Revenue Capacity Efficiency of Pear Trees and Its Decomposition

ADDITIONAL INDEX WORDS. Pyrus communis, Old Home × Farmingdale, trunk cross-sectional area, yield effi ciency, revenue effi ciency, nutrient responsiveness, data envelopment analysis ABSTRACT. In this paper we analyze the sources of variation in revenue per unit of trunk cross-sectional area (TCA) across a 0.87-ha block of 272 pear (Pyrus communis L.) trees in 2003. Revenue capacity effi ciency associated with TCA provides an overall measure of nutrient defi ciency and revenue ineffi ciency caused by environmental constraints in the fruit production process. Data envelopment analysis (DEA) is adopted to estimate revenue capacity effi ciency and its components. The defi ciencies of macro- and micronutrients are measured and optimal nutrient levels computed for each individual tree. These measures are aggregated for comparing between grids and between rootstocks. Yield effi ciency, fruit weight per unit of trunk cross-sectional area (TCA), has long been used as a measure of the fruit treeʼs productivity. The argument for the usefulness of this measure is that TCA has been shown to be linearly correlated with total aboveground weight of the tree, and thus fruit weight per unit of TCA refl ects the effi ciency of the treeʼs potential bearing surface to produce fruit (Westwood and Roberts, 1970). The value-based measure of yield effi ciency—economic value of fruit per unit of TCA—takes into account the quality and market value of fruit and thus measures the treeʼs economic performance. Accounting for variation in this measure across a commercial orchard can help to identify potential problems of individual trees, provide sound management recommendations, and enhance orchard profi tability. Unfortunately, this commonly observed variation has not been seriously studied and oftentimes is attributed to unexplained statistical disturbances in a regression of tree revenue on tree TCA (e.g., Seavert, 2002). Fruit production is the use of essential nutrients and sunlight to manufacture fruit through the process of photosynthesis. Gener- ally, defi ciency of essential nutrients in the soil and productive ineffi ciency are the two potential sources of relatively low revenue per unit of TCA. Sixteen nutrients are considered essential to plant growth; they are carbon, hydrogen, oxygen, nitrogen, phosphorous, potassium, calcium, magnesium, sulfur, iron, manganese, zinc, copper, boron, molybdenum, and chlorine. Each of the essential nutrients plays its unique, indispensable role in plant growth (Fageria, 1992). According to von Liebigʼs Law of the Minimum, crop yields are in direct relation with the minimum of one or more nutrients (Havlin et al., 1999). To the extent that TCA is a proxy of the treeʼs potential bearing surface and thus capacity of photosynthe- sis, revenue per unit of TCA is essentially a measure of revenue capacity utilization. Defi ciency of any of the essential nutrients in the soil can limit the realization of revenue capacity, resulting in relatively low revenue per unit of TCA. A tree with suffi cient essential nutrients in the soil may as well generate relatively low revenue in view of its potential bearing surface, owing to the constraint of environmental factors in the fruit production process. This is the so-called revenue ineffi ciency