APPENDIX F MODEL

 A MATHEMATICAL MODEL OF THE WORLD
 MARKET FOR FLORIDA GRAPEFRUIT

 To formulate a mathematical model of the Florida grapefruit industry it is assumed that

white seedless and red seedless grapefruit1 are the two relevant varieties of grapefruit. Let

 I, = inventory of trees age a

 of variety v, v=1,2, a=1,..-,22

Let v=1 denote white seedless grapefruit and v=2 denote red seedless grapefruit. The age index

a reflects the age of the tree. A value of a equal 22 encompasses all trees of age 22 and older.

These trees are collapsed into one category because yields tend to flatten at tree ages exceeding

22 years.

 Next, let

 Y. = yield in boxes of fruit per tree of age a and variety v

Then

 22
(1) Z, E I. 1Y
 a-I


and Z, is the total production of fruit of variety v.





 1Thus, seedy grapefruit are ignored in the analysis. Production of seedy grapefruit in
Florida has declined in recent years. In 1992-3, 1.75 million boxes were produced in Florida,
which accounted for 3.2% of total production.


 2The term "pink seedless" includes both pink and red varieties. The Florida Agricultural
Statistics Service (FASS) use the term "colored seedless" to refer to pink and red varieties.

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