Incentives to reduce crop trait durability.

(13) Note that because of the constraint [[PI].sub.L] - [P.sub.1L] [greater than or equal to] 0, this program is equivalent to the independent maximization of the profit in each period, as if the good was nondurable.

(14) The durable good monopoly payoff is greater than the nondurable good payoff, 2[[PI].sub.L] - [bar.[theta]] > [[PI].sub.L]. + [bar.[theta]]/4, as long as [bar.[theta]] < 4[[PI].sub.L]/5, which is always satisfied for [bar.[theta]] [less than or equal to] [[PI].sub.L]/2. Otherwise, the monopolist chooses the nondurable good strategy which yields a higher welfare. Yet some farmers (but few of them) inefficiently self-produce. Therefore, even when [bar.[theta]] [greater than or equal to] 4[[PI].sub.L]/5, welfare can be improved by reducing self-production if the self-production fee is used as an incentive tool (see Proposition 1).

(15) We can think of a situation where the monopolist switches to hybrid seed production only in the second period (i.e., after producing inbred line seed in the first period). However, this strategy is obviously dominated from the seed producer's viewpoint.

(16) These details are provided in the appendix posted on AgEconSearch.

(17) The second-period surplus of a farmer is [[PI].sub.L] - [theta] if he self-produces and zero if he buys the seed.

(18) We thank a referee for pointing this out.

(19) The analysis of a duopoly setting in which an entrant can introduce hybrid seed gives the same kinds of results with a differentiated market. However, the introduction of the fee has no impact on the equilibrium or on its efficiency.

(20) The monopolist has no interest in changing these prices. All of the farmers are willing to buy seed at such prices, so it is worthless to decrease them in order to sell more seed. Conversely, if the monopolist increases these prices, then farmers will no longer buy hybrid seed.

(21) Note that this program is similar to program (1) of the durable good inbred seed monopoly, except that here the monopolist earns [[PI].sub.H] - c in the first period from farmers who do not self-produce.

Stefan Ambec is researcher at Toulouse School of Economics (INRA-LERNA), Corinne Langinier is adjunct assistant professor, Department of Economics, Iowa State University and Stephane Lemarie is researcher at INRA-GAEL, Grenoble. Table 1. Seed Market and Seed Type for the Major Crops in France (2005)

Surface % Purchased % Hybrid Crop (Mha) Seed Seed Wheat 5.2 58% 2% Corn 3.2 100% 100% Barley 1.6 80% 0% Canola 1.2 75% 31% Sunflower 0.6 100% 100% Source: Semences et Progres (num 123, 124 and 125). Note: These five crops represent 90% of the cash crop surface in France. Table 2. Inbred Line Monopoly Strategy Prices Durable [p.sub.1L] = 2[[PI].sub.L] - [bar.[theta]]

[p.sub.2L] = [[PI].sub.L] Nondurable [p.sub.1L] = [[PI].sub.L]

[p.sub.2L] = [bar.[theta]] / 2

Monopoly Strategy Payoff Durable 2[[PI].sub.L] - [bar.[theta]] Nondurable [[PI].sub.L] + [bar.[theta]] / 4

Farmers' Loss of Strategy Surplus Welfare Durable [bar.[theta]] / 2 [bar.[theta]] / 2 Nondurable [[PI].sub.L] - 3[bar.[theta]] / 8 [bar.[theta]] / 8 Table 3. Inbred Line Monopoly with a Self-Production Fee Strategy Prices Durable [p.sub.1L] = [[PI].sub.L] -

[bar.[theta].sub.-[tau]]

[p.sub.2L] = [[PI].sub.L] Nondurable [p.sub.1L] = [[PI].sub.L] [tau] [member of] [p.sub.2L] = [bar.[theta]] / 2 + [0, [[PI].sub.L] - [tau] [bar.[theta]] / 2] Nondurable [p.sub.1L] = [[PI].sub.L] [tau] [member of] [p.sub.2L] = [[PI].sub.L] [[[PI].sub.L] - [bar.[theta]] / 2, [[PI].sub.L]]

Monopoly Strategy Payoff Durable 2[[PI].sub.L] - [bar.[theta]] Nondurable [[PI].sub.L] + [bar.[theta]] / [tau] [member of] 4 + [tau] [0, [[PI].sub.L] - [bar.[theta]] / 2] Nondurable 2[[PI].sub.L] - [([[PI].sub.L] - [tau] [member of] [tau]).sup.2] / [bar.[theta]] [[[PI].sub.L] - [bar.[theta]] / 2, [[PI].sub.L]]

Farmers' Strategy Surplus Durable [bar.[theta]] / 2 Nondurable [[PI].sub.L] - 3[bar.[theta]] / [tau] [member of] 8 - [tau] [0, [[PI].sub.L] - [bar.[theta]] / 2] Nondurable ([[PI].sub.L] - [tau]).sup.2] / [tau] [member of] 2[bar.[theta]] [[[PI].sub.L] - [bar.[theta]] / 2, [[PI].sub.L]]

Welfare Strategy Loss Durable [bar.[theta]] / 2 Nondurable [bar.[theta]] / 8 [tau] [member of] [0, [[PI].sub.L] - [bar.[theta]] / 2] Nondurable ([[PI].sub.L] - [tau]).sup.2] / [tau] [member of] 2[bar.[theta]] [[[PI].sub.L] - [bar.[theta]] / 2, [[PI].sub.L]]