Use of duality between production, profit and cost functions in applied econometric research, a didactic note

THE DEVELOPMENT OF DUALITY THEORY HAS OPENED UP POWERFUL APPROACHES TO APPLIED ECONOMETRIC RESEARCH IN PRODUCTION ECONOMICS, BUT THESE HAVE NOT YET BEEN WIDELY USED BY AGRICULTURAL ECONOMIC RESEARCHERS. ONE REASON IS THAT MOST OF THE THEORETICAL LITERATURE EMPLOYS MATHEMATICAL NOTATIONS NOT NORMALLY TAUGHT IN AN AGRICULTURAL ECONOMICS CURRICULUM. DISCUSSED HERE ARE THE PROFIT FUNCTION, EXAMPLES USING THE COBB DOUGLAS PRODUCTION FUNCTION, THE COST FUNCTION AS A SPECIAL CASE OF THE PROFIT FUNCTION, ONE-TO-ONE CORRESPONDENCE AND THEORETICAL RESTRICTIONS, ECONOMETRIC APPLICATION OF DUALITY CONCEPTS, EXTENSION TO MULTIPLE INPUTS AND OUTPUTS, THE TWO MAIN PROBLEMS WITH THE PROFIT FUNCTION APPROACH, AND THE GREAT FLEXIBILITY THAT APPROACH ALLOWS THE INVESTIGATOR. FIXITY OF INPUTS OR OUTPUTS IS EASILY ACCOMMODATED; DEVIATIONS FROM PURE PROFIT-MAXIMIZING BEHAVIOR CAN BE SYSTEMATICALLY BUILT INTO THE THEORETICAL FRAMEWORK; AND FACTORS AFFECTING PRODUCTIVITY, SUCH AS SOIL QUALITY OR CLIMATIC VARIABLES, CAN BE BUILT IN AS FIXED VARIABLES AND THEIR CONTRIBUTION TO PRODUCTION ESTIMATED. FINALLY, FAR MORE COMPLEX PRODUCTION PROCESSES CAN BE MODELED THAN IS POSSIBLE WITH THE STANDARD PRODUCTION FUNCTIONS.