THE WELFARE EFFECTS OF CONSUMING A CANCER PREVENTION DIET

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 D_j = d_j (p₁,..., PJ, k_j )    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 Y_j and
w_i 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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