Next, the time dimension is introduced into the model. Let t index the seasons.

Restating equation (1) to include seasons

 22
(2) Zw, =. Iw Y
 a-i


where Z,, is the production of variety t in season t. Note that in equation (2), yields are assumed

to be invariant over time.

 The tree inventory adjusts according to a linear process. Let

 sur, = survival rate of trees of age a and variety v

Then

(3) 1v,,,a+,,i = sur, 1, a = 1, .., 20

and for trees age 22 and older,

(4) I. 22, ,+1 = sur,221/2, + surz21421,

 New plantings are based upon current on tree prices and production costs. Following

Pana (1991), new plantings of white seedless trees are given by

(5) 11, = 300/(13+e3.785-.954PW)

where PRW, is the three-year moving average on-tree price of white seedless grapefruit deflated

by production cost. New plantings of red seedless grapefruit (12) are given by

(6) 21t, = 500/(1+e9.1-1.31PRP,)

and PRP, is the three-year moving average on-tree price of red seedless grapefruit deflated by

production cost.