Deterministic origins of cyclical adjustment paths in managed animal populations

Management of an animal herd embodies the classic economic trade-off between consumption and investment: a manager chooses to slaughter some animals today and retain others so they might reproduce and provide future consumption. When the decisions of U.S. cattle, hog and sheep managers are aggregated and plotted through time, they reveal strong cyclical population fluctuations generically referred to as cattle cycles. One notable exception is the U.S. dairy population which fails to exhibit cyclical tendencies despite having biological features nearly identical to beef. Farmers and policymakers often view cattle cycles as unwanted sources of market instability worthy of policy intervention.;A discrete-time, deterministic model of a multiple-age group animal herd is constructed to explore why cyclical aggregate behavior might arise in certain animal populations but not in others. The economic problem is as follows: a social planner with perfect foresight chooses an infinite sequence of feasible animal inventories to maximize the discounted sum of social welfare which depends upon consumption of various meat and milk outputs. Dynamics of the optimal population path are analyzed by studying the eigenvalues of the model's linearized Euler equations and by simulating particular examples via numerical dynamic programming.;The key result is that the recursive reproductive structure of the herd creates a complementary consumption-investment relationship which allows for an increase in meat consumption from one age group in the current period while simultaneously allowing an increase in the number of animals that will appear in that same age group in the next period. This means the herd can increase in size with little or no loss in current meat consumption when it grows in an oscillatory or cyclical fashion.;If animals can produce milk, cyclical adjustment is less likely to be optimal. Milk production helps alleviate the consumption-investment tradeoff present in many groups because forgoing meat production from mature age groups means gaining milk consumption. Milk allows more groups to feature investment with little or no penalty to current, total consumption and, therefore, cyclical adjustment is no longer necessary to circumvent the consumption-investment tradeoff present in most age groups when meat is the only output.