The Lemon Cycle

A Supply Response Model for Perennial Crops

“…Supply models for perennial crops using a linear programming approach have been developed by Dean and DeBenedictis [10] and Cingolani [9]. 4 The earlier studies by French and Bressler [14] and those immediately following were based on rather simple or limited behavioral assumptions and technical specifications. Among the more recent studies, Bateman [4, 5J considers several alternative conceptual models but assumes an infinite life for the perennial crop and thus does not deal with the removal aspect.…”

“…The conceived value of normal profit per unit could vary over time with the structure of the industry and possibly the level of average cost (particularly if cost levels vary mainly with general price levels). In the absence of some observable measures, 1t"t* and 1t"lt might be approximated as (13) 1t"t* = bso + bSlCt +USt and (14) Average costs (C t ) may vary with technological changes, with changes in factor prices (determined outside the farming community), and possibly with the level of industry output. For most U. S. produced commodities, cost changes due to technological and exogenous factor price changes seem likely to greatly outweigh or even submerge the effects of changes in total industry output.…”

“…With these considerations the expected profit functions may be specified generally as (15) 1t"t 8 = h(1t"t-l, 1l"t-2, ••. , Lt, V3t) and 14 For an example of a simulation approach which evaluates conditional changes in industry cost levels, see [15]. 17 Using the three bearing age groups given in the example above, the acreage in each class may be adjusted annually by the following set of equations: 2t= (1-r)A2t_1+(1-r)1:+5Nt_lO-(1-r)k+25Nt_3o,…”

“…By substituting (12), (13), (14), (IS), and (16) in (8) we obtain a new plantings equation in which the variables on the right are all predetermined with respect to N», Similarly, by specifying a relationship between 7l"til and an observable variable, such as 7l"t ll = 7l"t, acreage removed (equation (9)) may be expressed as a function only of predetermined variables. If we can reasonably assume the disturbance terms to be random variables with mean zero and constant variance, the parameters of these equations may be estimated by ordinary least squares.…”

“…Prior to 1960 there were almost no attempts to estimate such supply functions.> Some new ground was broken in a 1962 study by French and Bressler [14] which developed supply response for lemons in terms of new planting and removal relationships. This type of model developmen t, with modifications or simplifications, was later applied by other researchers to United States apples [8], cherries [11], pears [24], and tung nuts [18], with varying success.…”