CESifo Working Paper no. 5672 econstor Make Your Publications Visible. A Service of zbw Leibniz-Informationszentrum Wirtschaft Leibniz Information Centre for Economics González, Paula; Macho-Stadler, Ines; Pérez-Castrillo, David Working Paper Private versus Social Incentives for Pharmaceutical Innovation CESifo Working Paper, No. 5672 Provided in Cooperation with: Ifo Institute – Leibniz Institute for Economic Research at the University of Munich Suggested Citation: González, Paula; Macho-Stadler, Ines; Pérez-Castrillo, David (2015) : Private versus Social Incentives for Pharmaceutical Innovation, CESifo Working Paper, No. 5672, Center for Economic Studies and ifo Institute (CESifo), Munich This Version is available at: http://hdl.handle.net/10419/128373 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. www.econstor.eu Private versus Social Incentives for Pharmaceutical Innovation Paula González Inés Macho-Stadler David Pérez-Castrillo CESIFO WORKING PAPER NO. 5672 CATEGORY 11: INDUSTRIAL ORGANISATION DECEMBER 2015 An electronic version of the paper may be downloaded • from the SSRN website: www.SSRN.com • from the RePEc website: www.RePEc.org • from the CESifo website: Twww.CESifo-group.org/wp T ISSN 2364-1428 http://www.ssrn.com/ http://www.repec.org/ http://www.cesifo-group.de/ CESifo Working Paper No. 5672 Private versus Social Incentives for Pharmaceutical Innovation Abstract We provide a theoretical framework to contribute to the current debate regarding the tendency of pharmaceutical companies to direct their R&D toward marketing products that are “follow- on” drugs of already existing drugs, rather than toward the development of breakthrough drugs. We construct a model with a population of patients who can be treated with drugs that are horizontally and vertically differentiated. In addition to a pioneering drug, a new drug can be marketed as the result of an innovative process. We analyze physician prescription choices and the optimal pricing decision of an innovative .rm. We also characterize the incentives of the in- novative firm to conduct R&D activities, disentangling the quest for breakthrough drugs from the firm effort to develop follow-on drugs. Our results offer theoretical support for the conventional wisdom that pharmaceutical firms devote too many resources to conducting R&D activities that lead to incremental innovations. JEL-Codes: I100. Keywords: pharmaceuticals, R&D activities, me-too drugs, breakthrough drugs, incremental innovation, radical innovation. Paula González* Department of Economics Universidad Pablo de Olavide Sevilla / Spain pgonzalez@upo.es Inés Macho-Stadler Department of Economics Universitat Autònoma de Barcelona Bellaterra / Spain Ines.Macho@uab.es David Pérez-Castrillo Department of Economics Universitat Autònoma de Barcelona Bellaterra / Spain David.Perez@uab.es *corresponding author December 13, 2015 We appreciate valuable comments by Bruno Jullien, Justina Klimaviciute, Jorge Mestre-Ferrándiz and participants at the XXIX Jornadas de Economía Industrial (Barcelona), theWorkshop on Health Economics (UAB), the 16th European Health Economics Workshop (Toulouse), the XXXV AES Conference (Granada) and the 11th iHEA Conference (Milan). Financial support from Ministerio de Ciencia y Tecnología and FEDER (ECO2012-31962 and ECO2012-36480), Generalitat de Catalunya (2014SGR-142), Junta de Andalucía (SEJ-04992), ICREA Academia and the Severo Ochoa Programme (SEV-2011-0075) is gratefully acknowledged. Macho-Stadler and Pérez- Castrillo are fellows of MOVE and CESIfo. 1 Introduction It is widely recognized that of all the industrial sectors, the pharmaceutical industry is the sector that traditionally invests most heavily in research and development (R&D). In 2012, for instance, US biopharmaceutical research companies invested an estimated $48.5 billion in R&D (PhRMA, 2013). Regarding R&D intensity, and according to a recent report by the European Commission, spending on R&D in 2012 by the pharmaceutical industry amounted to 15.3% of its GDP in the US, 16.3% in Japan, and to 14.7% in the European Union (European Commission, 2013). However, there is a great deal of debate surrounding pharmaceutical R&D activities. Pharmaceutical companies are often accused of devoting too many resources to the mar- keting of apparent new products that are �follow-on�drugs of already existing drugs, rather than toward the development of breakthrough (�rst-in-class) drugs.1 In fact, a successful new �rst-in-class drug will often face competition from a series of follow-on drugs that are therapeutically similar to the pioneering drug. The angiotensin converting enzyme (ACE) inhibitors, a class of drugs used to manage high blood pressure, is illustra- tive of this. The �rst ACE inhibitor, captopril, was introduced in the US in 1981. Since then over 10 ACE inhibitors have been launched (Hernandez and Harrington, 2008).2 The development of follow-on drugs is cheaper and less risky than drugs with a novel mechanism of action, but they supposedly do not bring signi�cant therapeutic progress to patients (see, for instance, the discussions by Angell, 2004; Avorn, 2004; and Goozner, 2004). Defenders of incremental innovations argue, however, that medicines based on incremental improvements often represent advances in safety and e¢ cacy, along with pro- viding new formulations and dosing options that increase patient compliance (see diMasi and Paquette, 2004; Wertheimer and Santella, 2009; and the article by Doctor Henry I. Miller in the Wall Street Journal on January 1, 2014). This paper aims at contributing to this social debate. We build a theoretical model of innovation to investigate whether there exist arguments that allow us to support the conviction that pharmaceutical �rms devote too many resources to marketing me-too drugsandtoo fewto launchingbreakthroughdrugs. Ourmodel emphasizes thedistinction between radical and incremental innovation processes.3 Radical innovation processes may 1Follow-on drugs are sometimes called �me-too�drugs as they are close copies of existing drugs. 2Another example is omeprazole, the �rst proton pump inhibitor launched in 1989 to reduce gastric acid production. Proton pump inhibitors have since become the mainstay of treatment for acid-related gastrointestinal disease in adults, and omeprazole was followed by other proton pump inhibitors, with the most recent launched in 2009. 3The labels �radical�and �incremental�belong mostly to the managerial literature and does not o¤er a unique description of the di¤erence between the two concepts. In fact, the literature reveals that the de�nitions of radical and incremental innovations are still puzzling, both at the theoretical and at the 2 lead to breakthrough drugs, while incremental innovation processes pursue me-too drugs. In our model there is a continuum of patients in need of medical treatment. Patients can be treated with drugs that are horizontally and vertically di¤erentiated. Vertical di¤erentiation refers to the quality of the drug and includes the health gains experienced by patients. Horizontal di¤erentiation re�ects the adequacy of the drug for patients, as di¤erent patients in the population will experience di¤erent e¤ects of a given medication in terms of tolerability, side e¤ects or interaction with other medicines. In the market, there is a pioneering drug. We assume that the price of this drug is �xed, for example, because thepatentprotection that covered ithas alreadyexpiredandthedrug is soldat its marginal cost. Moreover, anewdrugcanbemarketedas theresultofan innovativeprocess by a pharmaceutical �rm that seeks to achieve an improvement over the existing medicine. Finally, there is a physician who makes drug prescription decisions. The physician acts as a perfect agent for the health system (which includes both patients and the health authority) and, hence, he makes prescription choices based on the price-e¤ectiveness of the drugs. In this simple set-up we �rst describe physician prescription choices, given the prices and the characteristics of the two drugs (when the innovation process is successful). Sec- ond, we characterize the optimal pricing decision of the innovative �rm, which anticipates the physician prescription behavior. The optimal price for the new drug depends on the di¤erences in cost-e¤ectiveness and the horizontal distance between the new drug and the pioneer. When the new drug is much more cost-e¤ective than the pioneer, the innovative �rm sets a price that leads the physician to prescribe the new drug to all patients. When the improvements in the cost-e¤ectiveness of the new drug are not substantial, or the two drugs are very horizontally di¤erentiated, then the price set by the innovative �rm leads to a drug replacement treatment only for some patients. In all other situations the new drug is not marketed. Finally, we characterize the incentives of the innovative �rm to conduct R&D activities and compare these private incentives with those that would be optimal from a social point of view. The paper distinguishes between radical innovation processes, seeking breakthrough drugs, and incremental innovation processes that aim at launching a me- too drug. In order to di¤erentiate these two kinds of innovations, we follow the approach of measuring the degree of innovativeness of a drug as the size of the di¤erences (either small or large) between the new drug and the pioneer. These di¤erences can emerge either in the horizontal or the vertical characteristics of the drugs. Innovations in the empirical level (see García and Calantone, 2002, for a critical review of the innovativeness terminology). In particular, the degree of innovativeness of a product is measured using various dimensions including the level of risk implied in the innovation strategy, the type of knowledge to be processed or the level of investment needed to move onto a new trajectory. 3 vertical dimension imply a better quality of treatment (or a lower production cost) for all the patients su¤ering from the disease.4 Horizontal innovations would be advances that bene�t some but not all patients because drugs may have lower side e¤ects for a certain group of patients.5 Moreover, in order to account for the fact that the level of risk (or uncertainty of the �nal outcome) is typically larger in the case of radical innovations, we consider that the outcome of a radical innovation process by the innovative �rm takes values on a large support and has a greater variance. The paper provides some interesting �ndings. We show that for incremental innova- tion processes pursuing me-too drugs, the social value of the innovation coincides with the private bene�ts of the �rm (as the innovative �rm appropriates all the health sys- tem bene�ts derived from the launching of the me-too drug). If we consider, instead, R&D activities searching for breakthrough drugs, then private and social incentives for conducting research are not aligned. In particular, the incentives for conducting research by the �rm are inferior to those socially optimal as there are patients that -despite the larger price of the new drug- bene�t from it. These results allow us to show that if a pharmaceutical company can only adopt one of the two types of innovation processes due, for instance, to budget constraints, it may happen that the �rm has an incentive to seek a me-too drug although R&D activities oriented to search for a radical innovation are socially superior. At the same time, it never happens that the innovative �rm prefers to develop a radical innovation when devoting the resources to incremental innovations is preferable from a social point of view. Our results thus o¤er theoretical support for the conventional wisdom that pharmaceutical �rms devote too many resources to conducting R&D activities that lead to me-too drugs. The theoretical literature on incentives for pharmaceutical innovations is not abun- dant, although there is an increasing number of papers that study the interaction between the pricing policy constrained by various forms of regulation and the e¤ort of innovation 4Examples of innovations that would be classi�ed as vertical in our model would include the afore- mentioned captopril (ACE-inhibitor) and omeprazole (protone pump inhibitor), and also cimetidine (H2-receptor antagonist), propranolol (ß-adrenoceptor antagonist), lovastatin (HMG-CoA-reductase in- hibitor), and sumatriptane (5-HT1B/1D-receptor agonist) among others. All these are drugs that, when marketed, met a given need much more e¤ectively than available treatments and were bene�cial for all patients in the treatment of their disease. Also, innovations in antibiotics that allow administration once a day, giving patients the possibility of being treated at home, or at least the possibility to reduce hospitalization time, are vertical innovations according to our classi�cation. Finally, second-generation antihistamines have some (vertical) improvements over �rst-generation antihistamines like, for instance, less frequent dosing. 5For example, in the market for statins, Lovastatin, pravastatin, and �uvastatin represent the class members with the lowest potency to reduce cholesterol levels but which are attractive candidates for use in treating patients who have proven intolerant of more potent statins such as atorvastatin, simvastatin or rosuvastatin (Kapur and Musunuru, 2008). 4 by pharmaceutical �rms. Ganuza, Llobet, and Domínguez (2009) �nd a bias in the phar- maceutical industry toward small innovations. Their result relies on the low sensitivity of a part of the demand (due to the loyalty of some physicians) to changes in prices. This lack of price-sensitivity provides an excessive reward for small innovations and con- sequently downwardly distorts the incentives of pharmaceutical �rms. In our model, the physician acts as a perfect agent for the health system, so that the di¤erence between the social value and the private bene�ts that the �rm obtains from innovation arises from a di¤erent source: the ability of the pharmaceutical �rm to appropriate or not the health system surplus through the price. The existence of physicians that are loyal to innovative drugs also plays an important role in Antoñanzas, Juárez-Castelló, and Rodríguez-Ibeas (2011). They study the incentives of an incumbent pharmaceutical �rm to launch an up- graded drug through innovation before it faces generic competition. The paper shows that the equilibrium level of innovation exhibits an inverted U shape, as innovation increases when the proportion of loyal physicians is low and decreases when it is high. Finally, Bardey, Bommier, and Jullien (2010) focus on the long-run impact of reference pricing on pharmaceutical innovation by �rms. Their model shares some similarities with ours as it makes a clear distinction between incremental and radical innovations in a setting where drugs are horizontally and vertically di¤erentiated. However, the distinction they make between the two types of innovations di¤ers notably from ours. In addition to this, they model a patent race where the innovative process is deterministic and competition in R&D leads to the dissipation of �rms�pro�ts. They show that the short-term and long-term e¤ects of price regulation may be antagonists. In their simulation using French data, they �nd that favoring radical innovation processes at the expense of cost-reducing innovations may generate medium/long-run increases in health expenses, despite potential short-run bene�ts. The rest of the paper is organized as follows. The following section presents our model. Section 3 studies prescription decisions by the physician. Section 4 analyzes pricing decisions by the innovative �rm and characterizes the market equilibrium. In section 5 we discuss the bene�t to the health system derived from the launch of the new drug. Section 6 discusses private versus social incentives to innovate. Section 7 proposes a simple model of innovation. Section 8 discusses the robustnesss of the results when the physician acts as a perfect agent for the patient. Finally, the last section o¤ers some concluding remarks. All the proofs are in the Appendix. 5 2 The Model There is a continuum of patients in need of medical treatment. We normalize the size of the population of patients to 1: Patients su¤er from the same illness and are identi�ed by a horizontal characteristic x; with x distributed uniformly on the interval [0;1] : The parameter x represents the type of the patient and measures the heterogeneity regarding the patient genotype or any other characteristic that may induce the disease to have di¤erent e¤ects among patients. Patients can be treated with a drug. We consider that drugs are both horizontally and vertically di¤erentiated. Thus, a drug is de�ned by a pair of characteristics: (x̂; ĥ): The �rst characteristic x̂ 2 [0;1] captures the horizontal di¤erentiation and re�ects the adequacyof thedrug fordi¤erentpatients. It iswidely recognizedthatdi¤erentpatients in a population experience di¤erent e¤ects of a given medication in terms of tolerability, side e¤ects or interaction with other medicines.6 In our model, where patients are distributed along the interval [0;1], a particular location (type) of a patient re�ects the patient�s ideal drug. That is, a drug with characteristic x̂ has the ideal type for a patient located at x̂. Those patients who fail to obtain a drug of their ideal type face a cost, and the farther patient type x from x̂ is, the lower the bene�ts he enjoys (or the larger the side e¤ects he su¤ers) when he is exposed to the drug.7 The second characteristic of the drug incorporates the vertical di¤erentiation and it refers to the gross e¤ectiveness ĥ of the drug. This is a quality dimension that a¤ects the whole population and it includes the health gains experienced by patients (which may comprise either one or both quality and quantity of life). We assume ĥ > 0; where ĥ = 0 would mean that the drug has the same e¤ect as no treatment, and the higher the ĥ the better the drug for all the patients.8 In order to determine the health gain of a type-x patient treated with drug (x̂; ĥ); we need to consider both dimensions together. The health gain of a patient of type x when drug (x̂; ĥ) is prescribed is b � ĥ� l jx̂�xj � , where jx̂�xj is the distance between the 6For example, in the pharmaceutical market for blood pressure control, the drugs available to treat hypertension may act via the central nervous system, the heart (beta blockers), the kidney (diuretics, saluretics) or the vessels (alpha blockers, ACE inhibitors, AT1 and calcium antagonists). The e¢ cacy and side e¤ects of these medicines di¤er across patients and, hence, a¤ect physician prescription patterns. 7There is no drug that unambiguously dominates another on the horizontal dimension, as patients with a di¤erent x react di¤erently to a drug x̂: If two drugs with a di¤erent x̂ are available, there are patients that bene�t more from one of the drugs, while others would be better o¤when treated with the other. 8In Bardey et al. (2010) drugs are also vertically and horizontally di¤erentiated, although their vertical characteristic is binary while ours is a continuous variable (which allows us to consider small and large di¤erences in the vertical dimension). 6 horizontal characteristic of the drug and the type of the patient, l > 0 scales the loss of e¤ectiveness or the extent of side e¤ects and b is the marginal utility of being healthy. If we denote by p̂ the price of drug (x̂; ĥ), the bene�t to the health system of treating patient x with drug (x̂; ĥ) and paying price p̂ for this drug is H(x; x̂; ĥ; p̂) = b � ĥ� l jx̂�xj � � p̂: We assume that there is a pre-existing drug (x0;h0), x0 2 (0;1), on the market. The price p0 of this pioneering drug is exogenously �xed and does not react to the launch of a new medicine. In markets where drug (x0;h0) is produced by a number of �rms, this assumption can be easily justi�ed on the grounds that the exclusivity of the pioneering drug has already expired and a generic drug has entered the market.9 Without loss of generality, we assume that p0 = c0, being c0 the marginal cost of providing the drug. For simplicity, we assume that all patients bene�t from the pioneering drug, that is, the whole market is initially covered by that drug.10 There is a pharmaceutical �rm (that we call �rm 1), di¤erent from the one selling (x0;h0) ; that can undertake an innovation process.11 This process is uncertain both be- cause it may or may not lead to a new drug and because the characteristics of the potential new drug are ex-ante random. If �rm 1 adopts an innovation process and the process is successful then a new drug is discovered. We denote by (x1;h1) the characteristics of the new drug that will be marketed and by c1 its marginal cost. This drug may use the same active principle as the pioneering drug or it may use a di¤erent one. What is relevant in our model is the location of the drug in the space of horizontal and vertical characteristics. We assume that the �rm producing the new drug freely chooses the price p1: To identify the di¤erences between the new drug and the pioneer, we de�ne �x � ��x1 �x0�� ; �h � h1 �h0; �c � c1 � c0: That is, �x 2 R+ is the distance between the �types�of the drugs. Similarly, �h 2 R indicates the di¤erence in quality between the two drugs, and �c 2 R denotes the 9In the US, the generic share of prescriptions rose from 19% in 1984 to 78% in 2010 (Berndt and Aitken, 2011). There is evidence that once generic drugs enter the market, both the price and sales revenue of pioneering drugs tend to drop by about 80% over the next year (Yin, 2012). 10This hypothesis requires that b � h0 � l ��x0 �x��� � c0 � 0 for all x 2 [0;1], that is, c0 � Min � b � h0 � l � 1�x0 �� ;b � h0 � lx0 � . 11For simplicity in the exposition, we have adopted the view of an entrant in the pharmaceutical market launching a new drug. All our analysis would remain valid if, alternatively, we had assumed that there were several �rms producing the pioneering drug and that one of them could undertake the innovation process, as in Ganuza et al. (2009). 7 di¤erence in marginal costs (the new drug may be more expensive or cheaper to produce than the pioneer). Finally, there is a physician who makes drug prescription decisions. We assume that the physician acts as a perfect agent for the health system, which includes both the patients�utility and the cost incurred by the health authority. Hence, the physician assigns the medication to patients based on the price-e¤ectiveness of the two drugs.12 Notice that, given the physician behavior, whether the patients bear a copayment or the drug is fully reimbursed by the health authority, there is no di¤erence implied in the results since the physician takes into account the true cost of the drugs (paid either by the patients or the health authority).13 The timing of our game is as follows. In the �rst stage, �rm 1 decides its innovation strategy. In case the innovation process succeeds, the characteristics (x1;h1) as well as the marginal cost c1 of the new drug are known. In the second stage, the innovative �rm sets the price p1 it charges. Finally, in the third stage, provided the new drug is marketed, the physician allocates the drugs to patients (if only the pioneering drug is available, the physician will prescribe it to all the patients). As usual, we solve the game by backward induction. 3 Prescription of Drugs We now analyze the last stage of the game if a new drug with characteristics (x1;h1) has been marketed at a price p1. At this stage of the game, the physician decides which patients are prescribed the pioneering drug (x0;h0) and which ones the new one (x1;h1). The physician takes into account both the expected e¤ectiveness of the drugs and their price. Ifbothdrugsprovide identicalbene�ts to thehealthsystemwhentreatingapatient, we adopt the convention that the physician prescribes the new drug. Following the physician�s decision, the market will be split between the new drug and the pioneer. Depending on both drugs�characteristics, as well as the price p1 decided by the innovative �rm, three di¤erent scenarios may arise. We illustrate them in Figure 1. First, the physician prescribes the pioneering drug to all patients if the price p1 of the new drug is very high when compared to its health bene�ts . We denote pmax the price above which no patient is prescribed the new drug (that happens even when pa- 12This assumption allows us to focus on �rm incentives to pharmaceutical innovation, leaving aside any distortion caused by the potential strategic behavior of agents as a consequence of the di¤erent views they share. 13In section 8 we discuss the robustness of the analysis in a model where the physician only takes into account the patients�utility. In that model, the reimbursement policy has an in�uence not only on physician prescription choices but also on the pricing and innovation decisions by the �rm. 8 H b(h0 − lx − x0) − c0 0 0 1 x x0 x1 if p1 > pmax if p1 ∈ (pall, pmax) if p1 < pall b(h1 − lx − x1) − p1 b(h1 − lx − x1) − p1 b(h1 − lx − x1) − p1 Figure 1: Bene�ts of the health system with the two drugs and split of the market as a function of p1, c0, (x0;h0), and (x1;h1). tient x1 is not treated with (x1;h1) if p1 > pmax). Formally, pmax is characterized by H(x1;x1;h1;pmax) = H(x1;x0;h0;c0); or b(h1 � l jx1 �x1j)�pmax = b(h0 � l jx1 �x0j)� c0; which implies pmax � c0 + b(�h + l�x): If p1 = pmax, the market for the new drug is 1�x1 if x1 > x0; it is x1 if x1 < x0; and it is the whole market if x1 = x0 (the rest of the patients are prescribed the old drug). Note that pmax is increasing in b, l, �x, �h, and c0. Therefore, for a given p1, it is more likely that the old drug will keep all the market if health has a low marginal value (b low), the disparities in the side e¤ects of the drug for di¤erent patients are small (l low), the di¤erence between the two drugs is also small (�h and �x are low), and/or the pioneering drug is very cheap to produce. Second, the physician prescribes the new drug to all patients if the price p1 is low enough. This is the case if p1 is so low that it is optimal to treat patient x0 with the new drug. The cut-o¤ value pall below which all patients are treated with (x1;h1) is characterized by b(h1 � l jx1 �x0j)�pall = b(h0 � l jx0 �x0j)� c0; that is, pall � c0 + b(�h � l�x): Given the expression of pall, a given p1 is more likely to be lower than pall for large values of c0, b, and �h, and for low values of l and �x (i.e., when the di¤erence between 9 the patient who pro�ts more from each drug is low). We note that pall = pmax if x1 = x0: Finally, the physician prescribes each drug to a subset of the patients for p1 2� pall;pmax � . To identify the market for each drug, consider �rst the case where x1 > x0. Thetwodrugsprovidethesamebene�ts toapatientof type ~x 2 (x0;x1) if b(h0 � l(~x�x0))� c0 = b(h1 � l(x1 � ~x))�p1. That is, the type of the indi¤erent patient is ~x � x0 + (l�x ��h) 2l + (p1 � c0) 2bl : The physician prescribes treatment (x0;h0) at a price c0 to those patients whose type lies in the interval [0; ~x); whereas patients with a type in the interval [~x;1] are treated with (x1;h1) at a price p1: Similarly, for p1 2 � pall;pmax � and x1 < x0 the indi¤erent patient is ~x � x0 � (l�x ��h) 2l � (p1 � c0) 2bl and the markets for the new drug and the pioneer are [0; ~x] and (~x;1], respectively. 4 The Optimal Pricing Policy In this section we study the optimal price decision of �rm 1 if, as a result of the innovation process, a new drug with characteristics (x1;h1) has been achieved. Firm 1�s incentive to price high or low depends on the drug di¤erences in terms of vertical characteristics (both in quality, measured by �h; and in marginal cost, measured by�c), andhorizontal characteristics (measuredbythedistance intype�x). Thestrength of the incentivesalsodependsonthe sizeof the submarket (the subsetof patients) inwhich the innovative �rm more directly competes with the pioneering drug. If x1 is on the right of x0 (i.e., x1 > x0), then the competition is �ercer on the right of x0 than on the left of x0. That is, the size of the submarket in which �rm 1 directly challenges the pioneering drug is 1�x0. Similarly, if x1 < x0, the competition is more intense to the left of x0, that is, in a submarket of size x0. We denote by M the size of this submarket: M � 1�x0 if x1 > x0 and M � x0 if x1 < x0. We also denote M � 1 if x1 = x0 (although M does not play any role when �x = 0). Proposition 1 summarizes the price decision of the pharmaceutical �rm. Except for the region of parameters where there is no room for the �rm to make pro�ts, the new drug is always o¤ered at a price in the interval � pall;pmax � : For convenience, we de�ne pint � 1 2 � c0 + c1 � + blM � 1 2 b(l�x ��h); the candidate price for an interior solution. 10 In Proposition 1, we also use the function g(�x), which is de�ned as follows: g(�x) � �x +2 � 2�M �2 p 1�M � if �x > p 1�M � (1�M) � (1+M ��x) (1�M +�x) �x otherwise. The function g(�x) is increasing, continuously di¤erentiable and ful�lls g(�x = 0) = 0. Finally, as �h and �c have similar e¤ects and as they often appear together in the mathematical expressions, we denote the composite e¤ect of these two vertical variables as �y � �h � 1 b �c: The parameter �y can be interpreted as a measure of the di¤erences in cost-e¤ectiveness between the new drug and the pioneering one. The larger the value of �y the more cost-e¤ective the new drug is compared to the pioneer. Proposition 1 The optimal price decision p1� of �rm 1 and its pro�ts �1(p1�) are as follows: Region a: If �y � �l�x then the new drug is not prescribed: p1� = c1 and �1(c1) = 0. Region b: If �y 2 (�l�x; lg (�x)) then the new drug replaces the pioneer for a subset of patients. If in addition Region b.i: M � 1 2l (�y +3l�x) then p1� = pmax and �1(pmax) = b(M ��x)(�y + l�x) : Region b.ii: M < 1 2l (�y +3l�x) then p1� = pint and �1(pint) = b 2l � lM + 1 2 (�y � l�x) �2 : Region c: If �y � lg (�x) then the new drug takes over the entire market: p1� = pall; and �1(pall) = b(�y � l�x): The optimal pro�t function �1 is continuous in �x;�h, and �c: Wenowo¤ersome intuitions forProposition1. Whendi¤erences inthecost-e¤ectiveness between the new drug and the pioneer are very negative, that is, for low values of �y, there is no price above the marginal cost under which �rm 1 can sell its drug. More 11 x h 10 x0 Reg c p1* = pall h0 Reg b.ii p1* = pint b.i pmax Reg b.i p1* = pmax b.ii pint Reg a p1* = c1 Figure 2: Optimal pricing policy by �rm 1 in the drug space (x;h) when c1 = c0: precisely, in Region a, where the �aggregate�di¤erence �y + l�x between the two drugs is not positive, �rm 1 makes zero pro�t. On the contrary, in Region c the cost-e¤ectiveness of the new drug far outperforms that of the pioneer and �rm 1 decides to set a price for which the new drug is prescribed to all patients. In this case, the price that allows the �rm to serve the entire market pall is large enough so that for the �rm it is worth setting pall instead of increasing the price further and losing some patients. Finally, for intermediate values of �y (Region b, which only exists if �x > 0), the optimal price decision by �rm 1 depends on the size of submarket M. If M is su¢ ciently large, then �rm 1 sets the maximum price compatible with selling the drug pmax because the number of patients that are treated with the new drug under this price is fairly large. In contrast, for low values of M; �rm 1 would sell the drug to too few patients at pmax and, therefore, it prefers to cut the price and it sets pint. Figure 2 represents the optimal pricing policy by the innovative �rm for every combi- nation of (x1;h1) ; for a given value of �c; b and l: The �gure is drawn for �c = 0: For a positive (resp. negative) �c, all the �gure would move upwards (resp. downwards) in a proportion 1 b �c. Figure 2 is not symmetric with respect to the vertical x0 because, in this example, x0 6= 1 2 : It isworthnoticingthatalthoughtheoptimalpricedecisionp1� of�rm1 is continuously increasing in the quality of the drug (i.e., in �y) inside each region, it is neither continuous nor increasingwhen�y moves fromRegionbtoRegionc. At theborderof the tworegions, 12 where �y = lg (�x), pmax > pall (in Region b.i) and pint > pall (in Region b.ii). Therefore, the price p1� decreases from either pmax or pint to pall if a marginal increase in �h moves the drug from Region b to Region c. On the other hand, the price p1� is continuous in �y (and in �x) at the border of the Region b.i and Region b.ii. Finally, the optimal price p1� increases with the horizontal di¤erentiation �x in Region b.i, but decreases with �x in Region b.ii and Region c. Corollary 1 provides some comparative statics of �rm 1�s pro�ts with respect to the level of di¤erentiation between the two drugs, �x and �h: We will use these expressions in section 6 and subsection 7.3 where we compare the private and social incentives to develop a new drug. Corollary 1 The comparative statics of �rm 1�s pro�ts are as follows: Region b.i: �1 is increasing and linear in �y. It is a concave function in �x; increasing up to �x = 1 2l (lM ��y) and decreasing afterwards. Region b.ii: �1 is increasing and convex in �y and it is decreasing and convex in �x: Region c: �1 is increasing and linear in �y and it is decreasing and linear in �x: Corollary 1 shows that the pro�ts of the innovative �rm are always larger the more cost-e¤ective the new drug is -that is, the larger the di¤erence h1 �h0 and/or the smaller the di¤erence c1 �c0. Regarding the horizontal characteristic of the drug, �rm 1�s pro�ts are decreasing in �x; except in Region b.i, where they are increasing for low values of �x: 14 5 Bene�t to the Health System The launch of the new drug a¤ects the bene�t of the health system. We now move to discuss the health system surplus in the di¤erent price regions. Recall that in our model the doctor is a perfect agent for the health system. Therefore, he only prescribes the new drug when the surplus of the health system is higher than, or equal to, the surplus obtained using the pioneer drug. We denote by �CS the gain 14An increase in the horizontal di¤erentiation between the two drugs has two opposite e¤ects on the pro�ts of �rm 1. On the one hand, for a given price, the market share of �rm 1 decreases because more patients prefer the pioneering drug, which has a negative impact on the pro�ts of the �rm. On the other hand, a larger di¤erentiation allows the �rm to increase the price, which may have a positive impact on its pro�ts. In relative terms, the positive e¤ect of the price is less and less important as the demand for the new drug decreases, that is, as the horizontal di¤erentiation increases. In our model, the positive e¤ect only outweighs the negative one when �x is small. 13 in patient health, net of the price, as a consequence of the launch of the new drug. Proposition 2 provides the expressions for �CS in the regions identi�ed in Proposition 1. Proposition 2 Given the optimal pricing policy p1� of �rm 1; the variation of the health system surplus �CS due to the launch of the new drug is: Region a: �CS(c1) = 0. Region b.i: �CS(pmax) = 0: Region b.ii: �CS(pint) = b 16l (�y +3l�x �2lM)(�y �5l�x +6lM) : Region c: �CS(pall) = bl�x (2M ��x). Some interesting insights can be extracted from Proposition 2. In the scenario where the new drug is sold at pmax (Region b.i), total surplus is the same before and after the launch of the new drug. The reason is that the �rm charges the largest potential price, pmax; and it therefore extracts all the surplus from the patients that in equilibrium are prescribed the new drug. In contrast, in Region b.ii, the �rm decides to charge pint < pmax to attract some new patients and, thus, the health system surplus increases when the new drug is marketed. Finally, in the scenario where drug 1 takes over the market (Region c) the health system also bene�ts from the launch of the new drug when �x > 0. In this case, the health advantages of the new drug outweighs the larger price charged by the innovative �rm, so that the health system ends up strictly better o¤. We also provide some comparative statics of the health system surplus with respect to the level of di¤erentiation of the two drugs, �x and �y: Corollary 2 The comparative statics of the health system surplus are as follows: Regions a and b.i: �CS does not change with �y or �x: Region b.ii: �CS is increasing in �y: It is increasing up to �x = 115l (14lM ��y) and then decreasing in �x. Region c: �CS is independent of �y and it is increasing in �x: Moreover, �CS is continuous at the border between Region b.i and Region b.ii but it discontinuously increases when �y increases (or �x decreases) and the drug moves from Region b to Region c. Corollary 2 shows that the gains derived by the health system from the launch of the new drug depend on the cost-e¤ectiveness of this drug as compared to the pioneering drug (i.e., on �y) only in Region b.ii. In this region, the higher the cost-e¤ectiveness 14 (either due to advantages in quality or costs) of the new drug, the higher the gain in the surplus. In the other regions, a larger cost-e¤ectiveness of the drug is fully translated into a higher price. Notice that health system surplus is certainly more sensitive to the horizontal characteristic �x. In particular, it tends to be increasing in �x; except in the region where the new drug replaces the pioneer for some patients (Region b.ii), where the health system surplus is decreasing for high values of �x. As �x increases, the innovative �rm cannot appropriate all the surplus through a higher price because its market would be too reduced. 6 Private versus Social Incentives Before analyzing the innovation stage (in section 7), we brie�y discuss here the di¤erence in incentives for R&D between the innovative �rm and a social planner who takes into account the sum of the health system surplus and the �rm�s bene�ts. R&D incentives in our model come from the bene�ts that the parties involved derive from the launching of the potential new drug. To discuss the di¤erence between private and social R&D incentives, it is worth noting that the innovative �rm and the health system have di¤erent preferences regarding the characteristics of their best drug, given the pioneering drug on the market. Figure 3 represents the comparative statics of �rm 1�s pro�ts and health system surplus with respect to vertical and horizontal changes in the new drug as compared to the pioneer (corollaries 1 and 2).15 In general, the �rm cares a great deal about increasing the quality of the drug, either through a more e¤ective or a less costly drug, whereas the health system (as it takes the price into account) only bene�ts from the launching of a better-quality drug if such a drug is well-suited to those patients far from x0 (Region b.ii). Additionally, the pro�ts of the innovative �rm decrease with the degree of horizontal di¤erentiation between the two drugs, except when the di¤erentiation is small and the quality of the two drugs is similar (the left-hand part of Region b.i). On the contrary, the health system always bene�ts if new drugs focus on patients for whom the e¤ectiveness of the old drug is low. Figure 3 helps us to better understand the di¤erence between incentives to innovate for the �rm and for a social planner. For example, if the innovative �rm could launch a drug through a deterministic process then it would have an incentive to choose a drug with a higher quality but the same horizontal characteristic as the pioneering drug. In fact, if the new drug were available at no cost (or at a low cost), the optimal drug for �rm 1 would 15Figure 3 only represents the comparative statics for drugs on the right-hand side of x0; for those drugs on the left-hand side of x0 the comparative statics are similar. Moreover, the �gure does not point out the e¤ects that are zero. For example, in Region c, �CS is independent of �y and the �gure does not include information about the behavior of �CS with respect to �y in that region. 15 x h 10 x0 h0 Π1 ∆y & ∆CS ∆y CS Escriviu una equació aquí. Δy Π1 ∆x & ∆CS ∆x CS Escriviu una equació aquí. Δy Π1 ∆y CS Escriviu una equació aquí. Δy Π1 ∆x & ∆CS ∆x CS Escriviu una equació aquí. Δy Π1 ∆y CS Escriviu una equació aquí. Δy Π1 ∆x CS Escriviu una equació aquí. Δy O1 OCS OW ∆CS jumps up htop 1/2 Figure 3: Comparative statics and most preferred drugs in the drug space (x;h): be O1 = (x0;htop) in Figure 3, where htop is the highest possible quality. In contrast, consumers prefer drugs that are horizontally di¤erentiated from the pioneering drug. In terms of consumer surplus, the optimal drug would be OCS, the farthest from x0 in the horizontal dimension and at the border of Region c. Finally, if we de�ne the increase in social welfare as the sum of �rm 1�s pro�ts and the increase in the health system surplus,16 that is, �W � �1 +�CS, then balancing both �rm and consumer interests, the optimal drug from a total welfare point of view would be OW in Figure 3. The drug OW improves upon the pioneering drug as much as possible in the vertical dimension and it is also horizontally di¤erentiated from the pioneering drug, although the optimal di¤erentiation is far from the maximal. In fact, the drug OW would be horizontally located at 1=2 since this is the drug type that minimizes the side-e¤ects of the whole population of patients. 7 A Model of Pharmaceutical Innovation In this section we analyze the �rst stage of our game, the innovation stage, where �rm 1 chooses its R&D investment to maximize its expected pro�t. The innovation strategy of the �rm involves both the type of innovative process that it wants to adopt and the level of the resources invested in that process. We now describe a typology of drugs and 16We have assumed that the pioneering drug is sold at its marginal cost. Thus, the �rm (or any of the �rms) selling drug 0 always has zero pro�ts. 16 innovation processes and then discuss the �rm�s innovation decision. 7.1 Me-Too versus Breakthrough Drugs In the pharmaceutical industry, a crucial distinction is made between me-too and break- through innovations. The traditional distinction between these two types of innovation relies on the mechanism of the action of the drugs. However, several voices in the phar- maceutical industry have called for the adoption of a broader perspective when evaluating innovation in medicines.17 Our interpretation is that the di¤erence between me-too and breakthrough innovations rests on the distance between the new drug and the pioneer at either the horizontal axis and/or the vertical one. A me-too innovation represents a small change for some (or all) patients either in terms of quality of treatment, cost savings or side e¤ects. For example, a me-too innovation may open the possibility of administering smaller or fewer doses, or it might imply a slightly less invasive delivery (which we inter- pret as a small increase in y).18 A me-too innovation may also cause slightly lower side e¤ects for a subpopulation of patients (a small change in x).19 In contrast, a breakthrough innovation ensures a signi�cant increase in the quality of the new drug or a drug whose characteristics make it well-suited to patients who could not be well treated under the existing treatment.20 7.2 Incremental versus Radical Innovation Processes A �rm seeking a me-too or a breakthrough innovation would rely on di¤erent processes. In this sense, we de�ne an incremental innovation process as a process aiming at a me- too innovation with respect to the existing drug.21 Similarly, when the process pursues a signi�cant improvement (for all or a subpopulation of patients), or a substantial cost reduction as compared to the old drug, then we say that the innovation process is radical. 17See the report by Mestre-Ferrandiz, Mordoh, and Sussex (2012) for a thorough discussion of the nature of innovation in medicines. 18Insulin pens, for instance, are minimally invasive and have largely superseded the conventional insulin syringe. 19The antihistamine Clarinex (desloratidine), for instance, is a small variation of Claritin (loratidine) that has lower side e¤ects for those people with severe allergies and/or accompanying chronic respiratory problems. 20For instance, Prilosep, based on the �rst proton pump inhibitor (omeprazole), was considered a breakthrough. It proved to be more e¤ective than histamine-2 receptor antagonists to the management of peptic ulcer diseases. 21Sometimes, follow-on drugs are simply the natural outcome of simultaneous research programs into the same therapeutic target (diMasi and Paquette, 2004). In other cases, they are the result of an intentionally imitative research program (Garnier, 2008). The approach adopted in this paper is best suited to this second view of the innovation process. 17 Formally, an incremental innovation process (which we will denote by the sub-index in) pursues a drug with a small �x or �y whereas a radical innovation process (denoted by the sub-index ra) aims at a drug with a large �x and/or �y. 7.3 A Simple Model of Innovation In this subsection we propose a highly stylized model of R&Dinvestment with uncertainty. We assume that the result of the innovation process is uncertain and its outcome can only be poorly predicted, if at all. The uncertainty is greater for groundbreaking processes. There are two types of innovation strategies available to the pharmaceutical �rm. An incremental innovation process can lead to a drug that is similar to the pioneering drug, in the sense that it would have the same horizontal (or vertical) characteristic, that is, x1 = x0 (or y1 = y0) and a minor improvement in quality (or small di¤erences in side e¤ects).22 On the other hand, a radical innovation process results, in the case of success, in a drug (x1;y1) where y1 is random but higher than y0 and x1 is also random. This re�ects the idea that the innovative process represents a signi�cant departure from the old drug. Moreover, the side e¤ects may also be very di¤erent from those of the pioneering drug. We depict the two categories of processes in Figure 4.23 The crucial di¤erences between the two categories of processes is that the distribution of the outcome of a radical innovation process takes values on a large support and has a greater variance, which leads to higher chances of getting a breakthrough drug (Girotra, Terwiesch, and Ulrich, 2007; Singh and Fleming, 2010). Let us �rst consider incremental innovation processes. If an investment I is realized then there is a probability qin(I), increasing in I, of obtaining an innovation, while no drug is obtained with probability 1 � qin(I). If it is a vertical innovation process then, in the case of success, the new drug has characteristics (x1;y1), with x1 = x0 and y1 is distributed according to the density function fin(y1) that takes values in the interval [y0 � ver;y0 + �ver] ; where ver and �ver are small (in the sense that the new drug cannot be much more cost-e¤ective than the pioneer). Thus, for all I invested in a vertical 22Sometimes the incremental innovation process is developed by the same �rm that holds the patent for the pioneering drug in order to better compete with those �rms o¤ering generic versions of the drug once the patent has expired. Examples are Prilosec and Nexium, aimed at decreasing the amount of acid produced in the stomach. In 2001 the patent for Prilosec (which has omeprazole as an active ingredient), owned by AstraZeneca, expired and several generic versions of omeprazole entered the market. The same year, Nexium, whose active ingredient is esomeprazole (a version of omeprazole whose molecular orientation is left-handed), was also patented by AstraZeneca (our �rm 1). 23Note that our innovation process in the vertical dimension di¤ers notably from the vertical innovation analyzed by Bardey et al. (2010), where a vertical innovation is always synonymous with a breakthrough innovation. 18 x h 10 x0 h0 Vertical incremental IP Radical IP Horizontal incremental IP Figure 4: Incremental and radical innovation processes. incremental innovation process, expected private pro�ts �in(I) and social welfare Win(I) are �in(I) = qin(I) Z [y0� ver;y0+�ver] �1(x = x0;y)fin(y)dy; Win(I) = qin(I) Z [y0� ver;y0+�ver] � �1(x = x0;y)+�CS(x = x0;y) � fin(y)dy, where �1(x;y) and �CS(x;y) denote the �rm 1�s pro�ts and the increase in consumer surplus when the new drug has characteristics (x;y). The expressions for pro�ts and social welfare are similar for horizontal incremental processes. In this case, the R&D investment leads, in the case of success, to a drug (x1;y1) with y1 = y0 and x1 is distributed according to a density function hin(x) that takes values in the interval [x0 � hor;x0 + �hor] ; where hor and �hor are positive and small (in the sense that the new drug would be suitable for similar types of patient than the pioneer drug). Proposition 3 compares private and social incentives to adopt an incremental innova- tion process. Proposition 3 For an incremental innovation process pursuing a me-too drug, the opti- mal investment decision for �rm 1; I1in; and for the social planner, I � in; coincide: I 1 in = I � in. The intuition for this result derives from the fact that, for drugs close to the pioneering drug, the innovative �rm is always able to extract all the health system surplus. Consider a vertical innovation process. If it is successful and the drug has a characteristic y1 > y0, 19 �rm 1 gets some monopoly power because the new drug lies in Region c. The �rm will impact all the extra quality of the drug into a higher price and it is able to extract all the health system surplus (�CS = 0 in Region c when �x = 0). As the health system never bene�ts from the new drug, social and private incentives to innovate coincide as do their optimal investment levels. The intuition for the horizontal incremental process is similar: when the realization of ~x1 is close to x0; �rm 1 sets the maximum price that the health authority is willing to pay and it extracts all the surplus (�CS = 0). We now consider a radical process. If an investment I is made then there is a prob- ability qra(I), increasing in I, of success at getting a new drug (x1;y1).24 If the process is successful, the new drug has characteristics (x1;y1), where y1 takes values in the inter- val [y0 +�;y0 +�] and x1 takes values in the interval [0;1] ; where � can be positive or negative, � is positive, � < � and (x1;y1) is distributed according to a density function fra(x 1;y1).25 Therefore, expected private and social bene�ts for each level of investment I in a radical innovation process are �ra(I) = qra(I) Z [0;1] Z [y0+�;y0+�] �1(x1;y1)fra(x 1;y1)dy1dx1 and Wra(I) = qra(I) Z [0;1] Z [y0+�;y0+�] � �1(x1;y1)+�CS(x1;y1) � fra(x 1;y1)dy1dx1: Proposition 4 states the di¤erence between private and social incentives to invest in a radical innovation process. Proposition 4 For a radical innovation process pursuing a breakthrough drug the optimal investment decision for �rm 1; I1ra; is smaller than that for the social planner, I � ra: I 1 ra < I�ra. A radical innovation process leads, with a certain probability, to a drug that improves the health system surplus. First, the health system bene�ts when the process is successful if the new drug lies in Region c and x1 6= x0. In this case, the innovative �rm cannot appropriate all the surplus: at the maximum price at which it can serve all the market (pall), some patients are strictly better-o¤ with the new drug than with the pioneer. Similarly, if the successful process leads to a drug in Region b.ii then the interior price pint allows the health system to bene�t. A social planner would also take into account 24Typically, qra(I) would be (much) lower than qin(I) for any I: 25The function fra(x1;y1) may not take values for some intervals of characteristics. Figure 4, for instance, illustrates a process that never leads to very extreme drugs on the horizontal axis. In this �gure, � > 0 but this is not necessary in general. 20 this surplus that the �rm cannot extract from the health system and it would choose a higher investment level than the �rm. As shown in propositions 3 and 4, the �rm fully appropriates all the bene�ts derived from me-too drugs, whereas the health system can appropriate some surplus if a radical innovation process goes successfully. Proposition 5 uses these results to state the main policy implication of our analysis of the innovation incentives. Proposition 5 If �rm 1 can only adopt one category of innovation process (due, for instance, to �nancial or capacity constraints) then: (i) There are cases where �rm 1 prefers to adopt an incremental innovation process whereas the social welfare is larger when adopting a radical innovation process. (ii) There is no case where �rm 1 prefers to adopt a radical innovation process whereas adopting an incremental innovation process would generate a higher welfare. Proposition 5 provides some theoretical support to the social concern that pharma- ceutical �rms devote too many resources to market me-too drugs and too few to launch breakthrough drugs. Our model suggests that this disalignment between private and so- cial incentives is due to the lack of private incentives to pursue radical innovations. While private and social incentives to devote resources to pursue me-too drugs are aligned be- cause the �rm is able to appropriate all the bene�ts through the price, this is not true for �rst-in-class drugs. In the latter case, the �rm sets a price for the new drug which is low enough to serve all (or a good part of) the market and the consumers bene�t from it. 8 The Physician is a Perfect Agent for the Patients In the previous sections we have assumed that the demand for the drugs is decided by a physician who prescribes the drug that provides the highest bene�t to the whole health system. In this section we discuss the robustness of the results when the physician acts as a perfect agent for the patients, prescribing the drug that maximizes the patients�utility. Thus, the physician does not consider the whole cost of the drugs; he only internalizes the cost disbursed by the patient.26 We analyze two di¤erent reimbursement regimes: one in which patients pay a proportion of the price of the drugs not covered by health insurance (that is, there is a copayment), and a second one in which the old drug is fully �nanced by the health authority while the new one is not covered by health insurance. 26If the physician makes choices considering patient utility and health authority costs then we would be in the framework analyzed in the previous sections: the physician internalizes the whole price, regardless of whether they are paid by the health authority or by the patients themselves. 21 8.1 Patient Cost-Sharing of the Drugs Suppose that there is a copayment � 2 (0;1] so that patients are required to pay �p if the price of the drug is p. Then, the bene�t to the health system of treating patient x with drug (x̂; ĥ) and paying price p̂ for this drug is H(x; x̂; ĥ; p̂) while patients�utility, which determines the physician�s prescription of drugs, is U(x; x̂; ĥ; p̂) � b � ĥ� l jx̂�xj � ��p̂ = � � b � � ĥ� l jx̂�xj � � p̂ � : If the physician follows the function U(x; x̂; ĥ; p̂) instead of H(x; x̂; ĥ; p̂) to make his choices, then all the results concerning physician prescription choices and �rm 1�s pricing decisions for the case � = 1 (Proposition 1) would remain valid for any � by replacing, in the expressions of pmax, pall, and pint, the parameter b by b � . That is, the results in a model where patients pay a proportion of the prices are similar to those in a model without copayment where the marginal utility of being healthy is higher. Since sign � @p1 @� � = �sign � @p1 @b � , and pmax, pall, and pint are all increasing in b, the price of the new drug will be higher the lower the copayment �.27 In order to examine the results more deeply we need to distinguish two cases. In the case c1 = c0 (i.e., �c = 0), the regions in the drug space depicted in Figure 2 are independent of the parameter b. Therefore, at the optimal prices, the new and the old drugs are prescribed to the same patients for any value of �, although the price for drug 1 is larger as � decreases. This implies that, for �c = 0, an increase in the copayment (that is, a decrease in �) leads to a lower bene�t to the health system and to a higher pro�t to �rm 1. However, such increase in the copayment has no impact on total welfare because changes in � only induce changes in the monetary transfers between the health system and the innovative �rm. Thus, the optimal drug for �rm 1 would still be O1 (see Figure 3), the drug OW would still be optimal from a total welfare point of view (de�ned as the sum of the bene�ts of the health system and �rm 1�s pro�ts), and the point OCS would correspond to the optimal drug for the patient (that is, the drug that maximizes the function U). In the case c1 > c0 (�c > 0), the borders of the regions in Figure 2 shift vertically down, and the new drug is prescribed to more patients with than without copayment. Here, the increase in the monetary transfer from the health authority to �rm 1 due to the copayment comes combined with a misallocation of drugs from the health system 27This extension also corresponds to the case where there is no copayment but the physician gives di¤erent weights to the patient health (a weight of 1) and to the drugs�price (a weight of a). Equivalently, the model corresponds to a situation where the physician takes into account both the patients�utility and the pro�ts of the health authority and puts less weight on the second term. 22 perspective. The location of the optimal drugs O1, OW , and OCS in the drug space would be the same as in the case �c = 0 when Figure 3 is drawn using the new (shifted-down) borders. Finally, given that equilibrium prices are higher when the physician is a perfect agent for patients subject to copayment than when he is a perfect agent for the health system, the pro�ts of the innovative �rm are higher: the three functions �1(pmax), �1(pint); and �1(pall) are linear in b; hence, they increase as � decreases. Therefore, �rm 1�s incentives to innovate are also higher. This result holds both for incremental and radical innovation processes. When �c = 0, the regions in Figure 2 do not vary with � and, given the linearity of the pro�t functions in b, the trade-o¤ between the two types of processes is una¤ected: the �rm has relatively too many incentives to pursue an incremental rather than a radical innovation process. If �c > 0, low values of � imply that drugs close to the pioneer (in terms of h and x) that would not have been marketed without copayments are now prescribed. Therefore, �rm 1 has a stronger incentive to develop drugs whose additional therapeutic value is low, which suggests that it is yet more inclined to devote resources to incremental rather than to radical innovation processes. 8.2 The New Drug is Not Subsidized Suppose now that the health authority only covers the old drug, so that patients have to pay the full price of the new one, should it be prescribed. Thus, patients�utility when treated with the old drug is U(x;x0;h0;0) = b � h0 � l ��x0 �x��� ; while it takes the form U(x;x1;h1;p1) = b � h1 � l ��x1 �x����p1 when patients are prescribed the new drug. Then, physician prescription choices and pricing decisions by the �rm are obtained by considering the analysis conducted in the previous sections for the particular case c0 = 0: Both the physician and the �rm behave as if the price of the pioneering drug were 0. Since pmax, pall, and pint are all decreasing in c0, �rm 1 is induced to choose lower prices than in our initial model. Moreover, looking at Figure 2, reductions in c0 make the borders of the regions shift vertically up and, at the optimal prices, the new drug is prescribed to fewer patients as compared to the situation in which the cost of the pioneering drug is also taken into account. Thus, in this case, the �rm obtains lower pro�ts and it has lower incentives to innovate. However, its relative incentives to adopt radical innovation processes are now larger because me-too drugs do not provide any pro�ts. 23 9 Conclusion The proliferation of follow-on drugs is nowadays the subject of some debate. Proponents of follow-on drugs highlight that some of them are therapeutically superior to the pioneer. Moreover, patients and physicians bene�t from the access to a larger pool of therapeutic choices. But there are also voices warning that imitative drug development poses a threat, as it could reduce the incentive for �rms to develop �rst-in-class drugs. This paper seeks to contribute to this social debate. We have constructed a simple model where drugs are vertically and horizontally di¤erentiated. After studying the opti- mal price decision of a �rm introducing a new drug, we have analyzed the �rm incentives to invest in R&D when a pioneer drug is already on the market. In particular, we have disentangled the quest for breakthrough drugs from the search of follow-on drugs. In our model, both breakthrough and follow-on drugs are socially valuable. While private and social incentives to invest in R&D processes coincide for incremental innovation ventures, private incentives are lower than social ones when the process is rad- ical. Moreover, we interestingly �nd that pharmaceutical �rms are too prone to devoting resources (if scarce) to pursue incremental innovation processes so as to fully appropriate all the bene�ts derived from me-too drugs. Thus, these results somehow reproduce the social concern that the main problem regarding the rapid increase of me-too drugs is that they diminish the incentives for innovation in pioneering drugs. Our conclusions are obtained under some simplifying assumptions; we now discuss some of them. First, we have assumed that the pioneering drug is sold on the market at its marginal price. This hypothesis �ts well in markets where the patent for the pioneering drug has already expired and several generic drugs have been introduced. However, there are other markets where the pioneering drug is sold by one �rm at a price over its marginal cost. In such cases, the incumbent �rm may react to the launch of a new drug by reducing the price of its drug. Price competition between the two �rms will be �ercer the lower the horizontal distance between the two drugs. This seems to suggest that under price competitionthe incentivesof the innovative�rmtodi¤erentiate itself in thehorizontal axis increase, which may translate into more incentives to adopt radical innovation processes. In addition to this, if the patent covering the pioneering drug has not expired yet, an incremental innovation would be more likely to infringe on the patent than a radical one, which would further increase the �rm�s incentives to invest in radical innovations. Secondly, our innovative �rm freely chooses the price of the new drug. However, reg- ulations worldwide to control excessive market power of pharmaceutical �rms abound. It would be worth investigating whether price regulations (such as price ceilings or reference prices) would be an e¤ective tool to align the incentives of the �rm and the society. Price ceilings in our model, for instance, would undermine private incentives to innovate. Given 24 that the di¤erence in prices between the new and the pioneering drugs is higher for radical than for incremental innovations, the price ceilings should have a larger negative impact on radical than on incremental processes. Our analysis also suggests that price ceilings would have a larger impact on vertical rather than on horizontal innovations. Since verti- cal improvements allow the pharmaceutical �rm to charge higher prices, the �rm will be more constrained by the regulated price if it launches a new drug that is an improvement over the pioneer in the vertical dimension. Regarding reference prices, the restriction on prices might concern only those drugs that are close to the pioneer. In that case, the incentives for radical innovations may be less a¤ected by the regulation than those for incremental innovations as more di¤erentiated new drugs manage to charge a larger price and obtain higher pro�ts. Third, our results have been obtained under the assumption of risk neutrality for all the players involved. However, it is natural to think that pharmaceutical �rms exhibit a certain degree of risk aversion. If we relax the risk neutrality assumption to accommodate more realism, our main result would be reinforced as risk aversion would make �rms even more prone to adopt (safer) incremental innovations. Finally, in our model there is only one innovative �rm so we have not considered com- petition in research (in Bardey et al., 2010, several laboratories compete in the research sector of the pharmaceutical industry). If �rms compete in adopting incremental innova- tion processes, they will overinvest in comparison to the socially e¢ cient level, leading to more me-too drugs than the socially optimal number. At the same time, the innovative �rm will also increase its investment in radical innovation processes under the pressure of competition. And this could lead to investment levels closer to the socially optimal one. Thus, if �rms compete in research, the result that they devote too many resources to conducting R&D activities that lead to incremental innovations still holds. In this paper, we have identi�ed a problem of misalignment between private and so- cial incentives to innovate that results in a bias toward me-too drugs. A more normative analysis, in which di¤erent solutions to the problem can be addressed, is left for further research. Such policies could include direct R&D tax incentives, nonpro�t tax exemp- tions for research institutions, public �nancing of R&D activity, as well as many other instruments that attempt to stimulate various forms of research and innovative activity. Our analysis suggests that the optimal R&D policy should focus on providing incentives for radical innovation ventures. Finally, although there seems to be a great social awareness of the proliferation of me-too drugs, to date, economists have done little theoretical research on this issue. We hope that this study opens the door to further research into that area and that it will also stimulate the ongoing debate over the excessive launching of me-too drugs. 25 References [1] Angell, M., 2004. The truth about the drug companies. New York: Random House. [2] Antoñanzas, F., Juárez-Castelló, C., Rodríguez-Ibeas, R., 2011. Innovation, loyalty and generic competition in pharmaceutical markets. SERIEs 2, 75-95. [3] Avorn, J., 2004. Powerful medicines. New York, Knopf. [4] Bardey, D., Bommier, A., Jullien, B., 2010. Retail Price Regulation and Innovation: Reference Pricing in the Pharmaceutical Industry. Journal of Health Economics 29 (2), 303-316. [5] Berndt, E. R., Aitken, M., 2011. Brand Loyalty, Generic Entry and Price Com- petition in Pharmaceuticals in the Quarter Century after the 1984 Waxman-Hatch Legislation. International Journal of the Economics of Business 18 (2), 177-201. [6] diMasi, J., Paquette, C., 2004.TheEconomicsofFollow-onDrugResearchandDevel- opment Trends in Entry Rates and the Timing of Development. Pharmacoeconomics 22 (Suppl. 2), 1-14. [7] European Commission, 2013. The 2012 EU Industrial R&D Investment Scoreboard. European Commission. Joint Research Centre (JRC). Luxembourg: Publications O¢ ce of the European Union. [8] García, R., Calantone, R., 2002. A Critical look at technological innovation typology and innovativeness terminology. A literature review. Journal of Product Innovation Management, 19(2), 110-132. [9] Ganuza J., Llobet G., Domínguez B., 2009. R&D in the Pharmaceutical Industry: A World of Small Innovations. Management Science 55 (4), 539-551. [10] Garnier, J.P., 2008. Rebuilding the R&D engine in big pharma. Harvard Business Review 86(5), 68-70, 72-76, 128. [11] Girotra, K., Terwiesch, C., Ulrich, K.T., 2007. Valuing R&D projects in a portfolio: Evidence from the pharmaceutical industry, Management Science 5 (9), 1452-1466. [12] Goozner, M., 2004. The $800mpill: The truthbehind the cost of newdrugs. Berkeley, University of California Press. [13] Hernandez A.F., Harrington, R.A., 2008. Comparative e¤ectiveness of angiotensin- converting-enzyme inhibitors: is an ACE always an ace? Canadian Medical Associa- tion Journal 178 (10), 1316-1319. 26 [14] Kapur, N.K., Musunuru, K., 2008. Clinical e¢ cacy and safety of statins in managing cardiovascular risk. Journal of Vascular Health and Risk Management 4(2), 341-353. [15] Mestre-Ferrandiz, J., Mordoh, A., Sussex, J., 2012. The many faces of innovation. O¢ ce for Health Economics. Available at: http://www.ohe.org/publications/article/the-many-faces-of-innovation-119.cfm [16] Miller, H.I., 2014. Critics of �Me-Too Drugs�Need to Take a Chill Pill. Wall Street Journal, January 1st. [17] Pharmaceutical Research and Manufacturers of America, 2013. 2013 Biopharmaceu- tical Research Industry Pro�le. Washington, DC, PhRMA, July. [18] Singh, J., Fleming L., 2010. Lone Inventors as Sources of Breakthroughs: Myth or Reality? Management Science 56 (1), 41-56. [19] Wertheimer, A.I., Santella T.M., 2009. Pharmaceutical Evolution: The Advantages of Incremental Innovation in Drug Development. Competitive Enterprise Institute. Issue Analysis, no.2, April. Washington, DC. [20] Yin, N., 2012. Pharmaceuticals, Incremental Innovation and Market Exclusivity. Mimeo, Toulouse School of Economics. 10 Appendix Proof of Proposition 1. We distinguish three zones of parameters: c1 � pmax; c1 2 � pall;pmax � , and c1 � pall. We note that c1 � pmax if and only if �c � b(l�x + �h), i.e., �y � �l�x. Similarly, c1 � pall if and only if �c � b(�h � l�x), i.e., �y � l�x. We analyze the optimal �rm�s pricing in the three zones. Zone �y� �l�x: Given that c1 � pmax, there is no price above marginal cost at which the physician prescribes the new drug to some patients. Therefore, the best strategy for �rm 1 is to not sell its drug. Zone �y2(�l�x; l�x) : In this zone, c1 > pall and �rm 1 cannot select a price at which it makes a pro�t by selling to all the patients. If x1 > x0, the �rm chooses the price p1 that maximizes its pro�ts, taking into account that its drug will be prescribed to those patients with characteristic x 2 [~x;1). Hence, p1 2 [c1; pmax] maximizes �1(p1) = (p1 � c1)(1� ~x) = (p1 � c1) � 1�x0 � (l�x ��h) 2l � (p1 � c0) 2bl � : 27 We write the expression for the pro�ts as �1(p1) = (p1 � c1) � M � (l�x ��h) 2l � (p1 � c0) 2bl � , which is also valid for the situation where x1 < x0 (if x1 = x0, this zone is empty).28 The �rst-order and second-order conditions are �1p1(p 1) = M � (l�x ��h) 2l � (2p1 � (c0 + c1)) 2bl ; �1p1p1(p 1) = �1 bl < 0: The interior candidate to solution p1 satis�es �1 p1 (p1) = 0 and is given by p1 = p int = 1 2 � c0 + c1 � + blM � 1 2 b(l�x ��h): The concavity of the function �1(p1;�x;�h) implies that the candidate pint is the optimum if and only if it lies in the interval [c1;pmax]. First, pint > c1 if and only if 1 2 �c + blM � 1 2 b(l�x ��h) > 0, that is, �y > l�x � 2lM. Given that M � �x, the previous inequality is implied by �y > �l�x, which is satis�ed in this zone. Second, pint < pmax = c0 +b(l�x +�h) if and only if 1 2 �c + blM � 1 2 b(l�x ��h) < b(l�x +�h), from which it easily follows that pint < pmax if and only if M < 1 2l (3l�x +�y). Therefore, in this zone, p1� = pint if M < 1 2l (3l�x +�y) and p1� = pmax otherwise (p1 = c cannot be optimal because pro�ts would be zero). Zone �y� l�x: In this zone, �rm 1 can set the price pall that would allow it to attract all patients in [0;1] : It can also choose any price in the interval p1 2 � pall;pmax � , in which case the new drug will be prescribed to a subset of the patients. In this interval, the interior candidate to solution is pint, as in the previous zone. We check the conditions under which pint 2 � pall;pmax � . First, pint > pall if and only if 1 2 (c0 + c1) + blM � 1 2 b(l�x � �h) > c0 + b(�h � l�x); that is, M > 1 2l (�y � l�x): 28If x1 < x0, then ~x = x0 � (l�x ��h) 2l � � p1 � c0 � 2bl = M � (l�x ��h) 2l � � p1 � c0 � 2bl : 28 Note that at p1 = pint, �rm 1 serves a market of size M. However, this cannot be the best pricing strategy for the �rm because it can serve the whole market and obtain larger pro�ts by marginally decreasing the price. Therefore, if M � 1 2l (�y � l�x), setting the price pall and serving the whole market is certainly the optimal decision. Second, as we show in the analysis of Zone �y 2 (�l�x; l�x), pint � pmax if and only if M � 1 2l (3l�x +�y). Thus, for M � 1 2l (3l�x +�y) ; the candidates for solution are pmax and pall; for M 2 � 1 2l (�y � l�x); 12l (3l�x +�y) � the candidates for solution are pint and pall; and for M � 1 2l (�y � l�x), the optimal price is pall. Wenowanalyzetheconditions for�1(pmax) � �1(pall), that is, b(M ��x)(�y + l�x) � b(�y � l�x), or �y � (1+M ��x) (1�M +�x) l�x = lg (�x) : We note that the border �y = lg (�x) always lies in the zone �y � l�x, because b�y � blg (�x) � b(�y � l�x) if and only if g (�x) � �x, which is equivalent to (1+M��x)(1�M+�x) � 1, or M � �x, which holds. Similarly, �1(pint) � �1(pall) if and only if b 2l � lM + 1 2 (�y � l�x) �2 � b(�y � l�x) that, denoting t � (�y � l�x), can be written as � lM + 1 2 t �2 �2lt � 0, that is, f(t) � � t�2l � 2�M +2 p 1�M ��� t�2l � 2�M �2 p 1�M �� � 0: We are interested in the cases where M > 1 2l (�y � l�x) (because pall is certainly optimal otherwise), that is, t < 2lM. The function f(t) satis�es f(0) > 0: Moreover, f(2lM) < 0. Therefore, f(t) � 0 if and only if t is lower than the �rst root, that is, �y � l�x � 2l � 2�M �2 p 1�M � , or �y � l�x +2l � 2�M �2 p 1�M � = lg (�x) : We note that the change in the de�nition of the function g (�x) happens at the point where M = 1 2l (�y + 3l�x) (which separates the regions where either pint or pmax are candidates). Then, the value �x where the change happens is the solution of the following system of equations (in �x and �h): M = 1 2l (�y +3l�x) �y = l�x +2l � 2�M �2 p 1�M � that is, �x = p 1�M � (1�M) ; 29 which is a positive value. The function g (�x), as it is de�ned in the main text just before Proposition 1, is continuous because it is continuous at the point p 1�M�(1�M), and it is also continuously di¤erentiable. Once we have analyzed the optimal price in each of the three zones, it easily follows that the solution is continuous, in the sense that if the optimal price is pall (resp. pmax) in the second zone, then it is also optimal if we decrease �c and enter the third zone. Therefore, the optimal �rm 1�s pricing policy is the one described in the proposition. Finally, it is easy to check that the pro�ts are continuous: (a) over the line �y = 2lM � 3l�x, we have �1(pmax) = �1(pint): (b) If the condition �y = lg (�x) holds we have two cases: (b.1) For g(�x) � (1+M��x)(1�M+�x)�x, � 1(pall) = �1(pmax) and (b.2) for g(�x) � �x +2 � 2�M �2 p 1�M � , then �1(pall) = �1(pint). Proof of Corollary 1. We denote �1(�x;�y) the �rm 1�s pro�ts as a function of �x and �y. In Region b.i, where p1� = pmax: �1�y(�x;�y) = b(M ��x) > 0; � 1 �y�y (�x;�y) = 0: �1�x(�x;�y) = b(lM � (2l�x +�y)), which is positive for �y = �l�x and negative for �y = 2lM �3l�x; �1�x�x(�x;�y) = �2bl < 0: In Region b.ii, where p1� = pint: �1�y(�x;�y) = b 4l (2lM +�y � l�x) > 0; �1�y�y(�x;�y) = bl 4 > 0: �1�x(�x;�y) = � b 4 (2lM +�y � l�x) < 0; �1�x�x(�x;�y) = bl 4 > 0: In Region c, where p1� = pall: �1�y(�x;�y) = b > 0; � 1 �y�y (�x;�y) = 0: �1�x(�x;�y) = �lb < 0; � 1 �x�x (�x;�y) = 0: Proof of Proposition 2. Proofs for Region a and Region b.i are immediate. In Region b.ii the variation in health system surplus, that is, (in case x1 � x0)29 the di¤erence for patients in [~x;1] from being treated with drug (h0;x0) at price c0 and being treated with drug (h1;x1) at price pint; is the sum of the area de�ned by a triangle for [~x;x1] and the area de�ned by a rhomboid for [x1;1]. For the patients in [~x;x1], �CS = 1 2 (x1 � ~x(pint))(bh1 �pint � b(h0 � l(x1 �x0))+ c0) : Substituting ~x(pint) and pint; we have �CS = b 16l (�y +3l�x �2lM) . For the patients in [x1;1], �CS = (1�x1)(bh1 �pint � b(h0 � l(x1 �x0))+ c0) : Substi- tuting pint and using (1�x1) = (M ��x) ; we have �CS = b 2 (M ��x)(�y +3l�x �2lM) . 29The case x1 < x0 is similar. 30 Hence, adding both intervals, we obtain �CS(pint) = b 16l (�y +3l�x �2lM)(�y �5l�x +6lM) : In Region c the variation in the health system surplus is similar to the one previously analyzed, but taking into account that for pall (considering again that x1 > x0) patients in [0;x0] have the same surplus as without the new drug. For the patients in [x0;x1], �CS = 1 2 � x1 �x0 �� bh1 �pall � b � h0 � l � x1 �x0 �� + c0 � : Substituting pall we have �CS = bl�2x. For [x1;1], �CS = (1�x1) � bh1 �pall � b(h0 � l(x1 �x0))+ c0 � : Substituting pall and using (1�x1) = (M ��x) ;we obtain �CS = 2bl�x (M ��x) : Adding the two parts, we have �CS(pall) = bl�x (2M ��x) : Proof of Corollary 2. We denote �CS(�x;�y) the variation in consumer surplus as a function of �x and �y. In Region a and Region b.i all the derivatives are zero. In Region b.ii: �CS�y(�x;�y) = b 8l (�y � l�x +2lM) > b8l (�2l�x +2Ml) > 0: �CS�y�y(�x;�y) = b 8l > 0: �CS�x(�x;�y) = 1 8 (��y �15l�x +14lM) : We note that, at M = 12l (�y +3l�x) ; �CS�x(�x;�y) = 3 4 (�y + l�x) > 0 because �y > �l�x. Moreover, �CS�x(�x;�y) < 1 8 (�14l�x +14lM) : Hence, �CS�x(�x = M;�y) < 0: �CS�x�x(�x;�y) = �158 bl < 0 In Region c: �CS�y(�x;�y) = 0; �CS�y�y(�x;�y) = 0: �CS�x(�x;�y) = 2bl(M ��x) > 0: �CS�x�x(�x;�y) = �2bl < 0: Finally, the behavior of �CS at the borders between regions follows from the behavior of the optimal price p1� that we discussed following Proposition 1. Proof of Proposition 3. In case of a successful project, the new drug (x = x0;y) lies either in Region a (for y � y0) or Region c with x = x0 (for y > y0): In the �rst 31 case (see Proposition 2), �CS(x = x0;y) = �CS(c1) = 0. In the second case, �CS(x = x0;y) = �CS(pall) = bl�x (2M ��x) = 0 because �x = 0: Therefore, �in(I) = Win(I) for all I and the optimal investment levels for the two functions coincide. The argument for a horizontal incremental innovation process is similar because the new drug would lie in Region b.i where �CS(x;y = y0) = �CS(pmax) = 0. Proof of Proposition 4. There is some positive probability that the new drug (x1;y1) lies in Region c with x1 6= x0. Depending on the level of y1, there can also be a positive probability that the new drug lies in Region b.ii). In both regions, �CS(x;y1) > 0: Given that �CS(x;y) � 0 for every new drug, we have d�ra(I) dI < dWra(I) dI for every I, which implies that I1ra < I � ra. Proof of Proposition 5. Denoting by I1Z and I � Z for Z = in, ra the optimal level of investment in a process of type Z for �rm 1 and the social planner, respectively, then �in(I 1 in) = Win(I � in) �ra(I 1 ra) < Wra(I � ra): It may happen that Wra(I � ra) > Win(I � in) = �in(I 1 in) > �ra(I 1 ra) but it can never be the case that Wra(I � ra) < Win(I � in) = �in(I 1 in) < �ra(I 1 ra); which implies the result. 32 CESifo Working Paper No. 5672 Category 11: Industrial Organisation December 2015 Abstract