Productivity variation and group optimization

Abstract

Uncertain productivity exists in many empirical settings, settings that are often characterized by nonlinear relationships. This interaction between nonlinear relationships and uncertainty provides an abundance of opportunities to apply Jensen's inequality and the concepts surrounding it. Past research has acknowledged Jensen's inequality but never formalized its treatment in a production economics setting. In group production, individuals enter the production process and exit the production process at the same time. In this dissertation, I show that the effect of Jensen's inequality must be formally accounted for in a group production setting to ensure that maximum profit conditions are being met. I introduce the concept of the Jensen effect and an aggregation premium to aid in the discussion of how an adjustment needs to be made in group optimization to account for the fact that the marginal productivity of an average individual in a group is not equivalent to the average marginal productivity of all individuals in the group. Examples from swine production and beef production are used to show that due to the aggregation premium, the marginal productivity of the average weight individual in the group overestimates the average marginal productivity of the group. Therefore, for group optimization to occur, the animals should be marketed earlier than the date indicated by the average weight of the group. The magnitudes of the differences are modest but direction is consistent and it's this consistent direction that when applied to a large operation could have a significant economic impact. Most importantly, the concepts and terminology presented in this dissertation provide a formalized treatment of Jensen's inequality that previous work has failed to accomplish. It is a formalization that will aid future research discussions into the many areas where Jensen's inequality can play a pivotal role.