The diet problem, nutrient supply, and the cost of diversity applied to livestock feeds

This study investigates the cost of increasing production diversity for a livestock producer who minimizes the cost of supplying nutrients to animals, a problem comparable to the “diet problem”. Although researchers have extensively studied the benefits of diversity, the explicit cost of diversity remains understudied. Our approach combines a nonlinear programming model and a cross-entropy measure using an index for diversity proposed by Henri Theil that incorporates observed commodity mixes and a uniform prior based on information theory. The diversity index is comparable across countries. We provide an example from all 135 countries across the globe where feed rations for beef cattle contain cereal grains, considering prices with and without climate change. The marginal cost of an extra unit of diversity in the observed feed ration ranges across countries from $4 to $158 (average $25), compared to an average total production cost of $220 per ton of cereal grain. The marginal cost of diversity is lower in higher income countries than lower income countries. Changing the diversity index that we developed for different contexts, such as a count index for human dietary diversity, would mean researchers could apply our approach to the diet problem for humans.