Method of Developing Representative Farms 



The research procedure used in this study consists of defining a 

 universe of farms, selecting a number of benchmark farms to repre- 

 sent the universe, and developing optimum plans for these farms at 

 variable commodity prices by linear programming. The programmed 

 results are expanded to obtain an aggregate supply response for the 

 universe. The difference between the aggregate supply response ob- 

 tained by this procedure and one obtaineed by programming all farms 

 is defined as aggregation bias. 



A considerable effort was made to minimize the bias in the supply 

 estimation that could be attributetd to aggregation of benchmark farm 

 data. In the past, the selection of benchmark farm8 has been done rather 

 arbitrarily, usually on the basis of some common size measure. This 

 procedure, which is done without regard to the relative level of re- 

 sources on the farms, gives rise to a considerable upward bias in the 

 supply response. This can be easily demonstrated. If farms are cla-^i- 

 fied on the basis of the labor resource, any resulting subgroup may 

 contain some farms that are scarce in labor but have surplus capital, 

 and others on which the resource situation is reversed. When the re- 

 sources of such farms are averaged, the disproportionalities existing on 

 individual farms tend to be averaged out. Thus, the conventional bench- 

 mark will not reflect the restrictive resources of the individual farms, 

 and its expanded output overestimates the aggregate output. ^- 



Representative farms were constructed on the basis of estimated 

 homogeneous restrictions. ^^ Sample farms from the surveys were group- 

 ed according to their most limiting resource in the linear programming 

 model and benchmark farms were defined as the average of resources on 

 all farms within each group. This procedure differs from more con- 

 ventional methods of representative benchmark farm selection in that 

 it takes into consideration the relative availabilitv of resources and the 

 productivity of resources. Usually farms are classified on the basis of the 

 absolute magnitude of certain resources such as cropland, labor, and 

 number of livestock. The homogeneous restriction metliod of represen- 

 tative farm selection was used because the supply response of milk 

 based on the farms selected by this method contained a mininuim of 

 aggregation bias. 



'^Frick, G. E. and Andrews, R. A., "Aggregation Bias and Four Methods of 

 Summing Farm Supply Functions," Journal of Farm Economics, Vol. 47, No. 3, Pp. 

 696-700, August 1965. 



13 For a detailed discussion of this technique, see Seanius J. Sheehy. "Selection 

 of Representative Benchmark Farms in Synthetic Supply Estimation," Ph.D. Thesis, 

 Pennsylvania State University, August 196 !•; Seamus J. Sheehy and R. H. McAlcx- 

 ander, "Selection of Representative Benchmark Farms for Supply Estimation." 

 Journal of Farm Economics, Vol. 47, No. 3, Pp. 681-69S. August 1965. Also R. Barker 

 and B. F. Stanton, "Estimation and Aggregation of Firm Supply Functions." Journal 

 of Farm Economics, Vol. 47, No. 3, Pp. 701-712, August 1965. 



16 



