The Jensen Effect

Productivity variation exists in many empirical settings. In group production, individuals enter and exit the production process at the same time. In this work, Jensen's inequality is formally accounted for in a group production setting to ensure that maximum profit conditions are being met. The concept of the Jensen effect and an aggregation premium is introduced 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 individual in the group overestimates the average marginal productivity of the group. The magnitudes of the differences can be modest but the direction is consistent. Most importantly, the concepts and terminology presented provide a formalized treatment of Jensen's inequality that previous work has failed to accomplish.