## Model

An agricultural sector is producing a single crop in M locations, with varying climatic and agroecological conditions. Let j be a location indicator. Then j takes values from 1 to M. Before GMVs are introduced, farmers at each location use the best traditional variety given their conditions, and we assume that each location has its own distinct traditional variety. For simplicity, we assume that the gross benefits of production are measured in monetary terms. Output price denoted by P is assumed to be constant.

In the analysis, we consider several scenarios with respect to market and properties of genetic materials. Let s be a scenario indicator; s = 0 is the initial situation where only traditional varieties are used; s = m is the case in which locally optimized varieties are modified (GMVj), and 5 = g is the situation in which only one generic modified variety (GMV) is adopted. Let XSj denote output produced at location j under scenario s, which is assumed to be a function of land and genetic materials. The production function //(A)denotes the output produced on A acres of land in location j and scenario s. The marginal productivity of land for scenario 5 is MpSj{A) = df*/dA.

It is assumed that MpSj(À) and dMpSj/dA< 0 (decreasing marginal productivity of land in a location), which may reflect heterogeneity of land quality within a location.

Prior to the introduction of GMVs, when 5 = 0, the demand for land of variety j at location j is denoted by PMp°(A). The marginal cost of land grown with variety j is assumed to be constant and is denoted by Mc ¡, and the seed cost prior to biotechnology is assumed to be 0.3 Before the introduction of biotechnology, the acreage allocated to variety j, A®, was at the point when marginal benefits equal marginal cost of acreage, or (pMp%A°) = Mc°).

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