## Appendix

Analytical model of the economics of the conservation of PGRFA

This appendix presents an analytical model of the economics of the conservation of PGRFA. The goal of this model is to link together the economic concepts underlying the conservation of agricultural genetic resources, and to demonstrate the data needs for conducting a first-best economic assessment of the allocation of conservation funds. Let Ax be the number of the distinct cultivars collected (accessions) in period t. It is drawn from the number of uncollected cultivars in time 0 that are still extant in time t (i.e., those that have not been lost before collection), denoted as A", and put into ex situ collections in period t.7 In addition, A, includes cultivars not existing at period 0 that may be developed by cultivar selection activities of indigenous farmers in the program target area. The accessions are functions of the following variables:

A( = A [/„ S„ A" (/„ St,Al{), A0, Ax ,... At_, ], (1)

where It= investment by the United Nations fund in agri-biodiversity conservation, enhancement, and collection activities in program target areas, and the vector of socioeconomic and other factors in the program area that are causing the number of existing uncollected cultivars to decrease over time is denoted as St. The expected signs are dAt ldlt> 0,d A" ldlt > 0, dAt /dSt< 0, and dA? IdSt< 0, and it is assumed that dAt Idt = 0. To limit a biases associated with aggregation, assume that A and At represent varieties within a species category, although other grouping based on physical or regional characteristics can be formed. One would expect accessions to be stochastic variables.8

7 While the goals of CGRFA may be more than just limited to cultivars that are uncollected—in situ conservation can have other values, such as dynamic evolution and response to changes in pest and other environmental conditions (Brush, Taylor, and Bellon, 1992)—we limit the scope of the model for the sake of tractability.

8 Given annual accessions Att the total size of the ex situ collection at period t is denoted as

TAt and is simply t t TA, =£A,. +A0-^Lk . k=0 ¿=0

where A0 is the carryover stock at the beginning of period 0 and I, is the loss of prior levels of TA due to spoilage and other factors each period, and where "ex situ collection"

Crop breeding, and in return crop supply, is a function of the number of cultivars available for research. The general form for a supply response function for agricultural crop output with respect to gene bank size can be written as:

X,'= W,Zt,ht, TU,-s (1,-s), 4-s-i A (/„), ht],Ut) for / = s,...,T, (2)

where Xts is output given the vector of expected prices P,, vector of inputs Zh vector of environmental and other uncontrolled effects U,, vector of state of technology (excluding breeding research technology) ht, state of crop breeding research technology t„ and 5, the lag before accessions have impact. Note that h, appears outside the brackets as well as inside as much research on PGRFA is done using only the private collections of the breeding firm. For rt, dct ldit.s.i > 0, and dX,/dt, >0, i = 0, ..., t - s. Assuming that crop breeding research technology exhibits diminishing marginal returns with respect to A, d2r, /ctA,^_, < 0. At the farm level, crop breeding research related technical change can be modeled using the common specification (Alston, Norton, and Pardey, 1995) for the profit function for perfectly competitive farm unit j as rc; = g[P,(T,)JZ,j(zt),htJ,U,j ]. For this specification, t, can represent either output or input augmenting technical change. Crop breeding research can be either.

In the literature on measuring gains to agricultural research, a common practice is to assume that agricultural research induces shifts in the supply function, which then translates into changes in producer plus consumer surplus (de Gorter, Nielson, and Rausser, 1992; Alston, Norton, and Pardey, 1995). While the policymaker may have objectives other than maximizing producer plus consumer surplus, and while no measure is completely objective, this criterion has the benefit of being reasonably general and objective. Fisher and Hanemann (1990) were the first to apply this criterion in the context of agri-biodiversity. In a two-period model for measuring the option value of saving an identified native landrace, they model the benefits of saving a native corn landrace by assuming this a priori identified landrace impacts the corn supply curve through the intercept. A reasonable criterion for choosing the optimal level of conservation investment is to choose the level of investment that maximizes producer plus consumer surplus in a dynamic context, in which the increase in accessions is a function of conservation investment, and the change in agricultural supply is a function refers to the aggregate of all generally accessible ex situ collections. In practice, Lt can be treated as some fraction of particular age cohorts, but for simplicity's sake, its form is left unspecified in this analysis. As the basic analysis does not change if we consider TA instead of A, for the sake of brevity, we stick to using A in the text.

of the change in accessions, while allowing for both biophysical and economic uncertainty.

Suppose in this formulation that due to the new biodiversity conservation investment I", the supply curve either shifts to the right or rotates downward, such that y0 decreases to Yi, i.e., Yi = fAt |It = /")] and

Yo = f[T,( At |It = /')], where Yi andYo are either the intercepts resulting from the summation (whether vertical or horizontal) of the supply functions of each farm unit maximizing n.¡, or are the new and old slopes of the supply function, respectively, and where V is the base level and I" > /', and Yi and Yo > 0. The change in welfare in period t when Yo decreases to Yi is denoted as AW,. The net present value is

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