Virtual patent extension by cannibalization.

1. Introduction

In 1984, the Drug Price Competition and Patent Restoration Act, also known as the Waxman-Hatch Act, was enacted by the U.S. Congress. This legislation favored developers of patentable drugs by extending a patent's life to partially offset, up to five years, the marketing delay imposed by the Food and Drug Administration's approval process. However, this good news for the patentable drug developers was tempered by the bad news that marketing approval of generic substitutes for drugs coming off patent would also be accelerated. This shortened the previous time lag during which a patentee could maintain a virtual monopoly position on its brand-name product beyond its patent's expiration while the suppliers of generic substitutes were having their products approved. And according to Grabowski and Vernon (1992), generic entry did accelerate. Ever seeking to accentuate the positive and eliminate the negative, the patentable drug developers embarked on a new strategy of exercising their unique ability to market a generic version of a drug prior to its patent's expiration. The apparent purpose of the strategy is to prolong the manufacturer's dominance in the supply of the drug, in both its brand and generic versions, by gaining a first-mover advantage over rivals who can only provide a generic substitute after the patent's expiration. According to Yang (1994), Upjohn succeeded in controlling 90 percent of the generic market for its patented drug Xanax by introducing its own generic substitute one month before the Xanax patent expired; Syntex had similar success by introducing its own generic version of its patented drug Naproysn two months before its patent expired. (See Freudenheim 1997 for further developments of this practice.) The practice of pharmaceutical companies' introducing their own generic substitute for their name-brand product appears to have been rare in the past, according to Scherer (1993), despite Merck's introduction of a generic version of its patented drug Dalobid through a subsidiary after its patent expired.

Since the passage of the Waxman-Hatch Act, empirical studies conducted by Caves, Whinston, and Hurwitz (1991) and by Grabowski and Vernon (1992) sought to determine its effects on drug prices. The results of these studies were summarized by Comanor and Schweitzer (1995):

Average prices fell even though the prices charged for the original branded products are increased and not reduced when another firm enters. The original manufacturers do not usually compete with the new generic entrants on the basis of price but, rather, find it more profitable to concentrate on the segment of the market that includes brand-loyal customers. Such buyers are physicians and patients who prefer a particular brand and so continue to use it despite the presence of a lower-priced substitute. When generic manufacturers enter production, the price differential widens as the prices charged for the original branded products increase. (p. 188)

Scherer (1993, p. 99) refers to the divergence between the prices of the brand-name product and its generic substitute as "the generic competition paradox," and Frank and Salkever (1992) seek to explain it in terms of a market segmentation model in which the brand-name drug's supplier acts as a Stackelberg leader vis-a-vis the independent generic substitute suppliers but does not introduce its own generic substitute.

In this paper, we provide a fairly simple game-theoretic model that is consistent with the empirical findings and that enables us to analyze the impact on consumers, patentable drug producers, and generic drug producers of the patentable drug producer's strategy of introducing a generic version of their product before its patent expires. We assume, along with others, the presence of a price-sensitive segment of buyers who switch to the generic product if its price is below the brand-name product's and the presence of a brand-loyal segment that does not.

Two scenarios are compared. The first encompasses the traditional vision of the manufacturer producing only the patented drug prior to its patent's expiration and facing unlimited competition from generic substitutes thereafter. This competition from the generic substitute supposedly forces the price of the brand-name product to decline, possibly to its marginal cost of production. It is this scenario that serves as the standard of comparison for the second scenario. We model the first scenario as involving a single provider of the branded product after its patent expires facing competition from a Cournot oligopoly with n identical suppliers of its generic substitute. We then let the number of generic suppliers increase indefinitely to approximate a perfectly competitive market as the limit of the Cournot oligopoly. In the second scenario, the patentee introduces a generic product prior to the patent's expiration and thereby cannibalizes some of its brand-name product sales in order to secure a Stackelberg leadership position in the generic product market after the patent expires. The assumption that it is the brand-name drug's supplier's introduction of its generic substitute prior to its patent's expiration that enables it to achieve a Stackelberg leadership position in the generics market appears to be supported by claims of generic drug producers that "we have a better-than-even chance of having a majority market share if everyone launches their product on the same day" and by the actual experience of Smith-Kline Beecham that only achieved a minority share of the generic market when it introduced its generic substitute simultaneously with others after the Tagement patent expired (see Yang 1994). It is also consistent with Caves, Whinston, and Hurwitz's (1991) and Grabowski and Vernon's (1992) findings that the first generic entrant after the patent expires, in the absence of the brand-name supplier having introduced a generic product before the patent expires, realizes a first-mover advantage.

Our analysis suggests that a firm's strategy of introducing its own generic substitute for its brand-name product before its patent expires strictly dominates the strategy of sticking with the brand-name product before and after its patent expires only. Thus, the intuition that a patentee has to sacrifice profits in the first period by introducing a generic substitute for its brand-name product in order to establish a Stackelberg leadership position in the generic product's market after the patent expires is incorrect. Introduction of the generic product increases a patentee's profit above the level that it could achieve by only supplying the brand-name product both

before and after its patent expires. Moreover, in explaining the price increase of a brand-name product upon introduction of its generic substitute, we find that the brand-name product's supplier's introduction of its own generic product is essential. Thus, the brand product supplier's exercise of a Stackelberg leadership position vis-a-vis independent generic product suppliers, as in the Frank and Salkever (1992) model, without producing its own generic product, is not enough to assure a price rise in the brand-name product in our framework.

As for consumers, it appears that they are better off both before and after the brand-name product's patent expires when a patentee introduces a generic substitute prior to its brand-name product's expiration. For although a patentee's introduction of a generic substitute before the brand-name product's patent expires is accompanied by a rise of the brand-name product's price above the level when only it alone was produced, this increase is offset by the lower-priced generic substitute so that the average price of the two coincides with the price of the brand-name product when it alone is produced. And while the quantity of the brand-name product declines relative to the level when it alone is produced, the combined quantity of the brand-name product plus its generic substitute is above the level of the brand-name product when it alone is produced.

Comparison of prices and quantities after the patent's expiration under the two scenarios discloses that, with the patentee as a Stackelberg leader in the production of the generic product, its price is below the level when it only produces the brand-name product and the generic product is produced by Cournot competitors. Also, while the price of the brand-name product under the second scenario exceeds its price under the first scenario, when there are only a few suppliers of the generic product, it eventually declines below it as the number of the generic suppliers increases. However, with the unlimited increase in the number of generic suppliers, the weighted average price of the brand-name product and its generic substitute under the second scenario rises above the average price under the first scenario. Yet despite this, the total quantity purchased is higher under the second scenario than under the first, suggesting that consumers are better off, as they could have purchased the smaller quantity. All in all, our analysis suggests that both consumers and the brand-name product producers are better off when a generic substitute is introduced before the patent on the brand-name product expires. Only the producers of the generic substitute in competition with the patentee in the generic product market appear to be worse off, even though total producer profits are higher than if the branded product provider were not in the generic substitutes market.

[TABULAR DATA FOR TABLE 1 OMITTED]

2. The Models

Our models involve two periods (denoted 1 and 2). In the first period, the brand-name product's patent is in force and so only its owner may produce a substitute generic product. In the second period, the patent has expired, and anyone may produce a genetic substitute. In our first scenario, model C, the patentee provides only the brand-name product in the first period. After the patent expires, n symmetric entrants provide a generic substitute, while the former patentee continues to provide only the brand-name product. The patentee and the providers of the genetic substitute are assumed to engage in Cournot competition. The supposition that the suppliers of the generic substitutes engage in Bertrand competition is not supported by either the Caves, Whinston, and Hurwitz (1991) or the Grabowski and Vernon (1992) empirical studies. The traditional version of the brand-name product's supplier continuing to produce only it, while the generic substitute is provided under unlimited competition, is the special case of this model in which the number n of generic suppliers engaged in Cournot competition approaches infinity. Thus, the comparisons between this model C with the Stackelberg leader model includes comparisons between the Stackelberg model and the traditional standard of comparison.

In the second scenario, model S, the patentee introduces a generic substitute in the first period. Hence, it acts as a monopolist in both the brand-name product and its genetic substitute in the first period. This, we suppose, enables it to achieve a Stackelberg leadership role in the provision of the brand name and its genetic substitute along with n entrant providers of the genetic substitute in the second period. Table 1 describes the models.

We denote by B and G the overall quantity produced of the brand-name and generic products, respectively. Both products are virtually the same. Hence, their production costs are identical. We assume a constant marginal production cost of c. We also assume that the brand-name product provider will simply produce its generic substitute out of the existing production capacity that is employed to produce the brand-name product plus any other drugs that the provider produces (or that it can hire another company to produce the product, thus subcontracting production), so that there is no credibility issue regarding the provider's ability to provide the genetic substitute. Producers' profits will be denoted by [Pi]. The inverse demand functions are given by

[P.sub.B] = a - B - [Gamma]G (1)

and

[P.sub.G] = a - G - B, (2)

where [P.sub.B] and [P.sub.G] are the brand-name and generic product prices, respectively, and the parameter [Gamma] satisfying 0 [less than or equal to] [Gamma] [less than] 1 is a measure of the perceived substitutability of the two products. We assume that a [greater than] c holds. The demand functions can be derived from Equations 1 and 2, as follows:

[Mathematical Expression Omitted] (3)

[Mathematical Expression Omitted] (4)

According to Equation 2, buyers of the generic product, the price-sensitive segment, view both products as perfect substitutes, while according to Equation 1, the loyal buyers' segment of the brand-name product holds the generic product to be an inferior substitute (the perceived inferiority growing as [Gamma] declines). Thus, Equation 4 implies that at the same price, demand for the generic product is zero.

In terms of the underlying utility functions, the loyal buyers of the brand-name product can be thought to have a utility function of the form [U.sub.l] = B(G + k), where k [greater than or equal to] B at G = 0 and k is a constant. This utility function provides the familiar textbook picture of an indifference curve that yields a corner solution at which only the brand-name product is purchased when the prices of the brand-name product and its generic substitute are equal. It is only when the price of the generic substitute declines below the price of the brand-name product that both are purchased. As for the price-sensitive buyers, their utility function [U.sub.s] = B + G indicates that the brand-name product and its generic substitute are perfect substitutes and the one with the lower price is purchased exclusively.

Below, we present the two models in detail. The solutions to the model and the stage are presented as functions of the model and stage. For example, G(C.2) is the equilibrium quantity of the generic product in the second period of model C.

Model C

Period 1

The patentee is a monopolist producing only the brand product, and so the respective quantities of the brand and generic products are

G(C.1) = 0, B(C.1) - (a - c)/2. (5)

Their prices are

[P.sub.B] (C.1) = [P.sub.G] (C.1) = a + c/2 = [p.sub.m], (6)

where [P.sub.m] denotes the monopoly price. And the monopolist's profit is

[Pi](C.1) = [(a - c/2).sup.2]. (7)

Period 2

Here, the ex-patentee competes against n identical entrants, each producing the generic substitute at marginal cost c. It solves

[Mathematical Expression Omitted], (8)

while the ith entrant solves

[Mathematical Expression Omitted], (9)

where [g.sub.i] is the quantity of the generic substitute produced by the ith entrant, and hence G = [summation of] [g.sub.i] where n = 1 to n. The solution to Equation 9 is symmetric--namely, [g.sub.i] G/n for all i. Hence, the first-order necessary conditions to Equations 8 and 9 are

a - 2B - [Gamma]G - c = 0 (10)

and

a - G - B - C G/n = 0. (11)

The solutions to Equations 10 and 11 are

B(C.2) = (a - c) n/2 + n(2 - [Gamma]). (12)

and

G(C.2) = (a - c) n/2 + n(2 - [Gamma]). (13)

After substituting Equations 12 and 13 into Equations 1 and 2, and with some algebraic manipulation, we can establish that the brand-name product's price does not rise above the monopoly price level that prevailed before its patent expired and that the generic product's price approaches the competitive price as n [approaches] [infinity] by expressing [P.sub.B] (C.2) and [P.sub.G] (C.2) as convex combinations of the monopoly price [P.sup.m] and the perfectly competitive price c.

[P.sub.B] (C.2) = 2[(1 + n - [Gamma]n).sup.[P.sup.m] + [Gamma]nc/2 + 2n - [Gamma]n [less than or equal to] [P.sup.m] (14)

[P.sub.G] (C.2) = 2[P.sup.m] + n[(2 - [Gamma]).sup.c]/2 + 2n - [Gamma]n [less than or equal to] [P.sup.m]. (15)

Thus, the presence of competition from generic substitutes in the second period forces the price of the brand-name product to decline. As the number of generic producers, n, approaches infinity, the brand-name product's price declines to [2(1 - [Gamma])[P.sup.m] + [Gamma]c]/(2 - [Gamma]) [greater than or equal to] c, while the price of the generic product declines to the perfectly competitive price c. Hence, the brandname product commands a premium over the genetic even in the presence of intense competition so long as the generic is perceived to be an inferior substitute by some segment of the buyers, that is, 0 [less than or equal to] [Gamma] [less than] 1. Only if the two products are perceived to be perfect substitutes, [Gamma] = 1, does the price of the brand-name product decline to the perfectly competitive level. Thus, the prices in Equations 14 and 15 approach the traditional vision of the consequences of patent expiration on the branded product's price and generic product's price, respectively, as n [approaches][infinity].

Remark 1

If, following Frank and Salkever (1992), we suppose that, in period 2, the brand-name product producer exercises a Stackelberg leadership role vis-a-vis the independent generic product's supplier's in only supplying the brand-name product, then the brand-name producer's maximization problem, Equation 8, becomes subject to a constraint, namely, expression 11 - that is, it takes the dependence of the generic producers' optimal level of supply on its supply of the brand-name product into account. Upon substitution for G from Equation 11 into Equation 8, the brand-name product supplier's maximization problem becomes

[Mathematical Expression Omitted] ([8.sup.*])

From the first-order condition to Equation [8.sup.*], it follows that

[B.sup.*] = (a - c)/2, (12)

and by substitution into Equation 11 for B, that

[G.sup.*] = n/n + 1 (a - c)/2. ([13.sup.*])

Now, upon substitution from Equation [12.sup.*] and [13.sup.*] into the demand functions 1 and 2, it follows that

[Mathematical Expression Omitted] ([14.sup.*])

and

[Mathematical Expression Omitted] ([15.sup.*])

It is evident from Equation [14.sup.*] that the price set by the brand-name product supplier when it is a Stackelberg leader in the production of the branded product but not its generic substitute never exceeds the price [P.sup.m], that it sets when it is alone in the market (see Eqn. 6). Thus, Stackelberg leadership by the brand-name supplier with respect to the independent generic product suppliers in the supply of the branded product alone is not enough to explain the observed increases in the brand-name product's price after introduction of the generic substitute by independent suppliers. Moreover, it is not difficult to show that the brand-name product's price still does not rise above its monopoly level even if it is supposed that one of the independent generic suppliers achieves a Stackelberg leadership position in that market while the brand-name product's supplier continues to act as a Stackelberg leader only in the supply of the branded product to the entire generic market.

Model S

Period 1

Here, the patentee introduces a generic substitute in the first period so as to secure a Stackelberg leadership position in the second period. It solves

[Mathematical Expression Omitted]. (16)

From the first-order necessary conditions corresponding to Equation 16, it follows that

B(S.1) = G(S.1) = a - c/3 + [Gamma]. (17)

Substituting Equation 17 into Equations 1 and 2 gives the following:

[P.sub.B] (S.1) = (1 - [Gamma])a + 1[(1 + [Gamma])/3 + [Gamma][P.sup.m], (18)

[P.sub.G] (S.1) = 2(1 + [Gamma])[P.sup.m] + (1 - [Gamma])c/3 + [Gamma] [less than or equal to] [P.sup.m]. (18)

According to Equation 18, [P.sub.B](S) is a convex combination of the choke price a and the monopoly price [P.sup.m] and therefore is greater than or equal to the monopoly price. Thus, for [Gamma][not equal to] 1, the brand-name producer's introduction of the generic product is accompanied by a rise in the price of the brand-name product above its monopoly level. On the other hand, according to Equation 19, [P.sub.G](S) is a convex combination of the monopoly price [P.sup.m] and the competitive price c, and is therefore less than or equal to the monopoly price. However, note by Equation 17 that equal amounts of the brand-name product and the generic product are sold, and hence, by Equations 18 and 19, the weighted average of the prices [P.sub.B](S.1) and [P.sub.G](S.1) is [P.sup.m]. Also, from Equations 5 and 17, it is evident that the total sales of the brand-name product plus its generic substitute under this scenario exceed the total sales of the brand-name product alone under the first scenario.

Substituting Equation 17 into 16 and rearranging, the patentee's first period profit is

[Pi](S.1) = [(a - c).sup.2]/3 + [Gamma]. (20)

Note from Equations 7 and 20 that [Pi](C. 1) [less than] [Pi](S. 1), as 0 [less than or equal to] [Gamma] [less than] 1. Thus, by introducing the generic brand before the brand-name product's patent expires, the patentee realizes higher profits than by only producing the brand-name product. This, of course, relies on the assumption that some buyers even regard the brand-name supplier's own generic inferior to the brand-name product.

The intuitive reason for the increase in the brand product's price when the generic is introduced is that the demand for the brand-name product is less elastic than the demand for the generic product. And so, as is commonly the case, the product with the lower demand elasticity is priced higher than the one with the higher elasticity.

Period 2

Here, the patentee produces both the brand-name and generic products and acts as a Stackelberg leader to n entrants producing the generic version of the product. Given the quantities B and [g.sub.L] of the brand and generic drugs, respectively, produced by the leader, the jth entrant solves

[Mathematical Expression Omitted], (21)

where [g.sub.i] is the quantity of generic drug produced by the ith entrant. The first-order necessary conditions to Equation 21 yield a symmetric solution [g.sub.j] = g([g.sub.L], B) for all j, given by

g([g.sub.L], B) = a - c - [g.sub.L] - B/n + 1. (22)

The leader solves

[Mathematical Expression Omitted]. (23)

Substituting Equation 22 into 23, the first-order necessary conditions yield

a - c - (1 + [Gamma])B- 2[g.sub.L] = 0, (24)

(a - c - 2B)(1 + n - [Gamma]n) - [g.sub.L](1 + [Gamma]) = 0. (25)

From Equation 24, we obtain

[g.sub.L] a - c - (1 + [Gamma])B/2. (26)

Substituting Equation 26 into Equation 25 and adding and subtracting (1 - [Gamma]) to the denominator in the first expression yields

B(S.2) = (a - c) (2n + 1) (1 - [Gamma])/4 (1 + n - [Gamma]n) - [(1 + [Gamma]).sup.2]

= (a - c)(2n + 1)/3 + 4n + [Gamma]. (27)

Substituting Equation 27 into 26, and then substituting both expressions into Equation 22, we finally derive 

G(S.2) = [g.sub.L] + ng ([g.sub.L], B) = (a - c)(2n + 1)/3 + 4n + [Gamma]. (28)

Now substituting Equation 27 and 28 into Equations 1 and 2, we obtain

[P.sub.B](S.2) = 2a (1 + n - [Gamma]n) + c(2n + 1)(1 + [Gamma])/3 + 4n + [Gamma] (29a)

= 3{[a + 2[P.sup.m]]/3} + [4n + [Gamma]]{[4n(1 - [Gamma])[P.sub.m] + (4n + 1)[Gamma]c]/(4n + [Gamma])}/3 + 4n + [Gamma]. (29b)

Thus, the brand-name product price [P.sub.B](S.2) can be written as a convex combination of the choke price and the competitive price, Equation 29a, or as a convex combination of two convex combinations, Equation 29b. The first term in the numerator of Equation 29b is a convex combination of the choke price a and the monopoly price [p.sup.m], whereas the second term is a convex combination of the monopoly price [p.sup.m] and the competitive price c. Note that when n = 0, [P.sub.B](S.2) = [P.sub.B](S.1), the price the patentee sets in the first period when it monopolized both markets. In order for [P.sub.B](S.2) to exceed [p.sub.m], it follows from Equation 29a, after performing some algebra, that (1 - [Gamma])/4[Gamma] [greater than or equal to] n must hold. Now (1 - [Gamma])/4[Gamma]/[less than] 1 for [Gamma]/[greater than] 0.2 and (1 - [Gamma])/4[Gamma] is strictly monotonically decreasing in [Gamma]. It follows that for n [greater than or equal to] 1 and [Gamma] [greater than] 0.2, [P.sub.B](S.2) will decline below the monopoly price pro. If [Gamma] [less than or equal to] 0.2, it is possible for [P.sub.B](S.2) to exceed [P.sup.m] for n [greater than] 1. For example, for [Gamma] = 0.05 and n = 5, [P.sub.B](S.2) [greater than or equal to] [P.sup.m]. Hence, when the brand-name product is regarded as vastly superior to the generic - that is, it has a large segment loyal to the brand its price will continue to exceed the monopoly price [P.sup.m] even after the entry of a finite number of rival suppliers of the generic substitute.

The generic product's price, [P.sub.G] (S.2), can be bounded more tightly as a convex combination of the monopoly price [P.sup.m] and the perfectly competitive price, c.

[P.sub.G] (S.2) = 2(1 + [Gamma])[P.sup.m] + (1 + 4n - [Gamma])c / 3 + 4n + [Gamma] [less than or equal to] [P.sup.m]. (30)

Remark 2

Note that expression 23, the maximization problem faced by the brand-name product supplier who also introduces its own generic substitute and acts as a Stackelberg leader vis-a-vis the independent generic substitute suppliers, reduces to Equation [8.sup.*], the maximization problem in which the brand-name product supplier acts as a Stackelberg leader vis-a-vis the independent generic substitute suppliers but does not produce its own generic substitute, that is, if [g.sub.L] [equivalent to] 0. However, it was shown that in the latter case, the brand-name product's price does not rise after the introduction of generic substitutes by independent suppliers (see Eqn. [14.sup.*]). Thus, it is the brand-name product supplier's introduction of its own generic substitute along with its Stackelberg leadership role that drives up the brand-name product's price after the generic substitute appears. Of course, the brand-name product's price rises the most when the generic substitute is introduced by the brand-name product supplier before its patent expires. After the brandname product's patent expires and independent suppliers of the generic substitute enter the market, the brand-name product's price declines for all values of [Gamma], even if it remains above the monopoly level for some finite number of entrants.

3. Comparisons

We now turn to the differences among the two scenarios in terms of the equilibrium product prices. The first period price differences between models C and S follow from Equations 6, 18, and 19:

[P.sub.G](S.1) - [P.sub.G] (C.1) = -(a - c) 1- [Gamma]/2(3 + [Gamma]) [less than] 0, (31)

[P.sub.B](S.1) - [P.sub.B](C.1) = (a - c) 1 - [Gamma]/2(3 + [Gamma]) [greater than] 0. (32)

As for the second-period brand price changes, we have from Equations 29a and 14

[P.sub.B](S.2) - [P.sub.B](C.2) = a (a - c) [2n.sup.2][Gamma]([Gamma] - 1) + (1 - 4[Gamma] + [[Gamma].sup.2])n + 1 - [Gamma]/(3 + 4n + [Gamma])(2 + 2n - [Gamma]n). (33)

It can be easily verified that Equation 33 is positive for [Gamma] = 0 and negative for [Gamma] = 1 and n [greater than] 0. Also, Equation 33 is positive for n = 0 and negative for n [approaches] [infinity]. Thus, there exists by continuity a [[Gamma].sup.*], 1 [greater than] [[Gamma].sup.*] [greater than] 0 at which [P.sub.B](S.2) = [P.sub.B](C.2) and a finite [n.sup.*] [greater than] 0 such that [P.sub.B](S.2) = [P.sub.B](C.2). And therefore, the second period price of the brand-name product in scenario S may be above or below its second period level in scenario C, depending on the magnitudes of [Gamma] and n. However, by Equations 30 and 15, the price of generic product in a market with a Stackelberg leader never exceeds its equilibrium level of model C.

[P.sub.G](S.2) - [P.sub.G] (C.2) = -(a - c) [(2 - [Gamma])n + [[Gamma].sup.2]n + (1 - [Gamma])]/(3 + 4n + [Gamma])(2 + 2n - [Gamma]n) [less than or equal to] 0. (34)

Welfare Results

Turning first to the role of the 1984 legislation in inspiring brand-name product patentees to introduce generic substitutes before their patents expired, our analysis suggests that it would have been a profitable strategy in its absence. This is the implication of the following proposition.

PROPOSITION 1. Introduction of a generic version of a brand-name product before its patent expires in order to gain a first-mover advantage in the market for its generic substitute after its patent expires is a strictly dominant strategy for a patentee.

PROOF. From Equations 20 and 7, it is evident that producing both the generic product and the brand-name product before the patent expires is more profitable for a patentee than only producing the brand-name product. Indeed, the very fact that the solution to the optimization problem 17 calls for production of the generic product at a positive level alone indicates that production of both products is superior to production of only the brand-name product, as this option is not precluded. This argument also applies to the solution of the patentee's second-period optimization problem 23 that calls for production of both products at a positive level. Indeed, if the patentee as Stackelberg leader decides not to produce the generic product and to produce the quantity B(C.2), given by Equation 12, then from the solution of scenario C, it must be that the best reaction of the entrants will produce the amount G(C.2), given by Equation 13, of the generic drug. It follows that the Stackelberg leader can achieve the second period profits it earned in scenario C. Hence, it cannot do worse in the second period of scenario S, and since [g.sub.L] is positive, it does strictly better. Thus, in both periods, production of the brandname product and its generic substitute is as least as profitable for a patentee as production of the brand-name product alone. QED.

What this means intuitively is that a patentee makes more profit in the first period before the patent expires by introducing the generic product; the patentee is better off in the second period after the patent expires by selling both the brand-name and the generic products and being a Stackelberg leader than by only selling the brand-name product and facing n Cournot competitors selling the generic product. This, of course, raises the question as to why early introduction of the generic substitute was not used even before the 1984 legislation and, in fact, why the generic product is not introduced at the same time as the brand-name product. According to Scherer (1993), brand-name drug manufacturers feared that introduction of their own generic product would cannibalize their brand-name products' sales. Another possibility is that the early introduction of a generic substitute would thwart the branded products provider's efforts to cultivate a loyal following.

We deal with the consequences for consumers of patentees introducing a generic substitute before the patents on their brand-name drugs expire by comparing weighted average product prices and total quantities under the two scenarios in each of the periods. In the first period in scenario C, a patentee only produces its brand-name product and charges the monopoly price [P.sup.m] (see Eqn. 6). On the other hand, in the first period of scenario S, a patentee produces both its brand-name product and its generic substitute in equal amounts (see Eqn. 17). As noted above, the weighted average price of the two products is [P.sup.m]. Since the combined production of the brand-name product and its generic substitute exceeds the total amount of the brand-name product when it alone is produced, total drug expenditures are higher in scenario S than in scenario C. Of course, the cost of buying the same quantity of the brand-name drug, (a - c)/2, as is purchased in scenario C, is higher in scenario S, as its price exceeds the monopoly price [P.sup.m]. In fact, in the first period, it costs (a - c)2(1 - [Gamma])/4(3 + [Gamma]) more to purchase the amount (a - c)/2 of the brand-name drug in scenario S as in scenario C. However, the difference in the total drug expenditures between scenario S and scenario C is (a + c)(a - c)(1 - [Gamma])/4(3 + [Gamma]), which exceeds [(a - c).sup.2](1 - [Gamma])/4(3 + [Gamma]). Thus, the fact that consumers choose to purchase both the brand-name product and its generic substitute in the first period of scenario S when they could afford to buy only the quantity of the brand-name product in scenario C suggests that they are better off when the generic substitute is introduced before the brand-name product's patent expires.

In the second period, the total quantity produced of the brand-name product and its generic substitute is higher under scenario S than under scenario C. That is, B(S.2) + G(S.2) - G(C.2) - B(C.2) [greater than or equal to] 0, as can be demonstrated by performing the respective subtractions. However, the average price of the brand-name product plus the generic substitute under scenario [Mathematical Expression Omitted] that, weighted by Equations 27 and 28, ignoring (a - c), is

[Mathematical Expression Omitted] (35)

exceeds the average price of the brand-name product plus the generic substitute under scenario C, [Mathematical Expression Omitted], that, weighted by Equations 12 and 13 and ignoring (a - c), is

[Mathematical Expression Omitted]. (36)

Now using expressions 14, 15, 29a, and 30 for the respective prices in Equations 35 and 36, and letting the number of competitors in the generic product's market increase indefinitely, yields

[Mathematical Expression Omitted]. (37)

Thus, while from Equation 33 we know that as n [approaches] [infinity] [P.sub.B], [P.sub.B](S.2) declines below [P.sub.B](C.2), and from Equations 34 and 37 we know that [P.sub.G](S.2) - [P.sub.G](C.2) [less than or equal to] 0, nevertheless [Mathematical Expression Omitted]. This is because, as n grows, the weight on [P.sub.B](C.2) declines while correspondingly the weight on [P.sub.G](C.2) grows. Indeed, by setting the derivative of the right side of Equation 37 with respect to [Gamma] equal to zero, we get that the maximum difference between [Mathematical Expression Omitted] and [Mathematical Expression Omitted] occurs at [Gamma] = 3 - 5 1/2. But at this value of [Gamma], only about 20 percent of the weight in [Mathematical Expression Omitted] is on the brandname product's price, while 80 percent is on the genetic substitute's price. Note that when [Mathematical Expression Omitted], which corresponds to the average price in the first period under the two scenarios. And we have already argued that consumers are better off under scenario S than under scenario C in the first period. However, when entry into the production of the generic product is unlimited in the second period, it appears that consumers are worse off under scenario S than under scenario C, for the average price of the two products is higher in the former situation. But the fact that the total quantity purchased under scenario S exceeds the total quantity purchased under scenario C, despite the higher average price under the former situation, suggests that consumers are better off in scenario S than in scenario C since they could have chosen to purchase the lower quantity.

All this can be summarized as proposition 2.

PROPOSITION 2. Introduction of a generic version of a brand-name product by its producer before its patent expires in order to realize a first-mover advantage in the market for its generic substitute after its patent expires is advantageous to consumers.

Turning finally to the producers of the generic product, other than the patentee, our analysis suggests that they are worse off under scenario S than under scenario C. Intuitively, this is because they sell fewer units of the generic product when the patentee is a Stackelberg leader in this market and receive a lower price per unit than when each of them only faces (n - 1) identical, individual competitors. This can be demonstrated by noting that by Equation 28, the overall output of the generic producers, other than the patentee, is

ng([G.sub.L], B) = G(S.2) - [G.sub.L]. (39)

Since the total equilibrium quantity of the generic product in scenario S, G(S.2) = B(S.2) (see Eqns. 27 and 28), we can replace B in expression 26 for the output of a follower firm in the generic product market in scenario S with G. Hence, we get from Equation 39, employing Equations 28 and 26,

ng([g.sub.L], G) = (a -c) n - n[Gamma] - [Gamma] - 1/3 + 4n + [Gamma]. (40)

Subtracting the total quantity produced of the generic product when the market is supplied by Cournot competitors G(C.2) (see Eqn. 13) from Equation 40 gives

ng([g.sub.L], G) - G(C.2) = (a - c) -[n.sup.2](2 - [[Gamma].sup.2] + 3[Gamma]) - n(3 - [[Gamma].sup.2] + 4[Gamma]) - 2(1 + [Gamma])/(3 + 4n + [Gamma]) (2 2n - [Gamma]n) [less than] 0. (41)

So the n-followers in the production of the generic product in the second period of scenario S produce less than they do in the second period of scenario C, when they are Cournot competitors. We also know from Equation 34 that the price of the generic product [P.sub.G](S.2) is less than [P.sub.G](C.2). Thus, these generic producers sell a smaller quantity at a lower price in the second period of scenario S than in scenario C. And since their unit cost of production is constant at c, their unit profits decline, and therefore their total profits in scenario S are lower than in scenario C. All this can be summarized as proposition 3.

PROPOSITION 3. Introduction of a generic version of the brand-name product before its patent expires by its producer in order to gain a first-mover advantage in the market for its generic substitute after its patent expires is disadvantageous to the producers of the generic product in competition with the patentee.

However, we have already noted that the total quantity of the brand-name product plus its generic substitute sold in the second period is no lower under scenario S than under scenario C and at a no lower average price. Thus, since the average cost of production, c, is the same under the two scenarios, it follows that the total profit realized by the producers of the brandname product and its generic substitute is no lower under scenario S than under scenario C. Moreover, we have argued that consumers are no worse off under scenario S than scenario C in the second period. Finally, it has been argued that neither the producer of the brand-name product nor its consumers and consumers of its generic product are worse off under scenario S than under scenario C in the first period. Proposition 4 therefore follows.

PROPOSITION 4. Introduction of a generic version of a brand-name product before its patent expires leaves consumers and producers of the branded product and its generic substitute no worse either before or after the patent expires.

4. Summary

It appears that the suppliers of brand-name drugs have overcome their fear, however cautiously, that introducing their own generic substitute would cause even their most brand-loyal customers to realize that the two products were identical and lead to an erosion of the brand product's sales by introducing the generic product only shortly before the brand-name product's parent's expiration. Perhaps they reasoned that brand customers' loyalty was sufficiently established and that they would believe that the brand-name supplier's generic drug was designed only to meet the standards of competing generics rather than the standards of the brand product. Or they may have overcome their fear from the example of German brand-name drug producers who, according to Scherer (1993), had been introducing their own generic substitutes for some time. Also, they may have simply seen the handwriting on the wall that the growth of price-sensitive health maintenance organizations will drive the market into the genetic segment and they realized their unique ability to get a major piece of that action.

In any event, the brand-name drug manufacturers seem to have abandoned their passive response to generic entry by maintaining and even raising the price of the brand-name product on the theory that the demand for it was more inelastic than the demand for the price-sensitive segment; they have embarked on a new, aggressive strategy designed to serve the brand-loyal segment and capture a substantial share of the generic market. Given the reported success of this strategy, it is likely to continue and spread. More recently, producers of generic substitutes have countered this strategy by brand naming their own products (see Morrow 1998).

The overall result of the patentable drug manufacturers' effort to prolong their monopoly power beyond the patent's life by achieving an advantageous position in the sale of a generic substitute appears to benefit both them and the consumers. Early introduction of the generic product definitely benefits the patentee by raising its profits both before and after the patent on the brand-name product expires provided, of course, that this does not undermine the loyal segment of consumers. As for the consumers, they appear to be definitely better off in the first period, that is, before the patent has expired, as introduction of the generic product leads them to spend more in total on drugs and obtain more. However, since the introduction of the generic drug by the brand-name supplier is only a month or two before the brand-name product's patent expires, the first-period benefits to consumers and supplier are minimal. However, benefits to consumers and the brand-name supplier may be substantial in the second period. Only the generic product producers appear to lose from the patentee's establishment of a Stackelberg leadership position in this market despite the overall increase in producer surplus.

We are grateful to Professor John Beath of the University of St. Andrews and two referees for very useful comments.

References

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