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Economies of Scope and Scale of Multi-Product U.S. Cash Grain Farms:
A Flexible Fixed-Cost Quadratic (FFCQ) Model Analysis
Edouard K. Mafoua
Research/Teaching Associate
Department of Agricultural, Food and Resource Economics
Rutgers, The State University of New Jersey, New Brunswick, NJ 08901
Phone: (732) 932-9171, ext.252
E-mail: mafoua@AESOP.RUTGERS.EDU
May 15, 2002
Abstract
The evidence about the magnitude of scope and scale economies in U.S. cash grain farming is revealed
from the empirical estimation of the flexible fixed cost quadratic (FFCQ) model. This framework
explicitly disaggregates the crop output vector to take the heterogeneity of output and gives insight to
farmers to answer interesting questions such as: Are three-crop farms more cost efficient than two-
crop or single-crop farms? How important are economies of scope (fixed-cost and variable-cost
components) in two-crop farms and three-crop farms? Two-crop farms as well as three-crop farms
exhibit overall economies of scale and scope in all four-size categories that increase with the farm size.
They are able to lower the cost of producing crops in the same farm by spreading fixed costs over two
or three crops and/or by exploiting product cost complementarity, or diversifying risks.
Selected Paper, American Agricultural Economics Association Meeting, Long Beach, California, July 28-31, 2002.
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Economies of Scope and Scale of Multi-Product U.S. Cash Grain Farms:
A Flexible Fixed-Cost Quadratic (FFCQ) Model Analysis
1. Introduction
Measuring scope economies allows for an assessment of the benefits from output
diversification for multi-product firms in the agricultural industry. Increase in farm size may lead to
cost economies, but the presence of scope economies in diversified versus specialized farms may tend
to lower costs in terms of comparable level of output. In summarizing the major studies focusing on
this issue, Hallam (1993) discussed the diversity in the approa