Discussion Paper No. 1058

ADVERTISING REGULATIONSIN PHARMACEUTICAL MARKETS:
PRODUCT
VERSUSENLIGHTENMENT

Junichiro Ishida
Tsuyoshi Takahara

June 2019

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

Advertising Regulations in Pharmaceutical Markets:
Product Versus Enlightenment∗
Junichiro Ishida†
Tsuyoshi Takahara‡
June 17, 2019

Abstract
This paper analyzes the optimal content regulation of direct-to-consumer advertisement(DTCA) in a pharmaceutical market, with particular focus on the distinction between product and enlightenment advertisement. Firms are allowed to freely promote their own specificproducts under product DTCA, whereas they can only advertise the presence of a disease andits typical subjective symptoms under enlightenment DTCA. The content regulation changes
the nature of market competition and the incentive to invest in advertisement, thereby yielding
substantial welfare and policy implications. The overall welfare impact of the content regulation is ambiguous and depends, among other things, on the cost effectiveness of advertisement
and the market-size distortion induced by product DTCA. We also analyze the effect of freemarket pricing and argue that a less stringent advertisement regulation, i.e., product DTCA, isoften complementary to a less stringent price regulation.

JEL Classification Code: M37, I11, I18
Keywords: DTCA, Advertisement content regulation, Prescription decision∗

The authors acknowledge the financial support of the Japan Society for Promotion of Science (JSPS) via Grantsin-Aid for Scientific Research (15H05728).
†
Institute of Social and Economic Research, Osaka University. E-Mail: jishida@iser.osaka-u.ac.jp‡
School of Business Administration, Kwansei Gakuin University. E-Mail: takahara@a0.rusk.to1Introduction

Marketing activities, such as TV advertisement, play a very important role in the pharmaceuticalindustry. According to Sufrin and Ross (2008), Pfizer, Merck, and Bristol-Meyer-Squibb – thethree biggest pharmaceutical firms in the US – spend a greater share of expenditure on marketing
than R&D activities in 2005. Although a large fraction of advertisement is directed 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 Foodand Drug Administration (FDA) in 1997. Owing to some unique features of the industry, however, many experts and practitioners suspect the effectiveness of DTCA in pharmaceutical markets
by noting the possibility that it may distort prescription decisions. There is now a heated debate
worldwide about whether DTCA should be regulated, and if so, in what ways.
A body of evidence suggests that DTCA in the pharmaceutical industry can in fact be a doubleedged sword. As proponents of DTCA insist, it could serve an educational purpose by informing
patients of a particular medical condition and a potential treatment, thereby encouraging themto contact a health care provider at an opportune time. Opponents of DTCA argue, however,that it often misinforms patients, by selectively omitting risk factors or causes of the conditionand overemphasizing drug benefits (see Section 2.6 for more discussion on this).1 Among those,
Ventola (2011) notes:
If a patient’s request for an advertised drug is clinically inappropriate and the healthcare provider is unable or unwilling to correct the patients perception that it is a good
choice, this situation may lead to unnecessary or harmful prescribing. 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 be appropriate for them.
To sum up, giving information to patients is beneficial to the extent that it brings them toclinics in search of medical treatment, but anything more than that could just disturb the physicianpatient relationship and cause unnecessary complications. If this is the case, there may be a scope
1

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

2for welfare improvement by regulating the content of DTCA. One way to do this is to requirethat DTCA only describe the presence of a disease and its typical symptoms and treatments but
without any information about particular brand names or products – the type of advertisement often
called enlightenment or help-seeking advertisement. This is precisely what has been done in many
countries outside of the US where DTCA is permitted only if it is enlightenment in nature.2
At a glance, enlightenment DTCA can be an effective remedy for the distortion caused by
DTCA in pharmaceutical markets because it only provides minimal information to patients whilestill serving the educational purpose. However, the welfare impact of such a regulation is notnecessarily so straightforward, especially in pharmaceutical markets that are typically oligopolisticand dominated by a few major firms, as it alters the strategic nature of market competition. In
particular, under enlightenment 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 allin the end.
In this paper, we investigate how the content regulation of DTCA (hereafter, simply the content
regulation) affects pharmaceutical firms’ expenditures on advertisement and welfare to contributeto 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 how much 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(product DTCA); in the other, they can only provide general information about a disease and its
typical symptoms without specifying their own brand names (enlightenment DTCA).
The difference in the nature of DTCA gives different incentives to the pharmaceutical firms andinduces different responses from potential patients. Under enlightenment DCTA, no specific information about a particular product is available, and all informed patients are largely neutral withrespect to the two available products. Under product DTCA, on the other hand, informed patients2

Outside of the US, New Zealand is the only OECD country which allows DTCA that includes product names. In
other countries, there are some regulations on the extent that a firm can promote its own brands or products, virtuallyprohibiting product DTCA.

3

may develop a biased preference for a particular product, depending on the extent of exposure to
DTCA. Borrowing from Brekke and Kuhn (2006), we call them 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 effectof 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 while captive patients,
with a biased attachment, insist on the product they have in mind and needs to be persuaded if analternative measure is to be taken.
The key assumption we make here is that 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 the presence of the persuasion cost, which imposes an extra burden on thephysician, creates two forms of market distortion under product DTCA: on one hand, a fractionof captive patients may receive no treatment; on the other hand, they may also be prescribed thesuboptimal 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 thelatter as the “prescription distortion.” These two forms of distortion depend on various parameters
in a somewhat complicated way and play a major role in our welfare analysis.
Main results: We obtain several results regarding the costs and benefits of product DTCA vis-avis enlithenment DTCA. Our argument centers around the interactions between the two forms ofmarket distortion mentioned above and the strategic investment incentives that are crucially shapedby the context regulation in effect.
First, it is intuitively clear that the firms invest more in advertisement under product DTCA thanunder enlightenment DTCA. In fact, the advertisement competition is excessively strong under
product DTCA because of the potential of business stealing, as a consequence of which the firms
overinvest in advertisement compared to the first-best level. Under enlightenment DTCA, on theother hand, the incentives to inform patients via advertisement are substantially weaker due toit public-good nature, and the firms indeed underinvest compared to the first-best level. Despite
the apparent distortion in prescription decisions induced by product DTCA, the welfare effect of
4the content regulation is thus ambiguous because the stronger, though excessive, incentives toinvest in advertisement 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 impact of the content regulation. When the cost of advertisement is relatively high, the interests of the firms andpotential patients are better aligned, and there often exists a Pareto-improving policy choice. The
optimal policy in this case is largely determined by the extent of the market-size distortion induced by product DTCA: enlightenment DTCA is preferred when the market-size distortion ismore severe while product DTCA is preferred when it is less so. As the cost of advertisement
decreases, however, the overinvestment problem becomes more of a factor, and a serious conflictarises between the firms 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
the likelihood of being left out and helps them seek treatment in time. In general, patients are madebetter off product 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 the source ofmarket distortion in our setup, the welfare impact of the persuasion cost is not entirely negative.
This is 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 theprescription 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 of regulated
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 thehigher equilibrium price. This suggests that the two forms of regulation are often complementary
to each other in that a less stringent advertisement regulation, i.e., product DTCA, tends to becompatible with a less stringent price regulation – the type of policy mix adopted in the US – and5hence should be evaluated jointly.
Literature: The existing literature on DTCA in the pharmaceutical industry is mostly empirical(Rosenthal et al., 2003; Donohue et al., 2004; Iizuka, 2004; Iizuka and Jin, 2007; Bradford et al.,2010; Sinkinson and Starc, 2018), and there are only a handful of theoretical analyses, despite theongoing debate over the desirability of DTCA.3 Among them, our model is most closely related toand draws on Brekke and Kuhn (2006) who investigate the strategic relationship between DTCA
and detailing (marketing to physicians). A crucial difference is that their focus is on how muchinformation to disseminate to physicians via marketing while their DTCA is enlightenment innature as its only role is to bring them to clinics.4 Here, we attempt to shed light on a different
aspect of the problem by making a clear distinction between product and enlightenment DTCA.
To the best of our knowledge, this is the first work which emphasizes this distinction and analyzes
the impact of the content regulation of DTCA.
Our work also has an obvious connection to analyses of advertisement in industrial organization. In conventional analyses of advertisement, consumers precisely know their preferences (orpayoff functions). Here, the situation we deal with is somewhat special in that physicians, with
their expertise, posses far more knowledge about what patients need than patients themselves:specifically, we assume that patients are lined up on a Hotelling line without knowing their exact
location which only physicians 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 interventions. Although we cast our analysis in a specific context of advertisement competition, we believe that this problem can provide a broader perspective as it is arealistic and pervasive issue in the medical industry to what extent patients should be informed.
3

A recent exception is Bar and Lillard (2014) who analyze a situation where there are two alternative treatments,and one of them is advertised directly to patients by a profit-maximizing pharmaceutical firm.
4
In their model, there are captive and selective physicians, but on such distinction is made for patients.

6

2

The Model

2.1

Environment

We consider a market of prescription-only drugs for a particular disease that comprises of two pharmaceutical firms, potential patients (male) and a representative physician (female). In this market,
potential patients with unit mass are horizontally 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, where firm 0 is located at the left end of the Hotelling line whilefirm 1 is located at the right end. We suppose that the two firms supply pharmaceutical products for the same disease although their products are horizontally differentiated by their chemicalcompounds and consequent treatment effects.

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 byvisiting a physician. Let θi denote the fraction of patients who are exposed to firm i’s advertisement.
The demand for firm i’s product (product i) is assumed to be a function of (θi , θ−i ), i , −i anddenoted as Qi (θi , θ−i ). Firm i’s profit is then given byc
πi = pi Qi (θi , θ−i ) − θi2 ,2where pi denotes the price of product i, and c the cost effectiveness of advertisement.
As most of our key insight can be illustrated under regulated prices, we assume for now that thepharmaceutical prices are fixed exogenously at p = p0 = p1 based on factors that are not directly
related to the issue at hand. The assumption of regulated prices is a relevant one in most countries
outside the US while we will extend our analysis to allow the firms to set prices endogenously insection 5. To ensure the existence of interior solutions, we also assume that c is large relative to p.
Assumption 1. 2c > p.

7

2.3

Patients

A patient receives medical treatment when he visits a physician. The utility derived by patient 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” which measures the quality/characteristic diversion
between the two products.
The key assumption is that a patient’s type x can be observed only by the physician but notby the patient himself – a defining characteristic of the pharmaceutical industry – 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 specific product-patient type match. We assume that eachproduct is effective enough to ensure that it is beneficial even for the most “distant” patient (atx = 0.5).
Assumption 2. 2(v − λp) > τ.
The utility of patients who receive no treatment (either by their own or the physician’s choice)is normalized to 0.

2.4

Advertising regulation

Throughout the analysis, we consider two regulatory regimes on the content of DTCA: productand enlightenment. Under product DTCA, a pharmaceutical firm is allowed to provide information
about a specific product, including its brand name or the names of chemical components.5 Then,
5
An important premise of our analysis is that product DTCA is effective in raising the demand for its own product(via business stealing) and indeed generates different effects from enlightenment DTCA. Of course, if product andenlightenment DTCA make no difference, the whole debate over DTCA becomes groundless; the current debate over
DTCA reflects physicians’ perception that product DTCA does make a difference at some level. Although empiricalevidence on this issue may not be not conclusive (see, for instance, Iizuka and Jin (2007) who find no significant
effect of DTCA on the market share), there is in fact some evidence in support of this claim (Kalyanaram, 2008, 2009;
Liu and Gupta, 2011; Dave and Saffer, 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.

8

when the firms are allowed to engage in product 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 withprobability 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 );6• A patient is uninformed if he is exposed to advertisement from neither, which occurs withprobability (1 − θi )(1 − θ−i ).
In contrast, when the firms are restricted to enlightenment DTCA, they can only provide general
information about the presence of a disease and its symptoms without specifying particular brandnames or products. Under enlightenment 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 ).

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 toprovide no treatment (or an outside treatment). The physician is partly altruistic in that she cares
about the welfare of attending patients net of the “persuasion cost.” The utility of the physician
depends on the attending 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 givenby u(x, i). The physician thus simply prescribes the more suitable product for the patient.7
Second, if a patient is captive, he has developed a biased preference in favor of a particular
product and makes a specific request for it. We assume in this case that the physician either
6

We assume that a patient becomes captive when he is exposed only to one of the products. Although this may
appear a strong assumption to impose, our conclusions hold in a qualitative as long as there is a positive fraction ofpatients who become captive.
7
Under Assumption 2, it is never optimal to provide no treatment in this case.

9prescribes the product as requested or provides no treatment.8 If the physician takes the option ofno treatment, she must incur a persuasion cost d which includes time, effort, and psychologicaldiscomfort 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.

2.6

Discussion on distorted prescription decisions

The key premise of our analysis is that product DTCA may disturb the physician-patient 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 thatpatients 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; atthe same time, health-related problems are always emotionally arousing, and it is also very difficult
to stay perfectly rational by taking emotion entirely out of the decision process. On the other hand,
physicians are also humans with limited resources and persuasion is never free. A combination ofthese two factors necessarily gives rise to some distortion in prescription decisions.
To motivate our analysis further, there is also ample evidence which suggests that giving detailed information to patients via product DTCA creates seemingly unnecessary complications andpsychological pressures to physicians. Murray et al. (2003) report that many physicians feel that
DTCA worsens the time efficiency of the visit and have a negative response to the recent increase
in DTCA.9 Moreover, it is well documented that many physicians have prescribed inappropriate
drugs which are requested by patients.10 Kravitz et al. (2005) also report that patients’ requests
8

We assume that it is more costly to persuade a captive patient into taking the other product and hence do notconsider this possibility. More generally, we may assume that the physician can prescribe the unrequested product byincurring a cost D where D > d. Our setup can then be interpreted as the one in which D is prohibitively large. We
focus on this extreme case because our results do not change in a qualitative sense even when D is lower and finite
because any market distortion that can arise in this process will be captured thoroughly by two distortion measures, M
and φ, which we will define later.
9
Robinson et al. (2004) also report that “few (physicians) believe that these advertisements are a positive trend in
health care.
10
Frosch et al. (2010) and Ventola (2011) survey literature on the effect of DTCA on the physicians’ prescription
decision. In Frosch et al. (2010), they conclude that the request for the advertised product by the patients increases
both appropriate and inappropriate prescribing, though it is unclear which effect is greater. Weissman et al. (2004)
show that the physicians who consider DTCA positively prescribe more DTCA drug than the physicians who consider
DTCA negatively. Dai et al. (2005) insists that the marketing activities by Merck may grow the use of Vioxx, which
is discontinued due to fatal side effects.

10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 DTCA. Additionally, the persuasion cost may seem to differ acrosssymptoms. For instance, Kravitz et al. (2005) find that the influence of patients, especially brandspecific requests, on the prescription of antidepressants is higher for adjustment disorder than for
major depression and argue that DTCA may stimulate prescribing more for questionable than forclear indications. This line of 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
scientific evidence.

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 thepatient’s informational type as we describe below.
Suppose first that a patient is selective (exposed to both products). Under Assumption 2, thephysician recommends product 0 (1) if 0.5 ≥ x (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 forselective patients, this is the competitive segment of the market.
If a patient is captive (exposed only to one of the products), on the other hand, the physician
chooses either to prescribe the product he requests or to provide no treatment. 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 the benefit exceeds the persuasion cost, i.e.,v − λp − τ|x − i| ≥ −d.

11The demand for each product in the monopolistic segment is then given by)v − λp + d
M := min,1 .
τ
(By Assumption 2, M > 0.5, so that each firm can capture a larger market share, partly at theexpense of the physician who is forced to incur the persuasion cost.
Note that the presence of the persuasion cost generates two forms of distortion in prescription
decisions. First, there is a fraction of captive patients who end up with receiving no treatment. For
the sake of exposition, we call this the “market-size distortion,” the size of which is captured byM, as it limits the industry demand below its efficient level. We say that the market-size distortionis 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 fraction of captive patients who are prescribed the suboptimal product.
This form of distortion is called the “prescription distortion,” which we will discuss in depth when
we analyze the welfare 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 as given.
First, under product DTCA, a patient is selective with probability θi θ−i and captive of i with probability θi (1 − θ−i ). The demand for product i under product DTCA is then obtained asQiP =θi θ−i+ θi (1 − θ−i )M,2

where the superscript P stands for product DTCA. It follows from this that firm i’s problem under
product DTCA can be written asmax

θi ∈[0,1]c
pQiP − θi2 = p
2

θ θ

c
+ θi (1 − θ−i )M − θi2 .
2
2

i −i

The best-response function is given byθi =p[2M − θ−i (2M − 1)] .
2c

12



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

2M p
.
2c + p(2M − 1)Note that 1 > θ P by Assumption 1.
Second, there are no captive patients under enlightenment DTCA. The demand under enlightenment DTCA is hence given by
QiE =θi + θ−i − θi θ−i,2where, as above, the superscript E stands for enlightenment DTCA. As such, firm i’s problem
under enlightenment DTCA can be written asc
θi + θ−i − θi θ−i c 2
max pQiE − θi2 = p− θi .
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 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),13which holds for any M ∈ (0.5, 1]. In words, there is a private gain from DTCA when the firms
are allowed to promote their own products, giving them more incentive to invest in advertisement.
Moreover, we can show that the difference in the advertisement expenditures widens as c getssmaller. We summarize these findings below.
Proposition 1. The advertisement expenditure is higher under product DTCA than under enlightenment DTCA. Moreover, the difference between θ P and θ E is strictly decreasing in c.
Proof. We have already seen that θ P > θ E always holds. Note also that∂θ P ∂θ E
4M p
2p
−
=−
+
.
2
∂c
∂c
[2c + p(2M − 1)](2c + p)2
This is negative if
4M p
2p
>
,
2
[2c + p(2M − 1)](2c + p)2
which can be written as
2M(2c + p)2 > [2c + p(2M − 1)]2 .
With some computation, this is reduced to
4c2 (2M − 1) + 4cp + p2 [2M − (2M − 1)2 ] > 0,
which holds for any M ∈ (0.5, 1].

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 DTCA expands the potential market size due to higher
advertisement expenditures, prescription decisions are necessarily distorted. To see this, observe

14

that
∆Q := QP − QE =

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 product is higher under
enlightenment 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"#22c + p(2M − 1)
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 in 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 ≥ 0.5. For M ∈ [0.5, 0.5), there exists aninterior 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.
Proof. See Appendix.
[Figure 1 about here]

3.4

First best

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 to derive the15

first-best 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 first-best level under product DTCA can be obtained by solving the following problem:
" 2
#
c
θ
max p
+ θ(1 − θ)M − θ2θ∈[0,1]
2
2
Let θ P∗ denote the first-best level under product 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 dueto the business-stealing effect of advertisement: a firm can “steal” a fraction of captive patients byreaching out to them and transforming them into selective.
Similarly, the problem under enlightenment DTCA is defined aspc(2θ − θ2 ) − θ2θ∈[0,1] 2
2
max

As above, let θ E∗ denote the first-best level under enlightenment DTCA, which is given byθ E∗ =p.
c+ p

It follows from this that θ E∗ > θ E , i.e., the firms underinvest in advertisement under enlightenment
DTCA. Aside from the fact that there is no business-stealing effect, this is due to the fact thatadvertisement under enlightenment DTCA is a public good which also increases the demand forthe rival product as well. We summarize these findings in the following proposition.
Proposition 3. The firms overinvest in advertisement under product DTCA and underinvest under
enlightenment DTCA.

16

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 k what wecall the patient surplus (to be defined more precisely below). We consider a regulatory 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 one while it is “pro-patient” when ω is close to zero.11

4.2

Firm profit

We first examine how the content regulation affects the firms’ equilibrium profit. Letting ∆π :=22

πP − πE , ∆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
"
#
∆θ (2M − 1)p + c P
EEE= −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 this effect which is negative for any
1 > M. The second term captures the difference in the gains from demand expansion. Note thatthe sign of this effect is ambiguous, because the firms tend to overinvest under product DTCA,
diminishing their profit margins with excessive competition in advertisement.
We have already characterized ∆Q in Proposition 2. Also, from Proposition 1, we know ∆C ≥0, meaning that ∆Q < 0 is a sufficient condition for ∆π < 0. This implies that the firms are more
11

We do not take into account the persuasion cost incurred by the physician.

17likely to prefer enlightenment DTCA to product DTCA. In fact, this is always the case when M isrelatively small, i.e., the market-size distortion is relatively large, as the next proposition suggests.
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.
Proof. See appendix.
[Figure 2 about here]

4.3

Patient surplus

From the viewpoint of policymaking, the welfare of patients often carries more weight than that offirms. Since the payoff of uninformed patients is invariably zero, we only need to consider selective
and captive patients. Let PS S and PS C denote the patient surplus for selective and captive patients,
respectively. Also, define PS k as the total patient surplus under regime k = P, E, where2

PS P = θ P PS S + 2θ P (1 − θ P )PS C
PS E = θ E (2 − θ E )PS S .
First, selective patients always end up with the most suitable product. The patient surplus forthis group of patients is hence given by
PS S = 2Z 12(v − λp − τx)dx0τ
= v − λp − .
4On the other hand, captive patients are prescribed the requested product as far as the patient benefit
exceeds the persuasion cost. The patient surplus for this group of patients is given by
PS C =Z M(v − λp − τx)dx0= (v − λp)M − τ
18

M2
.
2

Defineφ :=4(v − λp) − 2τM,
4(v − λp) − τCsuch that Mφ := PS
which we use as a measure of the overall distortion in prescription decisions
PS S(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). There are hence two ways toimprove the patient surplus, either to increase the number of selective patients or to decrease thenumber of uniformed patients. More precisely, similarly as above, define ∆PS := PS P − PS E ,which is given by2∆PS = θ P PS S + 2θ P (1 − θ P )PS C − θ E (2 − θ E )PS S= −2θ P (1 − θ P )(PS S − PS C ) + ∆θ(2 − θ P − θ E )PS S(3)Again, the impact of the content regulation can be decomposed into two factors. The first termof the right-hand side of (3) captures the loss due to the distortion in prescription decisions under
product DTCA: this fraction of patients would have been selective under enlightenment DTCA but
become captive under product DTCA. Since PS S > PS C , this term is always negative. The second
term captures the demand-expansion effect under product DTCA, which is always positive.
To conduct comparative statics on ∆PS , we write (3) as∆PS =4M p[M pPS S + (2c − p)PS C ] p(4c + p)PS S−.
[2c + p(2M − 1)]2
(2c + p)2

From this, ∆PS > 0 if and only if"#2
4M 2 [p + (2c − p)φ]2c + p(2M − 1)>.
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 c tends to infinity.
19

Second, as the demand-expansion effect dominates, this condition holds at c = 0.5p. Following thesame procedure, we can establish the following claim which runs parallel to Proposition 2, except
for the effect of d which we will discuss in more depth in the next subsection.
p√√
Proposition 5. ∆PS > 0 for all c ∈ [0.5p, ∞) if M φ ≥ 0.5. For M ∈ [0.5, 0.5φ−1 ), there
exists an interior threshold cPS (v, d) such that ∆PS > 0 if and only if cPS (v, d) > c. Moreover,cPS (v, d) is increasing in v.
Proof. See appendix.
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, and there often exists a Paretoimproving regime, depending on the extent of the market-size distortion: enlightenment DTCA ispreferred when the market-size distortion is more severe (M close to 0.5) while product DTCA
is preferred when it is less so (M close to 1). As c decreases, however, a conflict arises between
them. In general, product DTCA becomes the preferred choice for patients when c is relatively
small, because the benefit of product DTCA is maximized while the distortion in prescription
decisions becomes more attenuated.12 However, the firms are generally worse off under product
DTCA because the overinvestment problem becomes more serious as the cost of advertisement
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 to patientsfor two reasons. First, the size of the market for captive patients is restricted as only a fraction Mof them receive any treatment (the market-size distortion). Second, among those who do receive
treatment, some of them are prescribed the suboptimal product (the prescription distortion). The
To see this, consider an extreme case where c = 0.5p and hence θ P = 1. In this case, the patient surplus ismaximized because patients are all selective. Patients are clearly made better off under product DTCA as it causes no
distortion while serving the educational purpose to the full extent.
1220

distortion in prescription decisions can be decomposed into two parts, where the ratio φ measures
the size of the prescription distortion (corrected for the market size). Obviously, there arises noprescription distortion (φ = 1) when τ = 0, i.e., when the two products are perfect substitutes.
One crucial determinant of the overall distortion Mφ is the persuasion cost d. An interesting
point to note is that the effect of the persuasion cost is not entirely negative because a change ind affects M and φ in different ways: an increase in d raises M (less market-size distortion) but
lowers φ (more prescription distortion). The former effect is conducive to more investment andcan be welfare-improving under product DTCA (as evidenced by the facts that QP and πP are bothincreasing in d). The effect on the patient surplus is, however, more ambiguous as it also involves
the prescription distortion. Below, we dissect how a change in the persuasion cost d affects thepatient surplus.
Since the distortion due to the persuasion cost only arises under product DTCA, we restrict ourattention only to this case. Recall that the patient surplus under product DTCA is given by
PS P = θ P [θ P PS S + 2(1 − θ P )PS C ].
Taking partial derivative with respect to d yields
∂PS P
∂θ P
∂PS C
= 2[θ P PS S + (1 − 2θ P )PS C ]+ 2θ P (1 − θ P )
.
∂d
∂d
∂d
The first term of the right-hand side reflects the indirect effect of d, which works through its 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∂PS Cd= − < 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. If v − λp > 3d, PS P increases with d for a sufficiently large c.

21

Proof. Observe that PS P is increasing in d if
[θ P PS S + (1 − 2θ P )PS C ]∂θ Pd> θ P (1 − θ P ) .
∂dτWith some computation, this condition can be written as
θ P PS S + (1 − 2θ P )PS C =2M p(PS S − PS C ) + (2c − p)PS C
Md>,
2c + p(2M − 1)τwhich converges to
PS C =

M(v − λp − d) Md>⇔ v − λp > 3d,2ττas c tends to infinity.
Q.E.D.
The proposition suggests that market distortions, in the form of a higher d, can be a blessingin 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 atsome 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.

22

5.1

Optimal pricing

We now consider a setting where each firm simultaneously chooses both the investment level θiand the price pi . Given the price pair (p0 , p1 ), patient x in the competitive segment ends up withproduct 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
QiP = θi θ−iτ − λ(pi − p−i )+ θi (1 − θ−i )(v − λpi + d),2τ

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

τ − λ(pi − p−i ),2τ

and the (symmetric) optimal price is given by pS := λτ . Similarly, if all patients are captive, eachfirm maximizespi (v − λpi + d),
and the optimal price is given by pC := v+d. Naturally, the equilibrium price is bounded between
2λpS and pC (and is in fact a weighted average of the two). This implies that free market pricing
23

has little bite when pC and pS are sufficiently close to each other, in which case the equilibrium
allocation can be approximated 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 toAssumptions 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 is beneficial even for the most distantpatient. The following assumptions provide sufficient conditions for these two properties.
Assumption 4. 2c > pC .
Assumption 5. 2(v − pC ) > 1.
Under these assumptions, the problem faced by firm i under product DTCA is formulated asmax

θi ∈[0,1],picpi QiP − 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 .
2ττWith abuse of notation, denote by θk and pk the equilibrium investment and price levels, respectively, under regime k = P, E. Imposing symmetry, the equilibrium values must solve
θP =2M(pP )pP
θ P τ + 2τ(1 − θ P )(v + d) θ P pC + 4τ(1 − θ P )p M
P
,
p
=
=
,
2c + pP [2M(pP ) − 1]λ[θ P + 4τ(1 − θ P )]
θ P + 4τ(1 − θ P )

24

(5)

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-defined solution.
Proposition 7. There exists a unique pair (θ P , pP ) that satisfies (5). Moreover, θ P is increasing inc while pP is increasing, with limc→0.5pS C θ P = 1, limc→0.5pC pP = pS , limc→∞ θ P = 0, limc→∞ pP =pC .
Proof. See appendix.
In contrast, the problem under enlightenment DTCA is quite straightforward and defined ascτ − λ(pi − p−i ) c 2
max pi QiE − θi2 = pi (θi + θ−i − θi θ−i )− θi .
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 andpE , are given by
θE =

5.3

pE
τ
τ
=
, p E = pS = .
E
2c + p2λc + 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 such a reform depends
obviously on the regulated price that has been imposes prior to the deregulation. For the sake of argument, suppose that the regulated price was initial set at p = pS (the lowest possible equilibrium
price), as it is perhaps natural to assume that pharmaceutical prices would rise after the deregulation. Under this circumstance, the equilibrium price jumps up to pP > pS under product DTCA
while it remains the same under enlightenment DTCA. Welfare implications of free market pric25

ing can then be illustrated by examining how the two welfare measures respond to an exogenous
variation in p.
As in the case with price controls, it is first instructive to observe the effect of a change in p on
the advertisement expenditures. With some computation, we obtain∂θ P c2pM 0 (2c − p)∂θ P 4Mc + 2pM 0 (2c − p)
=
=
−
+
,
∂p
[2c + p(2M − 1)]2
∂c p [2c + p(2M − 1)]2∂θ E
2c
∂θ E c==−,∂p(2c + p)2∂c pwhich 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 DTCA. In particular, when
M = 1 and hence M 0 = 0 (no market-size distortion), an increase in p is equivalent to a decrease inc, thereby allowing us to directly apply the results obtained in the previous section. The reason forthis is clear if we look at the firms’ objective function: if M = 1, the problem under product DTCA
can be normalized by p, so that only the price-cost ratio matters for the equilibrium allocation.
When M < 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 = −λ < 0, this makes theeffect of an increase in p somewhat weaker. We can still show, however, that the overall effect ispositive under some mild conditions. To this end, it suffices to show that 4Mc > 2λp(2c − p) for allc ∈ [0.5p, ∞). This condition clearly holds if c is sufficiently small and close to 0.5p. As c → ∞,this becomesM ≥ λp ⇔

v+d
≥ p,
2λ

which generally holds because v+d
is the upperbound of the equilibrium price. This argument
2λsuggests that the equilibrium advertisement expenditure is generally increasing in p under either
regime.
Given this result, we now turn to the equilibrium firm profit. Taking partial derivative withrespect to p, we obtainP∂πP θ P
0
P
P
P
P ∂θ
= [(2M p + 2M)(1 − θ ) + θ ] + [M p(1 − 2θ ) + (p − c)θ ]
.
∂p
2
∂p

26

(6)

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 the firms generally
overinvest, this indirect effect is always negative as any further increase in the investment levelfrom its equilibrium level can only lower the firm profit, given the price. Despite this apparent
tradeoff, we can show that the direct effect dominates, so that an increase in the price level generally
benefits the firms (see Proposition 8 below).
The situation is more complicated for the patient surplus. Taking partial derivative with respect
to p, we obtain
"
#
∂PS P
∂θ P
P
P ∂PS SP ∂PS C=θ θ
+ 2(1 − θ )+ [2θ P (PS S − PS C ) + 2(1 − θ P )PS C ]
,
∂p
∂p
∂p
∂p

(7)

where
∂PS C
∂PS S
= −λp,= −λ(M + M 0 p) − τMM 0 .
∂p∂p
Again, the first term captures the direct effect which is now negative. The second term is theindirect 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 priceincrease on the patient surplus is more ambiguous due to this tradeoff but is still positive when theprice is relatively low to begin with.
Proposition 8. (i) πP is increasing in p for all p ∈ (0, pC ]. (ii) PS P is increasing in p if p is
sufficiently small.
Proof. See appendix.
The first part of the proposition implies that the two forms of regulation are complementary inthat the benefit of a less stringent advertisement regulation, i.e., product DTCA, is amplified when
it is combined with a less stringent price regulation. As such, in the region where ∆PS > 0, product
DTCA and concurrent price liberalization are the right policy mix for a pro-business authority. Thisis, 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 effect27

is more than offset by an increase in the investment level.13 The intuition behind this result isthat 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 of second order andis dominated by the indirect effect which is of first order.

6

Conclusion

This paper investigates the effect of regulating the content of DTCA in a pharmaceutical market
with emphasis on the distinction between product and enlightenment DTCA. Owing to a uniqueinformation structure of the market, the two different forms of DTCA generate different incentives
to the pharmaceutical firms and induce different responses from potential patient. We argue that
although product DTCA may distort prescription decisions, this welfare loss is partly offset bystronger incentives to invest in advertisement, which subsequently reduce the fraction of uniformed
patients.
The overall welfare impact is ambiguous and depends, among other things, on the cost effectiveness of advertisement and the market-size distortion. When the cost of advertisement isrelatively high, the interests of the pharmaceutical firms and potential patients are better aligned,
and there often exists a Pareto-improving policy choice: enlightenment DTCA is preferred whenthe market-size distortion is more severe while product 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 DTCA emerges as the preferred choice for patients as the prescription distortionis more attenuated while serving the educational purpose, but the firms are made worse off due tothe overinvestment problem.

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30

W, J. S., D. B, A. J. S, M. N, K. Z, R. L,  S. F
(2004): “Physicians Report On Patient Encounters Involving Direct-To-Consumer Advertising,”
Health Affairs, 23, 219–233.

31

Appendix. Proofs of Propositions
Proof of Proposition 2
Proof. Define θk and Qk , k = P, E, as functions of v, p, d and c. The effects of v and d are identical.
Note that QP 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 = 18 > 0 at c = 0.5p and limc→∞ ∆Q = 0. It isalso straightforward to obtain∂QP∂θ P
4M 2 p[2c − p(2M − 1)]= [θ P + (1 − 2θ P )M]
=−
,
∂c
∂c
[2c + p(2M − 1)]3
∂QE
∂θ E
4cp
= (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>.
3[2c + p(2M − 1)](2c + p)3
Alternatively, the condition can be written as
F(c)G(c)3 >

1
,
M2

where
F(c) :=

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

Evaluated at c = 0.5p, the condition is reduced toF(0.5p)G(0.5p)3 =4(1 − M)
1
4
> 2 ⇔
> M.
3
M
M
5

32

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

c→∞

√
1
⇔
M
>
0.5.
M2

Note also that FG3 is increasing in c if
F 0G + 3FG0 > 0,

(8)

where
F 0 (c) =p(2M − 1) 0
4p(1 − M), G (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)>,2c [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 FG3 may increase at the beginning but must eventually decrease as c gets sufficiently large. Combined with the fact that FG3 must converge to 2 regardless of M, this fact allows
us to pin down the shape of ∆Q. There are three possible cases we need to investigate.
√
Case 1 ( 0.5 > M): In this case, FG3 > M −2 when c is relatively small. At some point, FG3 starts
decreasing and converges to 2 which is lower than M −2 . This means that ∆Q first decreases andthen increases, ultimately converging to 0. As such, there exists a unique threshold cQ (v, d) suchthat ∆Q > 0 if and only if cQ > c. Since ∆Q is increasing in v and d, the threshold cQ must also be
increasing in v and d.
√
Case 2 (0.8 ≥ M ≥ 0.5): In this case, FG3 must invariably be smaller larger than M −2 , which
implies that ∆Q is monotonically decreasing with ∆Q > 0 for all c > 0.5p.
33

Case 3 (1 > M > 0.8): In this case, FG3 is lower than M −2 when c is relatively small. As c getslarger, it increases but then decreases and converges to 2 which is larger than M −2 . This meansthat ∆Q first increases and then decreases with ∆Q > 0 for all c > 0.5p.
Q.E.D.
Proof of Proposition 4
Proof. Since
∂∆C
∂θ P
∂θ E
= 2θ P− 2θ E,∂c∂c∂c
we have
∂∆π
∂θ P
∂θ E
∂θ P
∂θ E ∆C= p[M − (2M − 1)θ P ]− p(1 − θ E )− cθ P+ cθ E
−
∂c
∂c
∂c
∂c
∂c
2
P
E
P2
E2
∂θ
∂θ
θ −θ
= (cθ P − M p)
− cθ E−.
∂c∂c2
Observe that2

2

∂θ P M p θ E∂θ E p
θP
=−
,
=−
,
2
∂c 2
2
∂c 4
which gives us∂∆π  P M p  ∂θ P  E p  ∂θ E
= 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
1
4[2c − p(2M − 1)]2c + p>2
M
6c + p2c + p(2M − 1)34!3
= H(c)G(c)3 ,(9)whereH(c) :=

4[2c − p(2M − 1)].
6c + pAs above, HG3 is increasing in c if H 0G + 3HG0 > 0. With some computation, we obtain
H 0 (c) =16p(3M − 1),
(6c + p)2

so that this condition becomes
16p(3M − 1)(2c + p)
48p(1 − M)[2c − p(2M − 1)]>,2(6c + p) [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)
M
This 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 > 56 , HG3 is increasing for all c ∈[0.5p, ∞); if 56 > M > 23 , HG3 first increases and then decreases.
To complete the proof, we now check the boundary conditions for (9). It is easy to verify that(9) holds at c = 0.5p if M > 32 , so that ∆π increases at the beginning. At the other end, as c → ∞,√√√this holds if 0.75 > M. Note also that 0.75 ≈ 0.866 > 65 . 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). For 0.75 ≥ M ≥ 56 , on the other hand, ∆π is35

increasing for all c, and hence ∆π < 0 for all c. We can also show that ∆π is increasing in v. Sincea decrease in v is equivalent to a decrease in M with p and d fixed, this means that ∆π < 0 for all√c if 0.75 > M.
Finally, since ∆π is increasing in v, it is clear that cπ is decreasing in v. To show that ∆π isincreasing in d, recall that the profit under product DTCA is given byπP =pθ P [2M − (2M − 1)θ P ] c P 2
− θ ,
2
2

from which we obtain∂θ P∂πP= 2[M pP (1 − 2θ P ) + (pP − c)θ P ]+ pP θ P (1 − θ P )
∂d
∂d
∂θ P
= −(2M − 1)pP θ P+ pP θ P (1 − θ P ).
∂d
Note also that∂θ P
2p(2c − p)
=
> 0.
∂d
[2c + p(2M − 1)]2
Given this, πP 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.
Q.E.D.
Proof of Proposition 5
Proof. Observe that ∆PS = PS4 S > 0 at c = 0.5p and limc→∞ ∆PS = 0. It is also straightforward
to obtain
∂PS P
∂θ P
8M p[2M p(PS S − PS C ) + (2c − p)PS C ]= 2[θ P PS S + (1 − 2θ P )PS C ]
=−
,
∂c
∂c
[2c + p(2M − 1)]3
∂PS E
∂θ E
8pc
= 2(1 − θ E )PS S=−
PS S .
∂c∂c(2c + p)336

It follows from this that ∆PS is decreasing in c if
M 2 2cφ − p[(2M + 1)φ − 2]c>.
[2c + p(2M − 1)]3
(2c + p)3(11)Here, we extend the definition of F in the proof of Proposition 2 and, with slight abuse of notation,
defineF(c; φ) =2cφ − p[(2M + 1)φ − 2),cso 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 toF(0.5p; φ)G(0.5p) =4(1 − Mφ)
1
4
> M.
> 2 ⇔
3
M
M
1 + 4φAs c → ∞, on the other hand, it converges tolim F(c; φ)G(c) = 2φ >

c→∞

p
1
0.5φ−1 .
⇔M>
M2Moreover, as in Proposition 2, we can show that FG3 is increasing in c ifp[(2M + 1)φ − 2)(2c + p) 12p(1 − M) 2c − p[(2M + 1)φ − 2)]>,c2 [2c + p(2M − 1)]c[2c + p(2M − 1)]2
which is simplified top[(2M + 1)φ − 2)(2c + p) 12p(1 − M) 2c − p[(2M + 1)φ − 2)]>,c2c + p(2M − 1)
If (2M + 1)φ ≤ 2, FG3 is weakly decreasing in c. If (2M + 1)φ > 2, we can essentially followpthe same argument as in Proposition 2. In either case, we can conclude that: (i) if M ≥ 0.5φ−1 ,37

∆PS > 0 for all c ∈ (0.5p, ∞); (ii) ifp0.5φ−1 > M, there exists an interior threshold cPS such that

∆PS > 0 if and only if cPS > c.
Finally, it is easy to verify that PS P is increasing in v while PS E is independent of it. That cPS
is increasing in v immediately follows from this fact.
Q.E.D.
Proof of Proposition 7
Proof. Define
2M(p)p2(v + d)p − 2λp2
θpS + 4τ(1 − θ)pC
S (p) :==
, 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 have
S (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> 0.
2c − p[2(v + d) − 1] − 2λp2 2This 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)[θpS + 4τ(1 − θ)pC ][θ + 4τ(1 − θ)]2
4τ(pC − pS )=−< 0,
[θ + 4τ(1 − θ)]2

P0 (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 means that
θ P is decreasing in c while pP is increasing. Moreover, it is easy to verify that θ P → 1 and pP = pS
as c → 0.5pS and θ P → 0 and pP = pC as c → ∞.
38

Q.E.D.
Proof of Proposition 8
Proof. By rearranging (6), we obtain"#∂πP θ P
∂θ P
0
P
P
=
(2M p + 2M)(1 − θ ) + θ − 2M p
.
∂p
2
∂p
Since
∂θ P 4Mc + 2M 0 p(2c − p)=,∂p
[2c + p(2M − 1)]2
πP is increasing in p if"
2M p 1 − θ P −0#
2M p(2c − p)
8M 2 pc
P
P
+
2M(1
−
θ
)
+
θ
−
> 0.
[2c + p(2M − 1)]2
[2c + p(2M − 1)]2

Substituting θ P yields#
2c − p
2M p(2c − p)
4Mc
8M 2 pc
2M p
−
+
−
> 0,
2c + p(2M − 1) [2c + p(2M − 1)]2
2c + p(2M − 1) [2c + p(2M − 1)]2"0

which is simplified to
M 0 p(2c − p) + 2Mc > 0.
When M = 1, M 0 = 0 and this condition clearly holds. When M < 1, we have
2Mc > λp(2c − p).

(12)

This condition holds at p = 0. Note also that the right-hand side is decreasing in p at first andthen becomes increasing while the left-hand side is strictly decreasing. This means that (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
39

which holds for any c.
Similarly, it follows from (7) that PS P is increasing in p if
[2θ P (PS S − PS C ) + 2(1 − θ P )PS C ]

h
i
∂θ P
> θ P λpθ P + 2(1 − θ P )[λ(M + M 0 p) + τMM 0 ] ,
∂p

where
τ
PS S − PS C = (v − λp)(1 − M) + (2M 2 − 1).
4With some computation, we obtain
2Mc + M 0 p(2c − p)
2c + p(2M − 1)hi
> M p λM p2 + (2c − p)[λ(M + M 0 p) + τMM 0 ] ,[2M p(PS S − PS C ) + (2c − p)PS C ]As p → 0, this condition is reduced to
4Mc2 PS C> 0,
2c + p(2M − 1)which always holds.
Q.E.D.

40

1
8

M = 0.95
M = 0.75
0
M = 0.6cFigure 1: The difference in market demand ∆Q (p = 0.6)

M = 0.950

M = 0.75

M = 0.6− 16p

cFigure 2: The difference in firm profit ∆π (p = 0.6)

41

PS S
4

M = 0.60
M = 0.95

cFigure 3: The difference in patient surplus ∆PS (v = 1.1, p = 0.6, τ = λ = 1)

∆Q > 0 if c small∆Q > 0∆π < 0∆π < 0 if c small∆PS > 0 if c small
0.5

√
0.5

∆PS > 0p√
0.75 0.5φ−1

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

42

M