Incentives to reduce crop trait durability.

Selling hybrid instead of durable inbred line seed is somewhat like leasing the durable good for one period instead of selling it. Waldman (1997) argues that a lease-only policy eliminates the market for the used good, which increases the producer's market power. In the case of seed, PBRs forbid the sale of self-produced seed and, thus, prevent the emergence of a secondary seed market. In our model, allowing for such a secondary market would render serf-production more attractive, because self-production would be assigned to the more efficient farmers. It would reduce further the seed dealer's market power and, hence, increase the incentive to reduce crop trait durability.

Shortening crop trait durability is similar to the planned obsolescence of durable goods (Bulow 1986; Waldman 1996b). Bulow (1986) formalizes the monopoly's incentive to uneconomically shorten the durability of goods in a two-period model. Our framework is different in two ways. First, we deal with a good that leaves the option for consumers to make it durable at a cost. The monopolist wants to introduce an uneconomical good that does not provide this option. Second, consumers have heterogeneous surplus captured by seed production costs when they have the option to make the good durable. As a consequence, for some values of the parameters, the monopolist chooses to produce both types of seed to differentiate consumers.

Our contribution is related to the literature on the impact of IPRs within the seed industry. Burton et al. (2005) examine the property rights protection of genetically modified (GM) crops in a two-period model. They compare sterile GM seeds with short-term and long-term contracts between the seed producer and farmers as strategies to protect IPRs. Their focus is mainly on enforcement and monitoring problems with long-term contracts that can be avoided with sterile GM seeds. Perrin and Fulginiti (2004) investigate the pricing of different types of seeds under different IPR regimes in a model close to that of Bulow (1982).

Finally, several contributions analyze the impact of IPRs within the seed industry on the incentives to enhance innovation. Their focus is on the standard trade-off between ex ante (stronger IPRs create more incentive to invest in research) versus ex post (deadweight loss due to market power) efficiency, and the difference between inbred line and hybrid seed is captured through different levels of a property rights parameter (Alston and Venner 2002; Lence et al. 2005). (8) Our analysis complements the above contributions in that the choice of the type of seed is endogenous, while the preliminary research stage is exogenous. Further, we study the impact of a fee paid by farmers who self-produce. (9)

The Model

We consider a two-period model in which a seed producer faces a continuum of farmers of mass 1. The discount factor is normalized to 1. Each farmer buys zero or one units of seed. The monopolist produces and sells inbred line seeds (L) at a marginal cost 0. As the technology becomes available (at no cost), she may also produce and sell hybrid seeds (H) at a higher marginal cost c > 0. The gross payoff to the farmer from using inbred line seed or hybrid seed is [[PI].sub.j] (with j = H, L) and is identical for all farmers. We suppose that [[PI].sub.H] > [[PI].sub.L], SO that hybrid seeds generate a higher payoff but are more costly to produce. Yet we assume that it is worthwhile to use hybrids, i.e., [[PI].sub.H] c > 0.

Not only do the two types of seed have different costs and profits, they also differ in their durability. Unlike hybrid seed, the inbred line harvest can be saved and used to produce seed for the next period's production. If a farmer buys inbred line seed at the beginning of the first period, he can produce his own second-period seeds at a cost [theta] that includes the cost of saving part of the harvest. Importantly, farmers differ in their self-production costs [theta], where [theta] is uniformly distributed between 0 and [bar.[theta]]. The density is f([theta]) and the cumulative function is f([theta]) on [0, [bar.[theta]]], where F(0) = 0 and F([bar.[theta]]) = 1. Thus, f([theta]) is the fraction of farmers with a cost less than [theta].

Two main arguments justify that the cost of producing inbred line seed is lower for the seed producer than for self-producing farmers. First, it is generally established that there are economies of scale at some stages of the production process (e.g., screening, seed dressing). Seed producers benefit more from these economies of scale because they produce seed for the whole market. Second, the yield obtained by self-production is slightly lower than that obtained from seed bought from seed producers. Here, we assume that self-production does not affect the profit [[PI].sub.L]/. Hence, self-production costs should be interpreted in a broader sense and should include the cost of the yield loss. (10)

In our setting, self-production by farmers is socially inefficient because the inbred line seed producer's marginal cost is equal to zero. Therefore, at the first-best, all seeds are produced by producers. Moreover, only one type of seed is produced at the first-best. Indeed, if a social planner can choose prices and decide whether to switch or not, he sets the price equal to marginal cost, i.e., zero for inbred line seed and c for hybrid seed. The two-period welfare is then 2HL if inbred line seeds are produced and 2([[PI].sbu.H] - c) if hybrid seeds are produced. Hence, the social planner switches to hybrid seed if [[PI].sub.H] - c [greater than or equal to] [[PI].sub.L], or equivalently, [[PI].sub.H] - [[PI].sub.L] [equivalent to] [DELTA][PI] [greater than or equal to] c; i.e., the harvest gain compensates for the incremental cost of producing hybrid seeds.

Yet the first-best outcome could be achieved with perfect competition in the inbred line seed market and with a monopoly setting in the hybrid seed market. The logic here is straightforward. Inbred line seed producers set their price at marginal cost zero (as in the case of price setting by a social planner). Farmers buy during each period, as it would be (weakly) more costly to self-produce ([theta] [greater than or equal to] 0). In order to enter the market, a hybrid seed producer has to set his price at [DELTA][PI] (such that [[PI].sub.H] - p = [[PI].sub.L]), or possibly just below. If [DELTA][PI] < c, the hybrid seed producer does not enter and only inbred line seeds are produced. On the other hand, if [DELTA][PI] [greater than or equal to] c, the hybrid seed producer enters and only hybrid seeds are produced. In this latter case, all of the farmers buy the hybrid seeds, and the (maximized) total surplus is shared between the farmers and the producer. Furthermore, hybrid seeds are efficiently produced. Therefore, any loss of efficiency in seed pricing or in the reduction of trait durability is due to the exercise of market power in the inbred line seed industry.

Inbred Line Monopoly

In this section, we consider a monopolist who sells only inbred line seed, at prices [P.sub.1L] and [P.sub.2L], during the first and second periods. The timing of decisions is as follows. In the first period, the monopolist offers a pair of prices {[P.sub.1L], [P.sub.2L]}. The farmers observe these prices, each decides whether or not to buy the seed at price [P.sub.1L], and then each decides whether or not to self-produce for the second period. In the second period, those who did not save part of the harvest have to decide whether to buy the seed at price [P.sub.2L].

Note that such timing requires the monopolist to be able to commit to the second-period price before the farmers decide to self-produce. In reality, it means that the farmers can save part of their harvest and decide, just before sowing, whether to use it as (self-produced) seed or to sell it on the spot market. The alternative "noncommitment" case will be addressed as an extension of our model in a later section.

We first derive the equilibrium, and second, we analyze the impact of the introduction of a self-production fee.

Equilibrium without a Self-Production Fee