P − θ E and ∆C := (θ P − θ E ) = ∆θ (θ P + θ E ), we obtainc∆π = p∆Q − ∆C2pθ P [2M − (2M − 1)θ P ] pθ E (2 − θ E ) c=−− ∆θ (θ P + θ E )
2
2
 2

(2M
−
1)p
+
c P
∆θ
E
E
E
= −p(1 − M )θ (1 − θ ) −(θ + θ ) − 2M p .
2
2

(2)

The impact of the content regulation on the equilibrium profit can be decomposed into
two factors. Evaluated at θ P = θ E , any difference in the profits can be attributed to the
distortion in prescription decisions. The first term of the right-hand side of (2) captures
13

We do not take into account the persuasion cost incurred by the physician, assuming that the number ofphysicians, and hence their impact on the overall welfare, are negligibly small.

18

this effect which is negative for any 1 > M . The second term captures the difference inthe gains from demand expansion. Note that the sign of this effect is ambiguous, because
the firms tend to overinvest under product-specific DTCA, diminishing their profit margins
with excessive competition in advertisement.
We have already characterized ∆Q in Proposition 2. Also, from Proposition 1, weknow ∆C ≥ 0, meaning that ∆Q < 0 is a sufficient condition for ∆π < 0. This implies
that the firms are more likely to prefer category-specific DTCA to product-specific DTCA.
In fact, this is always the case when M is relatively small, i.e., the market-size distortionis relatively large, as the next proposition suggests.
pp
Proposition 4. ∆π < 0 for all c ∈ [0.5p, ∞) if 0.75 ≥ M . For M ∈ ( 0.75, 1], there
exists an interior threshold cπ (v, d) ∈ (0.5p, ∞) such that ∆π < 0 if and only if cπ (v, d) > c.
Moreover, cπ (v, d) is decreasing in both v and d.
[Figure 2 about here]
4.3.

Patient surplus

From the viewpoint of policymaking, the welfare of patients often carries more weight thanthat of firms. Since the payoff of uninformed patients is invariably zero, we only need toconsider selective and captive patients. Let PSS and PSC denote the patient surplus forselective and captive patients, respectively.14 Also, define PS k as the total patient surplus
under regime k = P, E, where2

PS P = θ P PSS + 2θ P (1 − θ P )PSC
PS E = θ E (2 − θ E )PSS .
First, selective patients always end up with the most suitable product. The patient
surplus for this group of patients is hence given by
Z 12
PSS = 2(v − λp − τx)d x0= v − λp −

τ
.
4

14

In our model, some patients are misguided to demand the wrong product. There arises a conceptualissue in such a setting as to whether one should use true preferences or manipulated preferences to measure
welfare. We here choose the former, provided that a patient’s payoffs stem from the long-run impact on his
health rather than from the joy of consuming a particular drug.

19

On the other hand, captive patients are prescribed the requested product as far as thepatient benefit exceeds the persuasion cost. The patient surplus for this group of patientsis given by
PSC =

Z M

(v − λp − τx)d x0= (v − λp)M − τ

M2.
2

Defineφ :=4(v − λp) − 2τM,
4(v − λp) − τPSsuch that M φ := PSCS which we use as a measure of the overall distortion in prescription
decisions (more on this point later in section 4.4).
The welfare ranking among the three types of patient is clear: selective patients earn
the highest payoff while uninformed ones earn the lowest which is zero.15 There are hence
two ways to improve the patient surplus, either to increase the number of selective patientsor to decrease the number of uniformed patients. More precisely, similarly as above, define∆PS := PS P − PS E , which is given by2∆PS = θ P PSS + 2θ P (1 − θ P )PSC − θ E (2 − θ E )PSS
= −2θ P (1 − θ P )(PSS − PSC ) + ∆θ (2 − θ P − θ E )PSS .

(3)

Again, the impact of the content regulation can be decomposed into two factors. The firstterm of the right-hand side of (3) captures the loss due to the distortion in prescription
decisions under product-specific DTCA: this fraction of patients would have been selective under category-specific DTCA but become captive under product-specific DTCA. Since
PSS > PSC , this term is always negative. The second term captures the demand-expansion
effect under product-specific DTCA, which is always positive.
To conduct comparative statics on ∆PS, we write (3) as∆PS =4M p[M pPSS + (2c − p)PSC ] p(4c + p)PSS−.
[2c + p(2M − 1)]2
(2c + p)2

15

Some captive patients may earn negative payoffs (when persuasion is costly) but Assumption 2 ensuresthat PSC is always positive.

20

From this, ∆PS > 0 if and only if
4M 2 [p + (2c − p)φ]2c + p(2M − 1) 2>.
4c + p2c + p(4)

Clearly, there is a close relationship between ∆PS and ∆Q; we in fact obtain (1) if φ in(4) is replaced with 1. First, for the same reason as for ∆Q, ∆PS converges to 0 as ctends to infinity. Second, as the demand-expansion effect dominates, this condition holds
at c = 0.5p. Following the same procedure, we can establish the following claim whichruns parallel to Proposition 2, except for the effect of d which we will discuss in more
depth in the next subsection.
Proposition 5. ∆PS > 0 for all c ∈ [0.5p, ∞) if M

p

φ≥

p
p
0.5. For M ∈ [0.5, 0.5φ −1 ),there exists an interior threshold c PS (v, d) such that ∆PS > 0 if and only if c PS (v, d) > c.
Moreover, c PS (v, d) is increasing in v.
The overall welfare effects of the content regulation are summarized in Figure 4. There
are two crucial factors: the cost of advertisement c and the market-size distortion (which
in turn depends on various parameters such as v, p and d). When the cost of advertisement
is relatively high, the interests of the firms and potential patients are better aligned, andthere often exists a Pareto-improving regime, depending on the extent of the market-size
distortion: category-specific DTCA is preferred when the market-size distortion is more
severe (M close to 0.5) while product-specific DTCA is preferred when it is less so (M closeto 1). As c decreases, however, a conflict arises between them. In general, product-specific
DTCA becomes the preferred choice for patients when c is relatively small, because thebenefit of product-specific DTCA is maximized while the distortion in prescription decisions
becomes more attenuated.16 However, the firms are generally worse off under productspecific DTCA because the overinvestment problem becomes more serious as the cost ofadvertisement gets smaller.
[Figures 3 and 4 about here]
4.4.

Market distortions as incentives

As mentioned earlier, the distortion in prescription decisions is ultimately detrimental topatients for two reasons. First, the size of the market for captive patients is restricted
To see this, consider an extreme case where c = 0.5p and hence θ P = 1. In this case, the patient surplus
is maximized because patients are all selective. Patients are clearly made better off under product-specific16

DTCA as it causes no distortion while serving the educational purpose to the full extent.

21

as only a fraction M of them receive pharmaceutical treatment (the market-size distortion). Second, among those who do receive pharmaceutical treatment, some of them areprescribed the suboptimal product (the prescription distortion). The distortion in prescription decisions can be decomposed into two parts, where the ratio φ measures thesize of the prescription distortion (corrected for the market size). Obviously, there arises
no prescription distortion (φ = 1) when τ = 0, i.e., when the two products are perfect
substitutes.
One crucial determinant of the overall distortion M φ is the persuasion cost d. Aninteresting point to note is that the effect of the persuasion cost is not entirely negative
because a change in d affects M and φ in different ways: an increase in d raises M (lessmarket-size distortion) but lowers φ (more prescription distortion). The former effect is
conducive to more investment and can be welfare-improving under product-specific DTCA
(as evidenced by the facts that Q P and π P are both increasing in d). The effect on thepatient surplus is, however, more ambiguous as it also involves the prescription distortion.
Below, we dissect how a change in the persuasion cost d affects the patient surplus.
Since the distortion due to the persuasion cost only arises under product-specific DTCA,
we restrict our attention only to this case. Recall that the patient surplus under productspecific DTCA is given by
PS P = θ P [θ P PSS + 2(1 − θ P )PSC ].
Taking partial derivative with respect to d yields
∂ PSC
∂ θP
∂ PS P= 2[θ P PSS + (1 − 2θ P )PSC ]+ 2θ P (1 − θ P )
.
∂d
∂d
∂d
The first term of the right-hand side reflects the indirect effect of d, which works throughits impact on θ P . Since θ P is increasing in d (see the proof of Proposition 4), the indirect
effect is unambiguously positive. The second term captures the direct effect, where we
have
∂ PSC
d
= − < 0.
∂dτAs such, PS P (and hence ∆PS) increases with d if the positive indirect effect dominates
the negative direct effect. The following result confirms that there is a range of situations
where this holds true.
Proposition 6. Suppose v − λp > 3d and v − λp + d < τ. Then, PS P increases with d if c
is sufficiently large.
22

The proposition suggests that market distortions, in the form of a higher d, can be a
blessing in this environment because they induce the firms to invest more in advertisement.
Of course, this welfare improvement is at the expense of the physician who needs to incur
more cost, and it will ultimately come down to how we evaluate this welfare loss (which
we ignore in the current analysis).

5.

A model with free market pricing

We have thus far assumed that the pharmaceutical prices are regulated and fixed exogenously at some predetermined level. Although this is a reasonable assumption in many
countries, there is an important exception, namely the US, where pharmaceutical firms
can set the prices relatively freely. Here, we extend the baseline analysis to incorporate
price setting and illustrate how it would affect the equilibrium allocation.
5.1.

Optimal pricing

We now consider a setting where each firm simultaneously chooses both the investment
level θi and the price pi . Given the price pair (p0 , p1 ), patient x in the competitive segment
ends up with product 0 if
v − τx − λp0 > v − τ(1 − x) − λp1 ⇔τ − λ(p0 − p1 )> x.
τSimilarly, patient x in the monopolistic segment ends up with product i if
v − |x − i| − λpi > −d ⇔ v − λpi + d > |x − i|.
The market demands for firm i are hence given by
Q Pi = θi θ−iτ − λ(pi − p−i )+ θi (1 − θ−i )(v − λpi + d),2τ

under product-specific DTCA andQ Ei = (θi + θ−i − θi θ−i )τ − λ(pi − p−i ),2τunder category-specific DTCA.
To gain some intuition for the effect of the price competition, it is helpful to look at
each segment separately. First, if all patients are selective, each firm maximizespi

τ − λ(pi − p−i ),2τ23and the (symmetric) optimal price is given by pS := λτ . Similarly, if all patients are captive,
each firm maximizespi (v − λpi + d),
and the optimal price is given by pC := v+d2λ . Naturally, the equilibrium price is bounded
between pS and pC . This implies that free market pricing has little bite when pC andpS are sufficiently close to each other, in which case the equilibrium allocation can beapproximated by that under price regulation.
In what follows, we assume that the price competition is intense enough so that the
optimal price is lower in the competitive segment than in the monopolistic segment.
Assumption 3. pC > pS ⇔ v + d > 2τ.
5.2.

Advertisement expenditures

To analyze the firms’ investment problems, we make additional assumptions that are analogous to Assumptions 1 and 2 to simplify the analysis and focus our attention on more
relevant cases. First, c is assumed to be sufficiently large, so that the optimal investment
is bounded below 1. Second, the value of each product is high enough to ensure that it isbeneficial even for the most distant patient. The following assumptions provide sufficientconditions for these two properties.
Assumption 10 . 2c > pC .
Assumption 20 . 2(v − pC ) > 1.
Under these assumptions, the problem faced by firm i under product-specific DTCA isformulated asmax

θi ∈[0,1],picpi Q Pi − θi2 = pi2
τ − λ(pi − p−i )cθi θ−i+ θi (1 − θ−i )(v − λpi + d) − θi2 .
2τ2This yields a pair of first-order conditions:τ − λ(pi − p−i )pi
θ−i+ (1 − θ−i )(v − λpi + d) = θi ,c2ττ + λp−iλpi
θi θ−i+ θi (1 − θ−i )(v + d) = θi θ−i+ 2λθi (1 − θ−i )pi .
2ττ24With abuse of notation, denote by θ k and p k the equilibrium investment and price levels,
respectively, under regime k = P, E. Imposing symmetry, the equilibrium values must solve
θP =2M (p P )p P
θ P τ + 2τ(1 − θ P )(v + d) θ P pS + 4τ(1 − θ P )pC
P
,
p
=
=
, (5)
2c + p P [2M (p P ) − 1]λ[θ P + 4τ(1 − θ P )]
θ P + 4τ(1 − θ P )where M (p) := min{v − λp + d, 1} to denote its dependence on p. Although the problem
is now substantially complicated, we can still show that it always yields a well-definedsolution.
Proposition 7. There exists a unique pair (θ P , p P ) that satisfies (5). Moreover, θ P is increasing in c while p P is increasing, with limc→0.5pC θ P = 1, limc→0.5pC p P = pS , limc→∞ θ P =0, limc→∞ p P = pC .
In contrast, the problem under category-specific DTCA is quite straightforward anddefined asτ − λ(pi − p−i ) c 2c− θi .
max pi Q Ei − θi2 = pi (θi + θ−i − θi θ−i )θ ∈[0,1],pi
2
2τ
2
The first-order conditions are given bypi (1 − θ−i )[τ − λ(pi − p−i )]= θi ,2τcτ + λp−i= λpi .
2
The optimal price is simple and obtained independently of (θi , θ−i ), meaning that there
is no strategic relationship between pricing and advertisement. The equilibrium values,
denoted by θ E and p E , are given by
θE =

5.3.

pE
τ
τ
E
=
,
p
=
p
=
.
S
2c + p E
2λc + τλWelfare implications of free market pricing

Consider a regulatory authority which contemplates to deregulate pharmaceutical pricing
by granting firms a higher degree of discretion over pricing. The welfare impact of sucha reform depends obviously on the regulated price that has been imposed prior to the
deregulation. For the sake of argument, suppose that the regulated price was initially
set at p = pS (the lowest possible equilibrium price), as it is perhaps natural to assume25

that pharmaceutical prices would rise after the deregulation. Under this circumstance,
the equilibrium price jumps up to p P > pS under product-specific DTCA while it remains
the same under category-specific DTCA. Welfare implications of free market pricing canthen be illustrated by examining how the two welfare measures under product-specific
DTCA respond to an exogenous variation in p; below, we will hence focus on the case of
product-specific DTCA to illustrate welfare consequences of free market pricing.
As in the case with price controls, it is first instructive to observe the effect of a change
in p on the advertisement expenditure. With some computation, we obtain
4M (p)c + 2pM 0 (p)(2c − p)
2pM 0 (p)(2c − p)
∂ θP c
∂ θP
=
+
=
−
,
∂p
[2c + p(2M (p) − 1)]2
∂ c p [2c + p(2M (p) − 1)]2
which indicates that the effect of an increase in p mirrors that of a decrease in c, the only
difference being that it may also change the market-size distortion under product-specificDTCA. In particular, when M (p) = 1 and hence M 0 (p) = 0 (no market-size distortion),
an increase in p is equivalent to a decrease in c, thereby allowing us to directly apply
the results obtained in the previous section. The reason for this is clear if we look at thefirms’ objective function: if M (p) = 1, the problem under product-specific DTCA can benormalized by p, so that only the price-cost ratio matters for the equilibrium allocation.
When M (p) < 1, on the other hand, there is an additional effect on the market-size
distortion, and the problem can no longer be normalized by the price. Since M 0 (p) = −λ <0, this makes the effect of an increase in p somewhat weaker. We can still show, however,that the overall effect is positive under some mild conditions. To this end, it suffices toshow that 4M (p)c > 2λp(2c − p) for all c ∈ [0.5p, ∞). This condition clearly holds if c issufficiently small and close to 0.5p. As c → ∞, this becomesM (p) ≥ λp ⇔

v+d
≥ p,
2λ

which generally holds because v+d
2λ is the upperbound of the equilibrium price. This argument suggests that the equilibrium advertisement expenditure is generally increasing inp.
Given this result, we now turn to the equilibrium firm profit. Taking partial derivativewith respect to p, we obtain
∂ πP
θP
∂ θP
=
[(2M 0 (p)p + 2M (p))(1 − θ P ) + θ P ] + [M (p)p(1 − 2θ P ) + (p − c)θ P ]
. (6)
∂p
2
∂p
26

The first term of the right-hand side is the direct effect of a price increase which is always
positive. An increase in p also induces an indirect effect via an increase in θ P . Since thefirms generally overinvest, this indirect effect is always negative as any further increasein the investment level from its equilibrium level can only lower the firm profit, given theprice. Despite this apparent tradeoff, we can show that the direct effect dominates, so thatan increase in the price level generally benefits the firms (see Proposition 8 below).
The situation is more complicated for the patient surplus. Taking partial derivativewith respect to p, we obtain∂ θP∂ PS PP ∂ PSSPP ∂ PSC=θ θ+ 2(1 − θ )+ [2θ P (PSS − PSC ) + 2(1 − θ P )PSC ]
, (7)
∂p
∂p
∂p
∂p
where
∂ PSS
∂ PSC
= −λp,= −λ[M (p) + M 0 (p)p] − τM (p)M 0 (p).
∂p∂pAgain, the first term captures the direct effect which is now negative. The second term is
the indirect effect which stems from an increase in θ P . In contrast to the equilibrium profit,
the indirect effect is positive because more investment is always beneficial for patients. The
effect of a price increase on the patient surplus is more ambiguous due to this tradeoff but
is still positive when the price is relatively low to begin with.
Proposition 8. (i) π P is increasing in p for all p ∈ (0, pC ]. (ii) PS P is increasing in p if p is
sufficiently small.
The first part of the proposition implies that the two forms of regulation are complementary in that the benefit of a less stringent advertisement regulation, i.e., productspecific DTCA, is amplified when it is combined with a less stringent price regulation. As
such, in the region where ∆PS > 0, product-specific DTCA and concurrent price liberalization are the right policy mix for a pro-business authority. This is, however, not necessarily
true for the welfare of patients as they suffer directly from a higher equilibrium price. Still,when the price level is sufficiently low to begin with, this negative effect is more than offset by an increase in the investment level.17 The intuition behind this result is that at a
price sufficiently close to zero, the firms make almost no investment, and there are hence
no informed patients who directly suffer from a price increase. Although more patients
become informed and are forced to incur more cost as the price increases, this effect is ofsecond order and is dominated by the indirect effect which is of first order.
17

The same reasoning suggests that the patient surplus is increasing in p if c is sufficiently large.

27

6.

Conclusion

This paper investigates the effect of regulating the content of DTCA in a pharmaceuticalmarket with emphasis on the distinction between product-specific and category-specificDTCA. Owing to a unique information structure of the market, the two different formsof DTCA generate different incentives to the pharmaceutical firms and induce different
responses from potential patients. We argue that although product-specific DTCA may
distort prescription decisions, this welfare loss is partly offset by stronger incentives toinvest in advertisement, which subsequently reduce the fraction of uniformed patients.
The overall welfare impact is ambiguous and depends, among other things, on the costeffectiveness of advertisement and the market-size distortion. When the cost of advertisement is relatively high, the interests of the pharmaceutical firms and potential patients are
better aligned, and there often exists a Pareto-improving policy choice: category-specific
DTCA is preferred when the market-size distortion is more severe while product-specific
DTCA is preferred when it is less so. As the cost of advertisement decreases, however, a conflict emerges between the firms and patients. In general, product-specific DTCA emerges
as the preferred choice for patients as the prescription distortion is more attenuated whileserving the educational purpose, but the firms are made worse off due to the overinvestment problem.
Throughout the analysis, we deliberately restrict our attention to the policy issue of
product-specific versus category-specific. In reality, however, other policy instruments canoften be utilized in conjunction with the content regulation. Pricing regulation, which we
discussed in section 5, is a case in point. Another possible instrument is the cost of advertisement, which may be controlled via tax/subsidy schemes or pre-clearance procedures ofadvertisement. Our analysis suggests that the impact of these policy interventions should
not be evaluated in isolation, because a change in underlying parameters may also affectthe optimal form of content regulation. We argue that this gives rise to an additional policy
dimension to consider and hope to see more work along this line in future.

References
AMALDOSS, W. AND C. HE (2009): “Direct-to-Consumer Advertising of Prescription Drugs:
A Strategic Analysis,” Marketing Science, 28, 472–487.
AMIR, R., D. MACHOWSKA, AND M. TROEGE (2021): “Advertising Patterns in a Dynamic

28

Oligopolistic Growing Market with Decay,” Journal of Economic Dynamics and Control,
131, 104229.
BALA, R. AND P. BHARDWAJ (2010): “Detailing vs. Direct-to-Consumer Advertising in the
Prescription Pharmaceutical Industry,” Management Science, 56, 148–160.
BREKKE, K. R. AND M. KUHN (2006): “Direct to Consumer Advertising in PharmaceuticalMarkets,” Journal of Health Economics, 25, 102–130.
DAI, C., R. S. STAFFORD,AND

G. C. ALEXANDER (2005):“National Trends in

Cyclooxygenase-2 Inhibitor Use Since Market Release: Nonselective Diffusion of a Selectively Cost-Effective Innovation,” Archives of Internal Medicine, 165, 171–177.
DAVE, D. AND H. SAFFER (2012): “Impact of Direct-to-Consumer Advertising on Pharmaceutical Prices and Demand,” Southern Economic Journal, 79, 97–126.
FROSCH, D. L., D. GRANDE, D. M. TARN, AND R. L. KRAVITZ (2010): “A Decade of Controversy: Balancing Policy With Evidence in the Regulation of Prescription Drug Advertising,” American Journal of Public Health, 100, 24–32.
GROSSMAN, G. M. AND C. SHAPIRO (1984): “Informative Advertising with DifferentiatedProducts,” The Review of Economic Studies, 51, 63–81.
HUSKAMP, H. A., J. M. DONOHUE, C. KOSS, E. R. BERNDT, AND R. G. FRANK (2008): “Generic
Entry, Reformulations and Promotion of SSRIs in the US,” PharmacoEconomics, 26, 603–
616.
JACOB, N. T. (2018): “Drug Promotion Practices: A Review,” British Journal of ClinicalPharmacology, 84, 1659–1667.
JØRGENSEN, S. AND S.-P. SIGUÉ (2015): “Defensive, Offensive, and Generic Advertising ina Lanchester Model with Market Growth,” Dynamic Games and Applications, 5, 523–539.
KALYANARAM, G. (2008): “The Order of Entry Effect in Prescription (RX) and Over-TheCounter (OTC) Pharmaceutical Drugs,” International Journal of Pharmaceutical and
Healthcare Marketing, 2, 35–46.
——— (2009): “The Endogenous Modeling of the Effect of Direct-to-Consumer Advertising in Prescription Drugs,” International Journal of Pharmaceutical and Healthcare Marketing, 3, 137–148.
KRAVITZ, R. L., R. M. EPSTEIN, M. D. FELDMAN, C. E. FRANZ, R. AZARI, M. S. WILKES, L. HINTON , AND P. F RANKS (2005): “Influence of Patients’ Requests for Direct-to-Consumer Ad-

29

vertised Antidepressants: A Randomized Controlled Trial,” Journal of American Medical
Association, 293, 1995–2002.
KRISHNAMURTHY, S. (2000): “Enlarging the Pie vs. Increasing One’s Slice: An Analysis of
the Relationship Between Generic and Brand Advertising,” Marketing Letters, 11, 37–48.
LIU, Q. AND S. GUPTA (2011): “The Impact of Direct-to-Consumer Advertising of Prescription Drugs on Physician Visits and Drug Requests: Empirical Findings and Public Policy
Implications,” International Journal of Research in Marketing, 28, 205–217.
MURRAY, E., B. LO, L. POLLACK, K. DONELAN, AND K. LEE (2003): “Direct-to-Consumer
Advertising: Physicians’ Views of Its Effects on Quality of Care and the Doctor-Patient
Relationship,” Journal of American Board of Family Medicine, 16, 513–524.
PAREKH, N. AND W. H. SHRANK (2018): “Dangers and Opportunities of Direct-to-Consumer
Advertising,” Journal of General Internal Medicine, 33, 586–587.
ROBINSON, A. R., K. B. HOHMANN, J. I. RIFKIN, D. TOPP, C. M. GILROY, J. A. PICKARD, AND
R. J. ANDERSON (2004): “Direct-to-Consumer Pharmaceutical Advertising: Physician
and Public Opinion and Potential Effects on the Physician-Patient Relationship,” Archivesof Internal Medicine, 164, 427–432.
ROSENTHAL, M. B., E. R. BERNDT, J. M. DONOHUE, R. G. FRANK, AND A. M. EPSTEIN (2002):“Promotion of Prescription Drugs to Consumers,” New England Journal of Medicine, 346,
498–505.
SANTARSIERI, D. AND T. L. SCHWARTZ (2015): “Antidepressant Efficacy and Side-Effect
Burden: A Quick Guide for Clinicians,” Drugs in Context, 4, 1–12.
SHAPIRO, B. (2020): “Promoting Wellness or Waste? Evidence from Antidepressant Advertising,” Becker Friedman Institute for Research in Economics Working Paper.
SHIN, J. AND J. YU (2021): “Targeted Advertising and Consumer Inference,” Marketing
Science, 40, 900–922.
SINKINSON, M. AND A. STARC (2018): “Ask Your Doctor? Direct-to-Consumer Advertisingof Pharmaceuticals,” The Review of Economic Studies, 86, 836–881.
SUFRIN, C. B. AND J. S. ROSS (2008): “Pharmaceutical Industry Marketing: UnderstandingIts Impact on Women’s Health,” Obstetrical and Gynecological Survey, 63, 585–596.
VENTOLA, C. L. (2011): “Direct-to-Consumer Pharmaceutical Advertisement: Therapeuticor Toxic?” Pharmacy and Therapeutics, 36, 669–684.

30

WEISSMAN, J. S., D. BLUMENTHAL, A. J. SILK, M. NEWMAN, K. ZAPERT, R. LEITMAN, AND
S. FEIBELMANN (2004): “Physicians Report On Patient Encounters Involving Direct-ToConsumer Advertising,” Health Affairs, 23, 219–233.

31

Appendix: Proof
Proof of Proposition 1. We have already seen that θ P > θ E always holds. Note also that
4M p
2p
∂ θP ∂ θE
−
=−
+
.
∂c
∂c
[2c + p(2M − 1)]2 (2c + p)2
This is negative if
4M p
2p
>
,
[2c + p(2M − 1)]2
(2c + p)2
which can be written as
2M (2c + p)2 > [2c + p(2M − 1)]2 .
With some computation, this is reduced to
4c 2 (2M − 1) + 4cp + p2 [2M − (2M − 1)2 ] > 0,
which holds for any M ∈ (0.5, 1].
Proof of Proposition 2. Define θ k and Q k , k = P, E, as functions of v, p, d and c. The
effects of v and d are identical. Note that Q P is increasing in v if
2c + p(2M − 1) > 2M p,
which for any c > 0.5p. This suggests that ∆Q is increasing in v and decreasing in d.
With respect to a change in c, observe that ∆Q = 81 > 0 at c = 0.5p and limc→∞ ∆Q = 0.
It is also straightforward to obtain
4M 2 p[2c − p(2M − 1)]
∂ θP
∂ QP
P
P
= [θ + (1 − 2θ )M ]
=−
,
∂c
∂c
[2c + p(2M − 1)]3
4cp
∂ QE
∂ θE
= (1 − θ E )
=−
.
∂c
∂c
(2c + p)3
It follows from this that ∆Q is decreasing in c if
M 2 [2c − p(2M − 1)]c>.
[2c + p(2M − 1)]3
(2c + p)332

Alternatively, the condition can be written as
F (c)G(c)3 >

1
,
M2

where
F (c) :=

2c + p2c − p(2M − 1)
, G(c) :=.
c
2c + p(2M − 1)

Evaluated at c = 0.5p, the condition is reduced to
F (0.5p)G(0.5p)3 =4(1 − M )
1
4
> M.
>
⇔
M3
M2
5

As c → ∞, on the other hand, we havelim F (c)G(c)3 = 2 >

c→∞

p
1
⇔
M
>
0.5.
M2

Note also that F G 3 is increasing in c if
F 0 G + 3F G 0 > 0,

(8)

where
F 0 (c) =p(2M − 1)
4p(1 − M ), G 0 (c) = −.
2c[2c + p(2M − 1)]2

It then follows that (10) can be written as
12p(1 − M )[2c − p(2M − 1)]p(2M − 1)(2c + p)>,
c 2 [2c + p(2M − 1)]c[2c + p(2M − 1)]2
which is simplified top(2M − 1)(2c + p) 12p(1 − M )[2c − p(2M − 1)]>.
c2c + p(2M − 1)Note that the left-hand side is strictly decreasing while the right-hand side is strictly increasing. This means that F G 3 may increase at the beginning but must eventually decreaseas c gets sufficiently large. Combined with the fact that F G 3 must converge to 2 regardlessof M , this fact allows us to pin down the shape of ∆Q. There are three possible cases weneed to investigate.
pCase 1 ( 0.5 > M ): In this case, F G 3 > M −2 when c is relatively small. At some point, F G 3
starts decreasing and converges to 2 which is lower than M −2 . This means that ∆Q first33

decreases and then increases, ultimately converging to 0. As such, there exists a uniquethreshold cQ (v, d) such that ∆Q > 0 if and only if cQ > c. Since ∆Q is increasing in v andd, the threshold cQ must also be increasing in v and d.
Case 2 (0.8 ≥ M ≥p0.5): In this case, F G 3 must invariably be smaller larger than M −2 ,which implies that ∆Q is monotonically decreasing with ∆Q > 0 for all c > 0.5p.
Case 3 (1 > M > 0.8): In this case, F G 3 is lower than M −2 when c is relatively small.
As c gets larger, it increases but then decreases and converges to 2 which is larger thanM −2 . This means that ∆Q first increases and then decreases with ∆Q > 0 for all c > 0.5p.
Proof of Proposition 4. Since
∂ ∆C
∂ θP
∂ θE
= 2θ P− 2θ E,∂c∂c∂c
we have
∂ ∆π
∂ θP
∂ θE
∂ θP
∂ θ E ∆C
= p[M − (2M − 1)θ P ]− p(1 − θ E )− cθ P+ cθ E
−
∂c
∂c
∂c
∂c
∂c
2
E
P2
E2
P
∂θ
θ −θ
∂θ
− cθ E−.
= (cθ P − M p)∂c∂c2
Observe that
2

2

θP
∂ θP Mp θE∂ θE p
=−
,
=−
,
2
∂c 2
2
∂c 4
which gives us
Mp ∂ θP  E p ∂ θE
∂ ∆πP
= cθ −− cθ +
∂c
2
∂c
4 ∂c
P
M p[2c − p(2M − 1)] ∂ θp(6c + p) ∂ θ E=−
2[2c + p(2M − 1)] ∂ c4(2c + p) ∂ c22(M p) [2c − p(2M − 1)] p2 (6c + p)=−+.
[2c + p(2M − 1)]32(2c + p)3
From this, ∆π is increasing in c if
3
4[2c − p(2M − 1)]2c + p1>= H(c)G(c)3 ,2M
6c + p2c + p(2M − 1)34

(9)

whereH(c) :=

4[2c − p(2M − 1)].
6c + pAs above, H G 3 is increasing in c if H 0 G + 3H G 0 > 0. With some computation, we obtain
H 0 (c) =16p(3M − 1),
(6c + p)2

so that this condition becomes
48p(1 − M )[2c − p(2M − 1)]
16p(3M − 1)(2c + p)>,
(6c + p)2 [2c + p(2M − 1)][2c + p(2M − 1)]2 (6c + p)
which is further simplified to(3M − 1)(2c + p) 3(1 − M )[2c − p(2M − 1)]>.
(6c + p)[2c + p(2M − 1)](10)Note that the right-hand side is decreasing in c while the left-hand side is increasing.
Evaluated at c = 0.5p, (10) becomes
3M − 12(1 − M )>.
3(1 − M )MThis holds if and only if M > 23 . In the limit as c → ∞, on the other hand, (10) becomes
3M − 1> 3,
3(1 − M )which holds if and only if M > 56 . This means that: if M > 65 , H G 3 is increasing for allc ∈ [0.5p, ∞); if 65 > M > 23 , H G 3 first increases and then decreases.
To complete the proof, we now check the boundary conditions for (9). It is easy toverify that (9) holds at c = 0.5p if M > 32 , so that ∆π increases at the beginning. Atpp
the other end, as c → ∞, this holds if 0.75 > M . Note also that 0.75 ≈ 0.866 > 65 .
p
This means that for M > 0.75, ∆π increases at first, then decreases and converges to 0,
proving that there exists a threshold cπ (v, d) such that ∆π > 0 if and only if c > cπ (v, d).
p
For 0.75 ≥ M ≥ 56 , on the other hand, ∆π is increasing for all c, and hence ∆π < 0 for
all c. We can also show that ∆π is increasing in v. Since a decrease in v is equivalent to apdecrease in M with p and d fixed, this means that ∆π < 0 for all c if 0.75 > M .

35

Finally, since ∆π is increasing in v, it is clear that cπ is decreasing in v. To show that
∆π is increasing in d, recall that the profit under product-specific DTCA is given byπP =pθ P [2M − (2M − 1)θ P ] c P 2
− θ ,
2
2

from which we obtain
∂ πP
∂ θP
= 2[M p P (1 − 2θ P ) + (p P − c)θ P ]+ p P θ P (1 − θ P )
∂d
∂d
∂ θP
= −(2M − 1)p P θ P+ p P θ P (1 − θ P ).
∂d
If v − λp + d > τ and M = 1, we have ∂∂θd = 0, and π P is increasing in d. If not, we haveP

2p(2c − p)
∂ θP
=
> 0.
∂d
[2c + p(2M − 1)]2
Given this, π P is increasing in d if
1−θP >

2p(2M − 1)(2c − p)
⇔ 2c > p(2M − 1),[2c + p(2M − 1)]2

which holds for any c > 0.5p.
Proof of Proposition 5. Observe that ∆PS =PSS
4 > 0 at c = 0.5p and limc→∞ ∆PS = 0.

It is also straightforward to obtain
8M p[2M p(PSS − PSC ) + (2c − p)PSC ]∂ PS P∂ θP= 2[θ P PSS + (1 − 2θ P )PSC ]
=−
,
∂c
∂c
[2c + p(2M − 1)]3
8pc
∂ PS E∂ θE= 2(1 − θ E )PSS
=−
PSS .
∂c
∂c
(2c + p)3
It follows from this that ∆PS is decreasing in c if
M 2 [2cφ − p[(2M + 1)φ − 2]]c>.
3[2c + p(2M − 1)](2c + p)3(11)Here, we extend the definition of F in the proof of Proposition 2 and, with slight abuse ofnotation, define
F (c; φ) =2cφ − p[(2M + 1)φ − 2),c36

so that (11) is given by
F (c; φ)G(c)3 >1.
M2Note that F (c; 1) = F (c).
Evaluated at c = 0.5p, (11) is reduced to
F (0.5p; φ)G(0.5p) =4(1 − M φ)
1
4
> M.
>
⇔
M3
M2
1 + 4φAs c → ∞, on the other hand, it converges tolim F (c; φ)G(c) = 2φ >

c→∞

Æ
1
⇔
M
>
0.5φ −1 .
M2Moreover, as in Proposition 2, we can show that F G 3 is increasing in c ifp[(2M + 1)φ − 2)(2c + p) 12p(1 − M ) [2c − p[(2M + 1)φ − 2)]]>,c 2 [2c + p(2M − 1)]c[2c + p(2M − 1)]2
which is simplified top[(2M + 1)φ − 2)(2c + p) 12p(1 − M ) [2c − p[(2M + 1)φ − 2)]]>,c
2c + p(2M − 1)
If (2M + 1)φ ≤ 2, F G 3 is weakly decreasing in c. If (2M + 1)φ > 2, we can essentiallyfollow the same argument as in Proposition 2. In either case, we can conclude that: (i)ppif M ≥ 0.5φ −1 , ∆PS > 0 for all c ∈ (0.5p, ∞); (ii) if 0.5φ −1 > M , there exists aninterior threshold c PS such that ∆PS > 0 if and only if c PS > c.
Finally, it is easy to verify that PS P is increasing in v while PS E is independent of it.
That c PS is increasing in v immediately follows from this fact.
Proof of Proposition 6. Observe that PS P is increasing in d if
∂ θPd[θ PSS + (1 − 2θ )PSC ]> θ P (1 − θ P ) .
∂d
τ
P

P

Note that if v − λp + d < τ,
2p(2c − p)
2M p(2c − p)
∂ θP
∂ θP
P
P
=
,
θ
(1
−
θ
)
=
=
M
.
∂d
[2c + p(2M − 1)]2
[2c + p(2M − 1)]2∂d

37

The condition can thus be written as
θ P PSS + (1 − 2θ P )PSC >Md,τwhich converges toPSC =M (v − λp − d)Md>
⇔ v − λp > 3d,2ττas c tends to infinity.

Proof of Proposition 7. DefineS(p) :=

θ pS + 4τ(1 − θ )pC
2M (p)p2(v + d)p − 2λp2=
, P(θ ) :=.
2
2c + p[2M (p) − 1] 2c − p[2(v + d) − 1] − 2λpθ + 4τ(1 − θ )It is clear that S is upward sloping in p if M (p) = 1. If M (p) < 1, we haveS(p) =

2(v + d)p − 2λp2.
2c − p[2(v + d) − 1] − 2λp2

Given this, S is upward sloping in p if
S 0 (p) =2(v + d − 2λp)(2c − p) + 2(v + d − λp)p[2c − p[2(v + d) − 1] − 2λp2 ]2> 0.

This condition can be written as(v + d − 2λp)(2c − p) + (v + d − λp)p > 0,
which holds for any p ∈ [0, pC ]. Similarly, P is downward sloping in θ if
(pS − 4τpC )[θ + 4τ(1 − θ )] − (1 − 4τ)[θ pS + 4τ(1 − θ )pC ][θ + 4τ(1 − θ )]2
4τ(pC − pS )=−< 0,
[θ + 4τ(1 − θ )]2

P 0 (θ ) =which clearly holds. This shows that there is always a unique pair that satisfies (5).
It is also clear that S shifts downward as c increases while P is not affected. This meansthat θ P is decreasing in c while p P is increasing. Moreover, it is easy to verify that θ P → 1
and p P = pS as c → 0.5pS and θ P → 0 and p P = pC as c → ∞.

38

Proof of Proposition 8. By rearranging (6), we obtain


θP
∂ θP
∂ πP
0
P
P
=
(2M p + 2M )(1 − θ ) + θ − 2M p
,
∂p
2
∂p
where M 0 = −λ if v − λp + d < 1 and M 0 = 0 if v − λp + d ≥ 1. Since
4M c + 2M 0 p(2c − p)
∂ θP
=
,
∂p
[2c + p(2M − 1)]2
π P is increasing in p if
8M 2 pc
2M p(2c − p)
PP
0P
+ 2M (1 − θ ) + θ −> 0.
2M p 1 − θ −[2c + p(2M − 1)]2
[2c + p(2M − 1)]2
Substituting θ P yields
2M p(2c − p)
8M 2 pc
2c − p
4M c
0
−
−
> 0,
2M p
+
2c + p(2M − 1) [2c + p(2M − 1)]2
2c + p(2M − 1) [2c + p(2M − 1)]2
which is simplified to
M 0 p(2c − p) + 2M c > 0.
When M = 1, M 0 = 0 and this condition clearly holds. When M < 1, we have2M c > λp(2c − p).

(12)

This condition holds at p = 0. Note also that the right-hand side is decreasing in p at first
and then becomes increasing while the left-hand side is strictly decreasing. This meansthat (12) holds for all p ∈ (0, pC ] if it holds at p = pC . This is the case if




v+d
v+d
v+d
2 v−λ
+ d c = (v + d)c >
2c −
,
2λ
2
2λ
which holds for any c.
Similarly, it follows from (7) that PS P is increasing in p if
[2θ P (PSS − PSC ) + 2(1 − θ P )PSC ]



∂ θP
> θ P λpθ P + 2(1 − θ P )[λ(M + M 0 p) + τM M 0 ] ,
∂p

where
PSS − PSC = (v − λp)(1 − M ) +39

τ
(2M 2 − 1).
4With some computation, we obtain
2M c + M 0 p(2c − p)
[2M p(PSS − PSC ) + (2c − p)PSC ]2c + p(2M − 1)
> M p λM p2 + (2c − p)[λ(M + M 0 p) + τM M 0 ] ,As p → 0, this condition is reduced to
4M c 2 PSC> 0,
2c + p(2M − 1)which always holds.

40

ΔQ

1
8

M = 0.95

M = 0.75

M = 0.6cFigure 1. The difference in market demand ∆Q (p = 0.6)

Δπc
M = 0.95

M = 0.75

M = 0.6

Figure 2. The difference in firm profit ∆π (p = 0.6)

41

PS S
4

ΔPS
M = 0.60
M = 0.95
M = 0.95

M = 0.6ccFigure 3: The diﬀerence in patient surplus ΔPS (v = 1.1, p = 0.6, τ = λ = 1)
Figure 3. The difference in patient surplus ∆PS (v = 1.2, p = 0.6, τ = λ = 1)

ΔQ > 0 if c small

ΔQ > 0Δπ < 0Δπ < 0 if c small

ΔPS > 0 if c small
0.5

√
0.5

ΔPS > 0�√
0.75 0.5φ−1

Figure 4: The welfare eﬀects of the content regulation: summary
Figure 4. The welfare effects of the content regulation: summary

42

31

M