APPENDIX A


A MATHEMATICAL MODEL OF THE NORTH AMERICAN FRESH VEGETABLE
 MARKET

 The North American fresh vegetable market model was developed by modifying
the North American winter vegetable market model developed by Spreen et al.(1995).
The North American fresh vegetable market can be characterized as a spatial equilibrium
problem. The model is limited to those commodities which utilize methyl bromide as a
pre-plant fumigant. To mathematically state the model, let
 i index the supply regions, i = 1,...,I
 j index the demand regions, j = 1,...,J
 k index the commodities, k = 1,...,K
 m index the months, m=1,...,12
 Many producers in Florida utilize double cropping systems in which two different
commodities are produced on the same acre. Let
 li -index the cropping systems employed in supply region i, li = 1,...Li.
Define
 Wli = number of acres planted to cropping system li in region i.
Let
 dlikm = per acre yield of commodity k in month m from cropping system li.
So that
 Ulikm = dlikm Wl,
Is the production of commodity k in region I and month m for cropping system li. Let
 c ll = per acre preharvest production cost of cropping system li.
so that cli Wli is the total preharvest production cost associated with cropping system li.
 The total supply of commodity k from supply region I in month m is
 Zikm = 1 Ulikm,
 li
that is, total production of commodity k in region i and month m is the sum of the
production of that commodity from each cropping system.
 Let
 c2ik = per unit harvest and post harvest cost associated with commodity k in
region i. The parameter c2ik includes harvest cost, costs for hauling to the packing plant,
packing costs, and shipment to a distribution point.' It should be noted that post harvest
costs are assumed to be invariant to the month of harvest. Then c2ik Zikm is the post cost
associated with commodity k produced in region I and month m.
 The demand side of the model is delineated by defining
 Pjkm = ajkm bjkm Qjkm



 In the case of Mexico, charges are included for hauling from the production area in
 Sinaloa to Nogales and from Baja to San Diego. Charges for inspection and tariffs
 collected as the shipment crosses the border are also included in the cost.