Appendix: Mathematical Model
Demand Equations
The first equation is for market demand D. The demand for commodity j, where j is
a fruit, vegetable or other crop, depends upon its own price Pj, the price of other
commodities, and an exogenous demand shifter k that represents health preferences.
Demand will decline as prices rise.
1.1 Dj = dj (p1,..., PJ, kj ) for j = 1, . . ., J.
California Production Equations
This equation is based on the cost function to produce commodity Yj. The price of
commodity j is equal to its marginal cost. If the price increases, output increases.
1.2 Pj =∂Cj(w1,..., w1,Yj) /• Yj for j = 1, . . . , J; where C(*) is the cost function for Yj and
wi is the price of input i where i = 1, . . ., I.
Trade Equations
Two equations represent trade in this model. The first equation is for exports E and
the second is for imports M. In both equations trade depends on the price in the home
market. If the home market price increases, exports decline and imports increase.
1.3 Ej = ej (Pj) Export function for good j for j = 1, . . ., J.
1.4 Mj = mj (pj ) Import function for good j for j = 1, . . ., J. Imports are
from other states and from other countries.
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