Informational spillovers and the sequentiallaunching of pharmaceutical drugs1

Begoña Garcia-Mariñoso2 and Pau Olivella3

May 20, 2005

1We thank Pedro Barros, Xavier Martínez, Izabela Jelovac and the participantsat the BEC workshop at the Universitat Autònoma de Barcelona, for their com-ments and suggestions. The usual disclaimer applies. The authors acknowledge thefinancial support of the Fundación Banco Bilbao Vizcaya.

2Department of Economics. City University of London. Northampton SquareLondon EC1CV 0HB, United Kingdom. E-mail: b.garcia-marinoso@city.ac.uk

3Department of Economics and CODE. Universitat Autonoma de Barcelona.Edifici B, 08193 Bellaterra, Barcelona, Spain. E-mail: pau.olivella@uab.es

Abstract

This paper analyzes informational spillovers in the pricing of drugs, whichoccur as a result of sequential launching. With sequential launches andasymmetric information about the cost of a drug, the acceptation of a pricewhere the drug is first launched might reveal the firm’s private informationto subsequent players. The paper identifies the circumstances where suchinformational spillovers are possible and explains how the firm will preventthem by crafting the order of launches. The jointly necessary and sufficientconditions for informational spillovers to occur are: (i) the unit subsidy ofdrugs varies across countries; (ii) the firm enters a country with large ag-gregate demand first, and (iii) the prior that countries hold about the firmbeing low cost takes intermediate values. If these conditions hold, a firmwill chose to enter first a country with small aggregate demand (in order toprevent the spillover) if and only if the firm is impatient.(Preliminary draft, please do not quote without the author’s per-mision)

1 Introduction

The motivation of this paper is based on two real world observations. First,

when the health administration of a country sits down to negotiate the price

of a drug with a pharmaceutical company, it is usually unable to obtain a

low price. Indeed pharmaceutical prices have increased in the latest years

and are a growing component of national health care expenditures.1 Second,

the international launching of a pharmaceutical drug follows a sequential,

country by country, pattern.2

The first observation may be the result of a weak bargaining power of

the health administration ("the agency", henceforth) vis-à-vis the pharma-

ceutical company ("the firm", henceforth). This argument seems, however,

somewhat implausible as the agency has the threat of not subsidizing the

drug in case of a negotiation failure or even of forbidding the sales of the

drug altogether. We offer an alternative explanation: the existence of asym-

metric information. Namely, we suppose that the production costs are the

firm’s private information. Then it is clear that the agency must trade-off

the benefits of a low price with the risk of rejection by the firm. Hence,

even if the agency has full bargaining power,3 the presence of asymmetric

information may prevent marginal cost pricing.

As for the second observation, we do not aim at explaining why the

pricing decisions are sequential. We take this as a fact and aim studying

how the order of drug launches affects profits and welfare.

1OECD 2003 shows the growth in real terms of the pharmaceutical expenditure percapita of several countries between 1990 and 2001. This ranges from 111% for Sweden,99% for Australia, 90% for the US and 7% for Japan.

2That pricing is sequential is obvious if one thinks of "external referencing". This isa policy which is based on setting prices for drugs as an average of the prices negotiatedand observed in other countries. For example, in the Netherlands, the maximum price fora drug is the average of the prices in Germany, France, UK and Belgium (PharmaceuticalPrices Act 1996). Similarly, in Switzerland a cap on drug’s prices is set as the averageof the prices in Germany, Denmark, the Netherlands and the UK. (Health Insurance Law1996). In this paper we do not aim, however, to study the impact of external referencing.

3 In order to isolate our proposal from the “weak bargaining power” argument, weassume that agencies are able to make take-it-or-leave-it price offers to the firm. There isalso a technical reason for why we stick to take-it-or-leave-it offers by the agency: otherwiseone needs to resort to the tools of bargaining under asymmetric information, which usuallysuffer from extremely poor predictive power.

1

An important consequence of asymmetric information and sequential

pricing is that the acceptation of a price in a country might reveal the

firm’s private information. In particular, if some price offer is accepted,

the next agency knows that this price is acceptable to the firm (average

variable production costs are at most this price). Hence, one could say

that sequential pricing results in information spillovers. Our paper is a first

attempt to analyze the international pricing of a drug in the presence of

such information spillovers.

Notice that our game is one of signaling. The informed party (the firm)

decides whether to accept the price offered by the first agency before other

agencies (the uniformed party) make their offers. In consequence, we now

present the main results of the paper using the terminology that is standard

in this literature.

The main objective of our analysis is to respond to the following ques-

tions:

1. Given a certain order of drug launches, is an efficient firm able, in

equilibrium, to hide its true costs? In other words, is the pooling equilibrium

sustainable?

2. Does the efficient firm benefit form hiding its costs?

3. If the answer to both questions is yes, can the firm, by appropri-

ately choosing the order of launches, induce a pooling equilibrium?

4. Could an agency ever benefit from committing to offer a high price,

before the firm makes any decisions on the order of launches?

There are five groups of parameters that determine the answers to these

questions. The first group is how much the drug is subsidized in each coun-

try, which determines each citizen’s individual demand. Namely, citizens

pay only part of the price of the drug while the agency reimburses the rest

of the price to the firm. We refer to the part paid by the individual as “co-

payment”. The second group is each country’s population size, which is a

level effect determining each country’s aggregate demand. The third group

is a singleton: the firm’s intertemporal discount rate, which determines the

2

costs to the firm of delaying launch in a country. The fourth group is each

agency’s intertemporal discount rate, which determines the agency’s bene-

fits of attracting an early launch. The fifth and last group is each agency’s

prior beliefs about the firm’s true production costs. We assume, as it is

customary, that these prior beliefs are common across agencies. Henceforth,

we refer to the prior probability that the firm has low costs simply as “prior

belief”. This determines the agencies’ evaluation of the risk of rejection, by

a high cost firm, of a low price offer.

We fully characterize the equilibrium for different values of the common

prior belief on the firm being efficient. Let us first concentrate on a specific

case where the following two hypothesis hold:

(i) Individuals in country A bear a lower copayment for the drug than

individuals in B.

(ii) Country A has more population than country B and/or the firm is

sufficiently impatient.

Notice that if country A has a larger population than country B, this

reinforces (i) in the sense that country A has a larger aggregate demand.

However, we show that (i) has an additional effect: the agency in country

A suffers more than the agency in country B from increases in the price

of the drug. Because of this, caeteris paribus agency A is more willing to

reduce prices despite the risk of rejection. We say that "the agency in A has

higher price stakes than the agency in B." If the above hypothesis (i)-(ii)

hold, there are three cases. We start by describing the one with the most

surprising result.

Case a: If the prior belief is neither too high nor too low then the efficient

firm prefers to launch first in country B. This is surprising because, relatively

speaking, in this country aggregate demand is small. We prove that by

entering first country B the low cost firm manages to hide its costs because

agency B sets a high price. However, agency A subsequently sets a low

price. To understand why the firm prefers to enter country B first, suppose

that the firm enters first country A. Then agency A can risk setting a low

3

price that the efficient firm will not reject, despite that this uncovers his

true costs to the up-coming agency. Clearly, the firm looses too much by

foregoing a large demand and gains too little by hiding its low costs to a

low demand. Notice that in the last argument we have used the fact that

agency A has high price stakes: this is why it is wiling to accept the risk of

the firm actually having high costs. To sum up, that agency A has higher

price stakes and a larger aggregate demand constitutes a two-edged sword

for the firm: on the one hand it makes country A more attractive, but on

the other its high price stakes imply that agency A is more aggressive in her

price offer.

Case b: Prior beliefs are low. Then the firm prefers to launch in country

A first. In equilibrium not only is a low cost firm able to hide its costs, but

it moreover manages to get a high price from both agencies.

Case c: Prior beliefs are high. Then the firm is indifferent among the

orders of launches. A low cost firm is unable to hide its low costs and all

agencies set low prices.

Another important result refers to case a: Under hypothesis (i) and (ii)

and if A’s agency is impatient enough it would be better for her to commit

to a high price at the outset (before any launch was made) to prevent the

firm entering first the small demand country.

Finally, we can be more explicit about the (joint) necessity and suffi-

ciency of the hypothesis on country copayments, sizes, and agencies’s dis-

count rates for case a to be viable.

First, the assumption that countries differ in their copayment rates is

indispensable for case (a) to be viable. Second, the assumption that the

agency in the low-copayment country (country A) has a discount rate below

one is absolutely crucial as well. Namely, if this agency does not discount the

future then it is always indifferent among the orders of drug launches. This

in our opinion the other surprising result of our analysis. It means that

information spillovers are irrelevant in the absence of agency discounting.

Finally, the set of parameters under which case (a) is viable shrinks if the

low-copayment country has a smaller, instead of a larger, population size

4

than the other country; but is still non-empty.

A caution is needed here. The above results are obtained under the

assumption that agencies do not try to infer any information by observing

which country is entered first. This may be justified on the grounds that

agencies do not know whether the order of launches was strategically chosen

or determined by other factors that are independent of firm’s costs, like the

length of the approval process. In any case, we can extend our results to the

case where agencies do infer information from the order of launches: this

only reduces the set of parameters for which case (a) holds.

The literature on international pricing of a drug studies other types of

spillover effects whereby acceptation in a country may undermine the price

obtained in another. Namely, spillovers appear in the presence of parallel

imports. Indeed, if the price in the US for a certain drug is higher than

in Canada, there are incentives to import the drug from Canada to the

US. We rule out this phenomenon by assuming that patent rights are not

exhausted after the first sale. In other words, parallel imports are forbidden

in our analysis. A very similar spillover effect is produced under external

referencing, that is, if the US commits to copying the price set in Canada.

We also assume that agencies cannot commit to external referencing.

This related literature is mostly empirical. A few theoretical attempts

exist, however. Jelovac et al. (2005) assume that agencies do not have

full bargaining power, and show that external referencing may become a

useful tool to contain health expenditures. In particular, they show that

if a agency can commit to such pricing rules, doing so may be beneficial

to this agency if the alternative is an independent price negotiation but it

may greatly damage the bargaining power of the agency(es) upon which the

external referencing rule is based.

The paper is organized as follows. In section 2 we outline the model

under hypothesis (i)-(iii) above. In Section 3 we solve the game that starts

once the firm has decided to enter the large demand country first. In Section

4 we solve the game for the reverse order of launches and compare it with

the previous one. In Section 5 we summarize the results appearing after

5

relaxing some of the hypothesis. All the proofs are in the Appendix.

2 The model

The players of the game are two agencies (i = A,B), one for each country;

and a multinational pharmaceutical firm which is based on a third country.

Production costs and impatience

The costs of producing Q units of the drug are given by F+cQ. The firm can

be of two types, characterized by the constant marginal cost of production

c ∈ (c, c) with c < c. Denote by b0 the probability that both agencies assign,

a priori, to the firm having low marginal costs. We refer to b0 as the prior

belief. The firm discounts second period profits by a rate 0 < δ < 1 that is

independent of type.

Consumer copayment scheme

We focus on a proportional reimbursement or copayment scheme.4 Given a

full price p, a consumer only pays y = γip with 0 ≤ γi < 1, i = A,B. We

assume that the copayment is larger in country B, namely,

Assumption 1 γA < γB.

This assumption implies that for each given full price p, individual de-

mand is larger in country A.

Demand and surplus

Consumer are homogeneous across countries. An individual consumer’s de-

mand function is D. That is, if a consumer in either country pays y per unit

then her demand is D(y). Let P be the inverse of D. The properties of the

function D are the following.

Assumption 2 (i) P (0) > c > c; (ii) D is strictly decreasing and concave

(perhaps not strictly).

4For fixed copayment, results do not change qualitatively.

6

Part (i) implies that the market is always viable. Part (ii) implies that

demand is maximized when consumers pay zero, and that maximum demand

is finite. We denote this maximum demand by qmax = D(0). Denoting by p

the price that the firm obtains, the consumer demand in country i is D(γip).

In general, the gross consumer surplus as a function of firm’s price p and

copayment rate γ is given by

GCS(p, γ) =

D(γp)Z0

P (q)dq.

Net consumer surplus is given by

S(p, γ) = GCS(p, γ)−D(γp)γp.

We normalize the mass of consumers in country B to 1, and the mass

of consumers in country A to k. We assume that country A has a large

population. Formally:

Assumption 3 k ≥ 1.

Thus, for a given firm price p, the aggregate demand in country A is

kD(γAp) while the aggregate demand in country B is D(γBp).

Agencies’ objective function

Agencies are risk neutral.5 We define the agency’s payoff as per individual

and as a function of firm price and copayment rate. It is given by net

consumer surplus minus government costs. That is, we are assuming that the

agency’s mandate is to maximize net consumer surplus minus the associated

taxes. Hence, if a price p is accepted by the firm then the agency obtains

OF (p, γ) = S(p, γ)− p(1− γ)D(γp) =

GCS(p, γ)−D(γp)γp− p(1− γ)D(γp) =

GCS(p, γ)− pD(γp).

5Each agency deals with a large number of drugs. Under uncertain marginal costs,some price offers may be accepted and some may be rejected and in the end the agencyonly cares about average surplus generated.

7

Note also that this objective function is not economic welfare as it does not

include the firm’s profits. To justify this, recall that we assume that the

firm is not located in the country. The properties of the objective function

are given next. We express partial derivatives as subscripts.

Lemma 1 For all 0 < γ < 1 and p > 0, we have that OFγ(p, γ) > 0.

This implies that if the agency were to set the copayment, then γ would

be chosen to be 1 and the consumers would bear the full brunt of price

changes. However, we assume that the copayment in not chosen by the

agency. For instance, suppose that it is the Parliament who chooses γ be-

forehand. If the Parliament has other motivations rather than mere financial

costs and consumer surplus, intermediate values of γ will be legislated.6 One

could then ask why does the Parliament delegate the negotiation of the drug

price to an agency. Following the usual delegation-as-commitment argument

the agency would behave more aggressively if its mandate includes cutting

costs. In any case, we take the positive approach here as copayments below

100% are observed in reality.

Lemma 2 For all 0 < p < P (0) and 0 < γ < 1, we have that OFp(p, γ) < 0

while OFpγ(p, γ) > 0.

That is, for p in the indicated region, ceteris paribus the agency always

prefers lower prices. Intuitively, when price increases, this has three effects

on the agency’s objective function. First, the total government and con-

sumer outlay on inframarginal consumers increases, a negative effect. How-

ever, as price increases total consumer copayment increases (for γ > 0) and

hence demand decreases. This brings the other two effects on the agency:

gross consumer surplus is reduced, again a negative effect, but fewer con-

sumers need to be subsidized, a positive effect. The limit on p and the

6These could be equity or insurance considerations.

8

concavity of demand imply that the positive effect is not enough to com-

pensate the other two.7 The lemma also states that the absolute value of

the effect of a price increase decreases with the copayment rate γ. This is

due to the fact that as γ increases, the compensating positive effect gains

importance, as the consumer is less isolated from the price increase. An

important implication of the lemma is that with full information the agency

would always offer the smallest acceptable price, i.e., the minimum average

variable cost. In our set-up this coincides with the marginal cost.8

The next assumption states that, even if the drug was fully subsidized

and the agency was to pay the maximum price c, the agency would still

benefit form the drug.

Assumption 4 OF (c, 0) > 0.

Given Lemma 1 and Lemma 2, assumption 4 implies that OF (p, γ) > 0 for

any p ≤ c and γ ≥ 0.9From now on, denote the objective function of the agency in country j,

OF (p, γj), by simply OFj(p); for j = A,B.

Timing

The game has 5 stages. In stage 1, the firm chooses which agency to approach

first in order to launch the drug. In stage 2, agency i offers a take-it-or-leave-

it price pi. In stage 3 the firm accepts or rejects agency i’s price offer. If the

firm rejects it, she is not allowed to sell the drug in country i. If the firm

accepts, the drug is launched in country i and is included in this country’s

reimbursement list. In stage 4 the firm approaches the other agency j 6= i

in order to launch the drug and this agency offers a take-it-or-leave-it price

pj . Finally, stage 5 is analogous to stage 3, exchanging i by j.

7Note that if the copayment is fixed the positive effect does not exist and all theremaining effects of the price increase on the objetive function are negative.

8Hence, the country does not contribute to the fixed costs incurred when developingthe drug and free rides on the firm’s (and perhaps third country’s) investment.

9 In the case of linear demand, this assumption implies that P (0) > 2c, that is, theindividual’s maximum willingness to pay for the drug is at least twice the maximum unitcost, an extremely weak assumption for pharmaceutical drugs.

9

Price stakes

As announced in the introduction, prior beliefs are common. In the absence

of any information, suppose for now that agency A thinks that an offer

p = c will be accepted if and only if the firm is low cost whereas an offer

pA = c will be accepted by any firm. Then this agency will dare to offer

price p = c if k · b0OFi(c) ≥ k ·OFi(c). Notice that the previous comparisonis independent of the size of k.

The following is an important assumption about agency B’s objective

function.

Assumption 5 b0 < OFB(c)/OFB(c).

Assumption 5 states that agency B prefers to ensure acceptation (obtain-

ing OFB(c)) rather than risk rejection. That is, she has more to loose by not

being served as compared to the gains from a price reduction. As mentioned

in the introduction, we say that agency B has “low price stakes". This im-

plies that with no new information agency B will always choose pB = c. It

is important to note that due to the assumption that γA < γB, we have that

agency A has relatively higher price stakes. Formally,

Lemma 3 OFA(c)/OFA(c) < OFB(c)/OFB(c).

This lemma, together with the continuity of OFA, implies that if agency

A manages to obtain a price pA sufficiently close to c, then one could have

OFA(c)/OFA(pA) < OFB(c)/OFB(c). (1)

This fact will be proven formally later on. Suppose then that 1 holds.

Under assumption 5, we have two cases, depending on the location of b0. One

is that prior is low, that is, b0 ≤ OFA(c)/OFA(pA). The other one is that the

prior is intermediate, that is, OFA(c)/OFA(pA) < b0 < OFB(c)/OFB(c). If

assumption 5 is relaxed, we have a third case: b0 ≥ OFB(c)/OFB(c). The

analysis of this third case is relegated to Section 5.

Posterior beliefs

Suppose that agency i has been approached first. Denote by bα (pi), α =

10

R,A, the subjective probability that c = c of agency j 6= i’s after observing,

respectively, the acceptance (A) or rejection (R) of agency i’s offer pi.

In the next section we solve the subgame that starts once the order of

launches is set to be "first A and then B" and in section 4 we solve the

subgame that starts for the reverse order, and compare the two from the

perspective of the firm. In order to simplify the analysis, we make the

following assumption on the formation of beliefs by the first agency chosen.

Assumption 6 The first agency ignores the fact that she, and not the other

agency, is the first one to be approached.

We justified this assumption in the introduction and we briefly discuss

the consequences of relaxing it in Section 5.

3 Launch in country A first

We proceed by backward induction.

3.1 Stage 5

In this stage a low cost firm will accept any pB > c and reject any pB < c,

while a high cost firm will accept any pB > c and reject any pB ≥ c.

3.2 Stage 4

In this stage agency B will either set c or c. This implies that in stage 5

the high cost firm makes zero profits. Given Assumption 5, in a pooling

equilibrium with no information revelation, agency B would choose c.

3.3 Stage 3

Since the signaling game that the firm and agency B play depends on the

price set by agency A, we need to proceed in a case by case basis.

Case 1. Subgame that follows an offer of a price above c by agency A.

Proposition 1 If pA > c, both types of firms accept the price offer. In

other words, the equilibrium of the stage 3 subgame is pooling.

11

Case 2. Subgame that follows an offer of a price exactly c by agency A

This constitutes a more delicate situation since the high cost firm is

indifferent. Two lemmata are needed.

Lemma 4 Suppose that pA = c. That the high cost firm rejects with some

fixed positive probability 0 < λ ≤ 1 can never be part of an equilibrium of

the whole game. In other words, in equilibrium the high cost firm accepts

pA = c for sure.

Lemma 5 In equilibrium a low cost firm accepts pA = c.

To sum up, we have the following proposition:

Proposition 2 The conclusion of Proposition 1 is also valid if pA = c.

Case 3. Subgame that follows an offer of a price strictly below c by agency

A.

This is the relatively most interesting case, as separation may occur. We

proceed in several steps.

Lemma 6 A high cost firm rejects any pA < c.

The implication of this is that if an offer below c is accepted, the firm

fully reveals that it has low marginal cost. In contrast, a low cost firm

might hide its status by foregoing the profits in the first market by rejecting

c < pA ≤ c.10 The next definition will be used extensively.

Notation 1 Denote by epA the solution to (epA−c)D(γAepA) = δk (c−c)D(γBc).

We have the following.

Lemma 7 (1) The price epA is unique and satisfies c < epA < c, moreover

(p− c)D(γAp)

½> δ

k (c− c)D(γBc) if p > epA< δ

k (c− c)D(γBc) if p < epA.10This is the opposite to the usual signalling model where the efficient type incurs a

cost to reveal its type to the principal.

12

(2) A low cost firm accepts any p ≥ p̃A and rejects any p < epA. (3) Theprice epA can be made arbitrarily close to c by letting δ/k tend to zero.

The next proposition is a corollary of lemmata 6 and 7.

Proposition 3 There exists c < p̃A < c such that for all p < p̃A the equi-

librium of stage 3 is pooling as all types reject, whereas for all p̃A ≤ p < c

the equilibrium is separating as only the low cost accepts such p.

This last result is very important. It implies that under our assumptions

agency A can set some pA < c, which is accepted and therefore results in the

efficient firm fully disclosing its status to agency B. In the following stage

we examine whether it is in the interest of agency A to set this price.

3.4 Stage 2: Agency A’s pricing strategy

Given assumption 5 and depending on the relative positions ofOFA(c)/OFA(epA),OFB(c)/OFB(c), and b0; we have two cases:

Central Case: OFA(c)/OFA(epA) < b0 < OFB(c)/OFB(c);

Case 2: b0 ≤Min{OFA(c)/OFA(epA), OFB(c)/OFB(c)}11.A separating equilibrium with informational spillovers exists only in the

central case. Formally:

Proposition 4 (1) The central case is possible provided that assumption

1 holds and that δ/k is sufficiently small. (2) In the central case agency

A’s best price offer is pA = epA and a low cost firm’s profits are k(epA −c)D(γAepA). (3) In case 2 agency A sets pA = c and a low cost firm’s profits

are (c− c)[kD(γAc) + δD(γBc)].

Note that in the central case if the firm is low cost then it accepts the

price epA and agency B updates his beliefs (to one) and sets pB = c, which is

11Note that case 2 holds whether b0 ≤ OFA(c)/OFA(pA) ≤ OFB(c)/OFB(c) or b0 ≤OFB(c)/OFB(c) ≤ OFA(c)/OFA(pA). Both cases are possible.

13

also accepted. If the firm has high costs then the offer epA is refused, againagency B updates its beliefs (now to zero), but this is irrelevant because

agency B would have offered pB = c even in the absence of information. In

case 2, all firms accept pA = c, no information is revealed, and agency B

also offers price pB = c. We now turn to the first stage of the game.

4 Is entry reversal profitable? Approaching agencyB first

For a high cost firm the order of entry has no impact on profits. For a low

cost firm this is not the case. Note that entry reversal may only be beneficial

in the central case, where the game in which the firm enters first agency A

results in a separating outcome. In case 2, entering A first results in both A

and B setting a price of c, which is the best possible price outcome that an

efficient firm can hope for. Moreover, the large aggregate-demand country

is entered first and the firm is impatient. Hence we analyze entry reversal in

the case where OFA(c)/OFA(epA) < b0 < OFB(c)/OFB(c). That is, under

the assumptions that agency A have strong price stakes, B have weak price

stakes, and that prior beliefs be intermediate.

4.1 Stage 5

The same arguments made in section 3 apply here.

4.2 Stage 4

Since (i) OFA(c)/OFA(epA) < b0; (ii) epA > c; and (iii) OFA(p) is decreasing

in p, we have OFA(c)/OFA(c) < b0. This implies that in the absence of new

information, agency A will set pA = c. The only way that a low cost firm

obtains a higher price is that the firm fools agency A into believing that

it has high costs. As it is usually the case this can never be part of an

equilibrium. Formally,

Proposition 5 In equilibrium the low cost firm cannot obtain a price above

c from agency A when this agency is approached last.

14

4.3 Stage 3

Given that the firm cannot avoid a low price offer by agency A, the firm

ignores the ensuing game and accepts any offer pB ≥ c by agency B.

4.4 Stage 2: agency B’s pricing strategy

Subject to facing a low cost firm, agency B could offer the minimum price

p = c and be accepted. In this case agency B would get OFB(c). But the

firm could have high costs and then only an offer p ≥ c would be accepted.

Hence agency A will offer p = c only if Pr(c = c) · OFB(c) ≥ OFB(c).

Since agency A is now the first mover we have Pr(c = c) = b0. Note that

b0OFB(c) ≥ OFB(c) contradicts assumption 5. To sum up, agency B offers

pB = c, all firms accept, a high cost firm obtains zero and a low cost firm

obtains (c− c)D(γBc) in the first period and zero in the second. Therefore

a low cost firm obtains an intertemporal payoff equal to (c− c)D(γBc).

4.5 The choice of launch order in the central case

The previous analysis allow us to compute the optimal choice of launch order

under the assumption that OFA(c)/OFA(epA) < b0 < OFB(c)/OFB(c). We

have shown that the high cost firm is indifferent between drug launches since

she is unable to capture any (intertemporal) rents whatsoever no matter

what she chooses to do. Hence a high cost firm randomizes. A low cost

firm, on the other hand, prefers to face agency B first if (c − c)D(γBc) >

(epA − c)kD(γAepA). This inequality holds by construction of epA. Indeed,epA satisfies δ(c − c)D(γBc) = (epA − c)kD(γAepA) and if δ < 1 we have

(epA−c)kD(γAepA) < (c−c)D(γBc). Intuitively, the firm’s impatience makesagency A very powerful when it is approached first. Hence the firm prefers to

reverse entry and cash-in the rents coming from the smaller demand country.

Yet, if δ = 1, then the firm becomes indifferent between the two orders of

launches. This is summarized next.

Proposition 6 The firm strictly prefers to enter country B first if and only

if the central case holds and δ < 1.

15

4.6 agency A’s precommitment

A consequence of proposition 6 is that under its conditions, agency A suffers

from launch delay. In equilibrium agency A obtains δAb0OF (c), where δA

is this agency’s discount rate. If this agency was able to commit to offer

pA = c at the outset (before any launch decisions had been taken), this

would give incentives to a low cost firm to advance the launch in country A,

as A has larger aggregate demand. In this way agency A would obtain OF (c)

since all firm types would accept such a committed offer. This strategy is

beneficial if δAb0OF (c) < OFA(c), or if b0 < 1δA

OFA(c)OFA(c)

. This is compatible

with b0 > OFA(c)/OFA(epA) (as required by the assumption of the centralcase) if δA < OFB(p̃A)

OFB(c)< 1. This is if agency A is sufficiently impatient. To

sum up:

Proposition 7 Suppose that (i) δA < OFB(p̃A)OFB(c)

and that (ii) OFA(c)OFA(pA)

< b0 <

Min{ 1δAOFA(c)OFA(c)

, OFB(c)OFB(c)}. Then Agency A will find it beneficial to precommit

to setting pA = c.

5 Extensions

Several assumptions are indispensable for the order of launches to matter to

the firm. These are:

(1) δ < 1, as can be seen from proposition 6;

(2) that individuals in country A bear a lower copayment than in country

B, as if copayments were the same, lemma 3 would not hold;12

(3) OFA(c)/OFA(epA) < OFB(c)/OFB(c) (which in turn requires δ/k

small enough), since otherwise the central case would be empty;

(4) that b0 is intermediate, That is: OFA(c)/OFA(epA) < b0 < OFB(c)/OFB(c)

(i.e., assumption 5 and that we are in the central case).

We now identify which other assumptions can be relaxed and still the

order of launches matters. Firstly, notice that the result in lemma 3 is

12Without loss of generality we have assumed that the country with lower copaymentsis country A.

16

independent of δ and k. First we consider relaxing the coincidence, in the

same country, of a large population and a low copayment. Hence, suppose

that k < 1. Notice that all the results still hold, but that the existence of

the central case where OFA(c)/OFA(epA) < b0 < OFB(c)/OFB(c) requires

(see part 1 of proposition 4) that δ/k be sufficiently small. Since now k < 1,

the assumption may imply very low discount rates for the firm.

Secondly, by assumption 6, the first country approached does not use the

order of launches as a signal. This is at odds with the fact that a low cost

firm prefers to enter country B first. Formally, denote by BA the event that

country B is entered first. Then we have that the low cost strictly prefers

this, so that Prob(BA|c = c) = 1. In contrast, the high cost is indifferent

so that Prob(BA|c = c) = 1/2. Hence, if BA is observed, agency B would

update beliefs using Bayes’ rule. Hence

Prob(c = c|BA) = Pr(BA|c)b0Pr(BA|c)b0 +Pr(BA|c)(1− b0)

=2

1 + (1/b0),

which is larger than b0. Now, if b0 is larger than OFA(c)/OFA(epA), moreso will Prob(c = c|BA) be. However, the central case also requires thatProb(c = c|BA) < OFB(c)/OFB(c), which implies a reduction of the set of

parameters for which this case is viable. Figure 1 illustrates this point.

Finally, we have claimed that assumption 5 is indispensable for our main

results. Let us prove this end. In other words, we prove now that the

order of launches does not affect the firm’s profits when assumption 5 is

relaxed. Indeed, suppose that b0 ≥ OFB(c)/OFB(c). Since by lemma 3,

OFB(c)/OFB(c) > OFA(c)/OFA(c), this implies that in the absence of new

information, any agency to set prices in second place will chose c.13 Because

of this, the maximum profit that the efficient firm can achieve in the final

stage is zero. After an initial price offer has been made, the firm can chose

to mimic the behavior of the inefficient firm, yielding no new information,

or it can disclose herself as efficient. In both cases the firm is penalized

13Notice that if the weak inequality hods with equality then agency B is indifferentbetween offering pB = c and offering pB = c in the absence of new information. We areassuming that in this case agency B sets pB = c. If instead we had assumed that pB = c,then this instance would be incorporated to the central case and eliminated from case 2.

17

ex post with a price of c, thus attaining zero profit. Given the absence

of strategic considerations by the firm when accepting the first price offer,

the first agency to choose price will select the lowest acceptable price by

some firm. This could either be c so that all firms accept or c so that only

the efficient type accepts. As b0 ≥ OFB(c)/OFB(c) ≥ OFA(c)/OFA(c) the

first agency, be it A or B, chooses cand the efficient firm makes zero profits

regardless of the order of launches.

6 References

1. Garcia-Mariñoso, B. , Jelovac, I., and Olivella, P., (2005) Internation-

ally based price regulation and price negotiation patterns. Mimeo.

2. Danzon, P. and Towse, A. (2003) Differential Pricing for Pharmaceu-

ticals: Reconciling Access, R&D and Patents, International Journal of

Health Care Finance and Economics, 3, 183-205

3. Danzon, P., Wang, R. and Wang, L., “The Impact of Price Regulation

on the Launch Delay of New Drugs.” Health Economics, 14(3), 2005.

4. Danzon, P.,"The Economics of Parallel Trade." PharmacoEconomics.

March 1998. 13(3):293-304.

5. OECD (2003): Health at a Glance, Paris.

6. Windmeijer, F., E. De Laat, R. VDouven, R. and Mot, E. (2003) Phar-

maceutical Promotion and GP Prescription Behaviour, CPB working

paper.

7 Appendix

Proof of Lemma 1

Differentiate OF with respect to γ:

OFγ(p, γ) = γp2D0(γp)− p2D0(γp) = −D0(γp)(1− γ)γp,

18

which is positive if p > 0 and 0 < γ < 1.

Proof of Lemma 2

Differentiate OF with respect to p. Using P = D−1,

OFp(p, γ) = γpD0(γp)γ −D(γp)− pD0(γp)γ =

−D0(γp)(1− γ)γp−D(γp).

Take the derivative of the last expression with respect to γ to get the cross

partial derivative

OFpγ(p, γ) = −D00(γp)(1− γ)γp2 −D0(γp)(−1)γp−D0(γp)(1− γ)p−D0(γp)p =

−D00(γp)(1− γ)γp2 −D0(γp)(−1)γp−D0(γp)(1− γ)p−D0(γp)p =

− £D00(γp)γp2 + 2pD0(γp)¤(1− γ) ,

where p > 0, D00 ≤ 0, D0 < 0, and 0 < γ < 1. This proves OFpγ > 0. We

can now use this result to state that an upper bound on OFp is reached when

γ = 1. Hence to prove OFp(p, γ) < 0 it suffices to prove that OFp(p, 1) < 0.

Now OFp(p, 1) = −D(p), which is negative for p < P (0).

Proof of Lemma 3

Define Q(γ) = OF (c, γ)/OF (c, γ). Then sign[Q0(γ)] = sign[OFγ(c, γ) ·OF (c, γ) − OF (c, γ) · OFγ(c, γ)]. Since OFp < 0 by Lemma 2 we have

OF (c, γ) > OF (c, γ). By Lemma 1, OFγ > 0. Therefore sign[Q0(γ)] > 0 ifOFγ(c, γ) > OFγ(c, γ). This is guaranteed since OFγp > 0 by Lemma 2.

Proof of Proposition 1

Suppose that a high cost firm accepts pA > c. The worst that could happen

is that, in the next round, agency B offers c, which would be rejected. The

firm would get: k(pA − c)D(γApA) + δ · 0 > 0. Let her reject the offer, the

best that could happen is that, in the next round, agency B offers c. The

firm would then get 0. Hence a high cost firm has a dominant strategy:

always accept pA > c.

Let us now try to support an equilibrium where the low cost firm rejects

with probability λ > 0. If the low cost is to reject with probability λ then by

19

Bayes’s rule agency A’s beliefs upon rejection is that the firm is low cost for

sure (so pB = c), whereas the beliefs upon acceptation are that the firm is low

cost with probability bA(λ) = b0(1−λ)/(b0(1−λ)+ 1− b0). Let BR(bA(λ))

denote the best reaction by agency B given her beliefs. Now, if the firm

rejects the offer it obtains zero whereas if it accepts it obtains δ(BR(bA(λ))−c)D(γBc). To support this equilibrium one would need that rejecting by

a low costs is equally profitable to accepting (indifference condition). This

requires: 0 = δ(BR(bA(λ))−c)D(γBc) or BR(bA(λ)) = c. For BR(bA(λ)) =

c to be a best response requires that bA(λ) ≥ OFB(c)/OF (c). By assumption

5, this implies that bA(λ) > b0, or b0(1 − λ)/(b0(1 − λ) + 1 − b0) > b0, or

(after some algebra) b0 > 1, which is a contradiction. Hence in equilibrium

the low cost accepts for sure. The fact that this proof goes through for k < 1

is important for further reference.

Proof of Lemma 4

Suppose the high cost firm rejects pA = c. If agency 2’s beliefs that the firm

is low cost are large enough, it will offer pB = c and the high cost firm rejects,

thus obtaining 0+δ·0 = 0. Otherwise, agency 2 will offer c and the firm againobtains 0 + δ(c − c)DB = 0. Suppose now that the high cost firm accepts.

If agency 2’s beliefs that the firm is low cost are large enough, it will offer

pB = c and the firm rejects, thus obtaining (c− c)DA+ δ ·0 = 0. Otherwise,agency 2 will offer c and the firm again obtains (c− c)DA+ δ(c− c)DB = 0.

Now suppose that, out of indifference and by contradiction, the high cost

firm rejects with probability λ > 0. Now, instead of agency 1 offering pA = c

it may alternatively offer pA = c+ε, ε > 0, which ensures an acceptation by

any firm, be it low or high cost, by the Proposition 1. Letting 1− λ ∈ [0, 1]be the probability that the low cost firm was accepting pA = c, the increase

in payoff that agency A obtained by offering pA = c+ ε rather than pA = c

is

OFA(c+ ε)− [b0(1− λ) + (1− b0)(1− λ)]OFA(c).

The limit as ε tends to zero of the last expression is

OFA(c){1− [b0(1− λ) + (1− b0)(1− λ)]} = OFA(c)[λ̄(1− b0) + λb0]. (2)

20

Now λ > 0 implies that expression (2) is positive. In other words, by making

ε sufficiently small, agency A obtains larger profits by offering pA = c + ε

than by offering pA = c.

Given all this, in the stage where agency A chooses its offer pA, this

player solves

Maxε>0OFA(c+ ε).

But since OF 0A < 0, this problem has no solution, and therefore no equilib-

rium to the whole game exists where the high cost firm rejects pA = c with

positive probability.

Proof of Lemma 5

Suppose that a low cost firm accepts pA = c. The worst that could happen

is that agency B offer pB = c. The firm would obtain (c − c)kD(γAc).

Suppose that a low cost firm rejects pA = c. The best that could happen is

that agency B offer pB = c. The firm would obtain δ(c − c)D(γBc). Now

(c− c)kD(γAc) > δ(c− c)D(γBc) if and only if D(γAc) >δkD(γBc), which

is true since δ ≤ 1, k ≥ 1, γA < γB and pA = c. In sum, accepting is also

a dominant strategy for the low cost firm. Notice that the assumption that

k ≥ 1 could be relaxed provided δ is small enough.

Proof of Lemma 6

Suppose that a high cost firm accepts pA < c. The best that she could

hope for is that, in the next round, agency B offer c. The firm would get:

k(pA − c)D(γApA) + δ · 0 < 0. Let her reject the offer, the worst that couldhappen is that in the next round country B offer c, which would be rejected.

The firm would then get 0.

Proof of Lemma 7

Define g(p) = (p− c)D(γAp). Then p̃A solves g(p̃A) = δk (c− c)D(γBc). For

part (1) it suffices to check that

i) g(c) < δk (c− c)D(γBc);

ii) g(c) > δk (c− c)D(γBc); and

iii) g is concave.

Now (i) is satisfied, by direct substitution, since g(c) = 0. Similarly, note

21

that g(c) = (c − c)D(γAc) > δk (c − c)D(γBc) since δ ≤ 1, k ≥ 1, and

γA < γB. Finally, g00(p) = (p− c)D00(γAp)γ2A + 2D

0(γAp)γA < 0 since D0 is

negative and D00 is non-positive.

Part (2). If a low cost firm accepts c < pA < c, it reveals it is a low cost and

agency B sets pB = c. In this case the firm earns k(pA−c)D(γApA)+δ ·0. Ifthe firm rejects the price, agency B has no new information and sets pB = c.

In this case the firm earns 0 + δ(c − c)D(γBc). The proof for pA 6= p̃A

follows directly from part (1), where these payoffs are compared. As for,

pA = p̃A, a similar argument to the one used in Lemma 4 can be used to

prove that in equilibrium it cannot be the case that a low cost firm rejects

out of indifference.

Part (3). The equation determining epA is (epA−c)D(γAepA) = δk (c−c)D(γBc).

If δk = 0 then the only solution in the interval [c, c] is epA = c. The result

follows by continuity.

Proof of Proposition 3

Follows directly from Lemmata 6 and 7.

Proof of Proposition 4

Part (1).Assumption 1 ensures that Lemma 3 holds- By this lemma, OFA(c)/OFA(c) <

OFB(c)/OFB(c). Part (3) of lemma 7 states that epA can be made arbitrar-ily close to c by letting δ/k → 0. The result follows by continuity of the

denominator of the left hand side of the inequality.

Part (2). If pA < epA agency A will not be served. If instead she offers

pA = epA then she assures acceptation by a low cost firm. However, it

will be rejected by a high cost firm. Agency A’s expected payoff is then

b0 · k · OFA(epA), where we use the prior probability of low cost by virtue

of assumption 6. Any epA < pA < c will be accepted by the firm, (just as

pA = epA is). Since epA < pA, pA is never an optimal pricing strategy, as OFA

is decreasing. Finally, any price pA ≥ c will be accepted by all types of

firm. Agency A‘s payoff will be k · OFA(c). However, this is smaller thanb0 · k ·OFA(epA) since we are in the central case.Part (3). In case 2, agency A faces the same continuation game outlined

22

above after choosing its price offer. However, in comparing b0 · k ·OFA(epA)and k ·OFA(c), the latter is larger under the conditions of case 2, so agencyA prefers to ensure acceptation rather than reducing the price form c to epA.Proof of Proposition 5

We must prove this for each possible value of agency B’s offer. Suppose

agency B has offered a price pB > c. If the high cost accepts, the worst that

could happen is that, in the next round, agency A offers c. The firm would

get: (pB − c)D(γBpB) + δ · 0 > 0. Let her reject the offer, the best that

could happen is that, in the next round, agency A offers c. The firm would

then get 0. Hence a high cost firm has a dominant strategy: always accept

pB > c. Hence if a rejection is observed the only possible belief is that the

firm is a low cost one and pA = c. If an acceptation is observed then no new

information is revealed and in the absence of new information, pA = c.

Suppose agency B has offered a price pB = c. We also proved above

that it can never be a part of an equilibrium that a high cost firm rejects

out of indifference (agency B can reduce the risk of rejection to zero with

an arbitrarily small cost). Hence if this price is rejected it must also mean

that the firm is a low cost one. The rest of the argument follows as in the

previous case.

Finally, suppose agency B has offered a price pB < c. As proven in lemma

6 (adapting the proof so that k = 1 and A becomes B and viceversa), it is

a dominant strategy for a high cost firm to reject. Hence if the low cost

firm also rejects agency A is left with the prior, so again pA = c. If the low

cost firm accepts it reveals that is a low cost firm and therefore pA = c once

more.

23

Prob( )c c BA=

b0

Interval of admissible values for b0 without assumption 6

45o

( )

( )B

B

OF cOF c

( )

( )A

A A

OF cOF p

( )

( )A

A A

OF cOF p

( )

( )B

B

OF ccOF

Interval of admissible values for b0

under assumption 6

Figure 1. The set of admissible values of the prior that is consisten with information spillovers, with and without Assumption 6.