Pharmaceutical Patenting in Developing Countries and R&D

Transcription

1 Pharmaceutical Patenting in Developing Countries and R&D by Eytan Sheshinski* (Contribution to the Baumol Conference Book) March 2005 * Department of Economics, The Hebrew University of Jerusalem, ISRAEL. mseytan@mscc.huji.ac.il

2 "India, a major source of inexpensive AIDS drugs passed a new patent law that groups providing drugs to the world s poorest patients fear will choke o their supply of new treatments. (While) all Western countries grant "product patents", India has granted "process patents" which allow another inventor to patent the same product as long as it was created by a novel process... (thereby) creating competition that drives down prices... In Africa (it) helped drive the annual price of antiretroviral treatment down from $15,000 per patient a decade ago to about $200 now." New York Times, March 23, 2005

3 1 Introduction There is an ongoing controversy on the question of whether developing countries, particularly in Africa, should be exempt from pharmaceutical product patents 1. It is argued that in a world of AIDS, tuberculosis and other diseases that overwhelmingly a ict developing countries, economic welfare will be enhanced by allowing these countries to free-ride on pharmaceutical innovations made and patented in the rst world, compared to charging them monopolistic prices. The counter argument is that if drugs are supplied to developing countries at competitive prices this will lead to an increase in prices in the developing countries and, most importantly, will lead to a decrease in research and development expenditures (R&D) of the pharmaceutical industry with detrimental long term e ects on global welfare. The objective of this paper is to provide some insight into this issue 2. Based on a standard multiproduct monopoly model, we demonstrate that the e ects of exempting developing countries from pharmaceutical patent rights, while always increasing drug sales and welfare in these countries at prevailing R&D levels, may also lead to increased sales of drugs in developed countries and to an increase in R&D expenditures by the pharmaceutical industry. Total sales of Western pharmaceutical rms may increase because rms my nd it advantageous to sell in developing countries even at competitive prices. A larger output sold in developing countries will, in turn, induce, due to economies of scope, larger sales in developed countries and, consequently, to an increase in R&D expenditures, provided these reduce marginal common production costs. We present a model of a rm, representing the Western pharmaceutical 1 The Uruguay TRIPS rounds and then the Doha WTO conference required that patents be granted, but delayed enforcement until A de nitive survey of the issues and empirics is Kremer (2002). An interesting discussion on the e ects of patent restrictions on the level of R&D is Scherer (2004). 3

4 industry, which produces and sells a product (drug) in two markets; one represents the developed countries the other represents the developing countries. Costs of production display economies of scope, and have a joint costs component as well as separable costs. Joint costs depend positively on total output and negatively on research and development (R&D) expenditures. Presumably, with low or no R&D expenditures costs are prohibitively large, decreasing as R&D expenditures increase. Initially, the rm has a monopoly over both markets. The monopoly is based on patent rights. This equilibrium is compared to one where patent rights are enforced only in the rst market (developed countries) while in the second market (developing countries) the drug is supplied at a xed price which is lower than the monopoly price. This price, termed the competitive price, represents a potential in nitely-elastic supply by rms that are not bound by patent laws, such as in India, where patents are granted to speci c processes, not to products, and consequently a huge reverse-engineering industry ourishes. The rm faces a dilemma: either it undercuts the potential supply in market 2 by charging a price slightly lower than the competitive price, or it abandons the competitive market and remains only in the monopolized market. In view of the assumption about the costs structure, namely the existence of economies of scope, it is never optimal for the rm to share any market with competitors. Hence the stark alternatives. It is of interest to develop necessary and su cient conditions for the rm deciding on one or the other solutions. These are discussed in Section 5. The focus of our analysis is on the e ect of eliminating patent rights in market 2 on the output (equal to sales) in market 1 and on the level of R&D expenditures. Clearly, in market 2 output increases and welfare is enhanced. It is shown that the e ect on the level of sales in market 1 and on R&D expenditures is indeterminate. We state conditions on the costs function that will sign the outcome. 4

5 2 Monopoly and R&D We treat all pharmaceutical rms in developed countries as one rm which has, due to patent rights, monopoly power over a product, X. The rm is selling this product in two markets, numbered 1 and 2. Market 1 represents the developed countries, lumped together, and market 2 represents the developing countries, also lumped together. The rms outputs (and sales) in markets 1 and 2 are denoted by x 1 and x 2 and the prices it charges are p 1 and p 2, respectively. Demands for the product in the two markets are assumed to be independent 3. The levels of these demands depend implicitly on income, population size and other characteristics of these countries and, more importantly, on the incidence of the disease(s) for which this product provides treatment. All these factors are taken as given and hence are not brought up explicitly. Revenue in market 1 as a function of output is denoted R 1 (x 1 ) and for market 2 R 2 (x 2 ). Thus, prices p i, are p i = R i(x i ) x i, i = 1; 2. There are common ("set-up") production costs, denoted C, which depend on total output, x 1 + x 2, and on research and development expenditures, K : C = C(x 1 + x 2 ; K). These costs are assumed to display decreasing average costs (economies of scope) and decreasing or constant marginal costs: C(x 1 +x 2 ; K)=x 1 +x 2 decreases with x 1 +x 2, C 1 (x 1 +x 2 ; K) (= 0 and C 11 (x 1 + x 2 ; K) x 2 ) x 2 ) ) > Expenditures on R&D decrease costs: C 2 (x 1 + x 2 ; ) < 0 at a nonincreasing rate, C 22 (x 1 + x 2 ; K) > 0. It is, presumably, impossible to produce the drug without some positive K ( lim K!0 C(x 1 + x 2 ; K) = 1 will ensure a positive K), and as R&D increase expenditures, e ectiveness of the 3 Interdependence of demands may arise, for example, due to the possibility of reimportation. This is an interesting issue in itself, but it will carry us beyond the objective of this paper to analyze it in detail here. 5

6 product is enhanced, re ected in a decrease in costs 4. Unit costs of R&D are assumed to be constant, q. There are also separable costs in each market (marketing, etc.) assumed to display constant marginal and average costs. Denoting these unit costs by c i, i = 1; 2; total costs are given by C(x 1 + x 2 ; K) + c 1 x 1 + c 2 x 2 + qk (1) Total pro ts, ; are: (x 1 ; x 2 ; K) = R 1 (x 1 ) + R 2 (x 2 ) C(x 1 + x 2 ; K) c 1 x 1 c 2 x 2 qk (2) The rm is a natural multiproduct, patent-based, monopoly. Maximumpro ts i = R 0 i(x i ) C 1 (x 1 + x 2 ; K) c i = C 2(x 1 + x 2 ; K) q = 0 i = 1; 2 (3) Equations (3) are the standard conditions equating marginal revenue to marginal costs. Equation (4) equates the marginal bene t of R&D expenditures to marginal costs. In Appendix A we state su cient second-order conditions for the solution, denoted (bx 1 ; bx 2 ; K); b to be unique. Corresponding to the quantities (bx 1 ; bx 2 ), the market-clearing prices established by the monopoly are bp 1 = R 1(bx 1 ) and bp 2 = R 2(bx 2 ), respectively. bx 1 bx 2 Equations (3)-(4) are three equations in three unknowns, x 1 ; x 2.and K. It will be useful to display these conditions in two diagrams. Figure 1 displays conditions (3) for a given K = K. b 4 Alternatively, the level of K can be assumed to a ect demands positively. 6

7 F igure1 The shape of the two curves and their relative position at E are justi ed by the second-order conditions. Figure 2 displays condition (3) w:r:t: market 1 and condition (4) in the (x 1 ; K) plane. These curves are drawn for a given x 2 = bx 2. The curves are drawn for the case C 12 < 0. The shape and position of these curves at the equilibrium point, E, are determined by second-order conditions. F igure 2 7

8 Now, suppose that patent protection is not provided in market 2. It is assumed that there are rms who o er the drug at a xed price, bp 2. We disregard the dynamics of the process, namely, how long it will take for these rms to develop and bring to market a generic drug identical (or close) to the one o ered by the patent holder. We focus on the e ect of the opening of the market on long term equilibrium. Henceforth, market 1 is termed the monopoly market and market 2 is termed the competitive market. In the competitive market, the price p 2 may be equal to the variable costs c 2 of the monopoly rm, but this is not necessary. What is assumed, to make this an e ective change, is that the competitive price is below the monopoly price, p 2 < bp 2. Demand for the product in the competitive market at price p 2 ; x 2 ; is larger than the quantity sold by the monopoly when protected by its patent: x 2 > bx 2, where x 2 is the de ned by p 2 = R 2(x 2 ). Since average and marginal joint costs are, by assumption, non-increasing, the monopoly rm will choose one of two possibilities: charge a price just below p 2 and continue to satisfy the entire demand (rather than share it with other rms) or abandon market 2 and concentrate on the monopoly market. x 2 3 Staying in the Competitive Market Suppose rst that the rm stays in both markets. Then the conditions that determine the new levels of x 1 and K, denoted by (bx 0 1; K b 0 ), are (3), pertaining to i = 1; and (4), with x 2 = x 2 in both conditions. It can be shown that: Proposition 1 If market 2 becomes competitive and the rm stays in the competitive market, then the level of x 1 increases and the level of K increases (decreases) i C 12 is negative (positive) 8

9 Proof. Appendix B As stated above, Figures 1 and 2 describe the case C 12 < 0. In Figure 1, as x 2 increases from bx 2 to x 2, then, for a given b K, the optimal quantity of x 1 increases along the original curve. In Figure 2, the two original curves shift (the dotted curves) as x 2 increases to x 2. Hence bx 1 > bx 1 and b K > b K. In Figure 1, in turn, the shift to the dotted curve takes into account the increase in K, further increasing x 1 to the new equilibrium level bx 1. Here, as in subsequent analysis, the sign of C 12 turns out to be important. This is the e ect of an increase in R&D expenditures on common marginal production costs. There are no compelling reasons to assume a particular sign. Two examples: (a) C(x 1 + x 2 ; K) = f(x 1 + x 2 )h(k) (where, by our assumptions, f > 0; f 0 > 0; f 00 0; h > 0; h 0 < 0; h 00 > 0). In this case, C 12 < 0; (b) C(x 1 + x 2 ; K) = f( x 1 + x 2 h(k) ) (where f > 0; f 0 > 0; f 00 0; h > 0; h 0 > 0 and, as a su cient condition, h 00 < 0). Here, C 12 R 0 as f 00 (z)z + 1 Q 0. The rst functional form may be called the case when R&D f 0 (z) is cost augmenting, the second output augmenting. 4 Abandoning the Competitive Market Suppose that the rm, facing competition in market 2, decides to abandon this market, focusing on market 1. The pro t maximizing conditions are again (3) (for i = 1) and (4), with x 2 = 0 in both conditions. Denote this solution by (ex 1 ; K). e This is called in the literature the stand-alone solution. An argument similar to the previous analysis leads directly to the following result: 9

10 Proposition 2 If competition in market 2 leads the rm to abandon the competitive market, focusing on the monopoly market, then the optimal level of x 1 decreases while the optimal level of K decreases (increases) if C 12 is negative (positive). The results in Propositions 1 and 2 suggest a potential welfare dilemma. The elimination of patent rights in market 2 (developing countries) unambiguously increase sales in this market, either by the competitive fringe (generics) or by the previous patent holder, due to the threat of entry. The e ect on sales in market 1 and on the level of Research & Development expenditures is indeterminate. If both increase, then the overall welfare e ect is clearly positive. If, however, the levels of x 1 and K decrease this may entail a decrease in overall welfare if the welfare loss in market 1 exceeds the welfare gain in market 2. It is of interest to consider what conditions will lead the rm to choose one or the other strategy. 10

11 5 Undercut Price or Abandon the Competitive Market Pro ts of the rm,, are (x 1 ; x 2 ; K) = R 1 (x 1 ) + R 2 (x 2 ) C(x 1 + x 2 ; K) c 1 x 1 c 2 x 2 qk (4) The maximum of (4) is attained at (bx 1 ; bx 2 ; b K). If market 2 becomes competitive then the rm either undercuts the price p 2 and continues to clear demand or it abandons the competitive market, focusing on the monopoly market. The rm will stay in market 2 if the following condition holds: (bx 0 1; x 2 ; b K 0 ) > (ex 1 ; 0; e K) (5) where (bx 0 1; K b 0 ) is the Best Response of the output in market 1 and the level of K when the output in market 2 is x 2 and the rm stays in market 1, while (ex 1 ; K) e are the optimal corresponding levels when the rm abandons market 2 (termed the stand-alone solution). When the opposite inequality to (5) holds then the rm will leave market 2. In order to derive necessary and su cient conditions for these cases, de- ne the concept of incremental costs. The incremental costs of x 2, denoted IC 2 (x 1 ; x 2 ; K), is the di erence between the costs of production of x 2, given x 1 and K, compared to no production, x 2 = 0: IC 2 (x 1 ; x 2 ; K) = C(x 1 + x 2 ; K) + c 1 x 1 + c 2 x 2 C(x 1 ; K) c 1 x 1 (6) Notice that the incremental costs of x 2 depend on the levels of x 1 and K. A su cient condition for (6) is that 11

12 (ex; x 2 ; K) e > (ex 1 ; 0; K) e (7) This is a su cient condition because the best-response, (bx 0 1; K b 0 ); maximizes pro ts when x 2 = x 2. Rearranging terms, applying de nition (6), this is seen to be equivalent to R 2 (x 2 ) IC 2 (ex 1 ; x 2 ; K) e > 0 (8) Revenue exceeds incremental costs in market 2 when x 2 = x 2 and x 1 and K are at the stand-alone levels. A necessary condition for (6) is that (bx 0 1; x 2 ; b K 0 ) > (bx 0 1; 0; b K 0 ) (9) Since the stand alone solution, (ex 1 ; e K); maximizes pro ts when the rm abandons market 2. This condition, applying (6), can be seen to be equivalent to R 2 (x 2 ) IC 2 (bx 0 1; 0; e K 0 ) > 0 (10) That is, revenue exceeds incremental costs in market 2 when x 2 = x 2 and (x 1 ; K) are at the best response levels. 12

13 Appendix A The matrix 2 3 R 00 c 11 c 11 c 12 c 11 R 00 c 11 c c 12 c 12 c 5 22 has to be negative de nite. The necessary conditions are: R 00 i C 11 < 0; i = 1; 2; C 22 > 0; R 00 1R 00 2 C 11 (R R 00 2) > 0 and R 00 1R 00 2(C 11 C 22 C 2 12) R 00 1R 00 2C 22 < 0. Convexity of C ensures that the last condition is satis ed. We shall assume that all these conditions are satis ed at the monopoly pro t maximizing point (bx 1 ; bx 2 ; K). This, in turn, ensures that the solution to (3) (4) in the text is unique. 13

14 Appendix B The F.O.C. for the optimal x 1 and K are R 0 1(x 1 ) C 1 (x 1 + x 2 ) c 1 = 0 C 2 (x 1 + x 2 ) q = 0 (B.1) At the initial equilibrium x 2 = bx 2 (and, accordingly, x 1 = bx 1 and K = b K). Now x 2 = x 2 > bx 2. Treating the increase in x 2 as exogenous dbx 1 = 1 dx 2 (C 11C 0 22 C12) 2 and dk b = R00 1 dx 2 C 0 12 (B.2) Where 0 = (C 11 C 22 C 2 12) R 00 1C 22 > 0 Hence dbx 1 dx 2 > 0 and Sgn d b K dx 2 = SgnC 12 References [1] Scherer, F.M. (2004) "A Note on Global Welfare in Pharmaceutical Patenting", The World Economy, July, [2] Kremer, M. (2002) "Pharmaceuticals and the Developing World", Journal of Economic Perspectives, 4,