Optimal Decision in the Broiler Producing Firm: A Problem of Growing Inventory

Optimal producer behavior is examined in the production of products which may be regarded as growing inventories. Any one of several types of livestock produced by farm firms provides an example of such a product. This study focuses on the broiler producing firm. Weight-feed relations, derived from underlying weight and feed "growth functions," are regarded as deterministic. Broiler firms are assumed to be confronted with probabilistic prices with known probability distribution. Optimal policy takes the form of a set of cutoff prices, a cutoff price for each marketing age of the broiler over a relevant price range. If price at a given age (week) is above the cutoff price, the producer sells; if below, he keeps his flock for at least one more week. Most of the results are derived for the homogeneous case (that is, the probability distribution of prices is assumed to be the same in each week). but this assumption is subsequently relaxed to derive one form of an interseasonal decision model. Optimal policies are derived under two alternative assumptions regarding the form of the probability distribution of prices-the normal and the uniform. The sensitivity of the homogeneous model to changing variance of prices is also examined. 1 INTRODUCTION PRODUCTION DECISION models involving growing inventories have long been discussed by economists. The problem of time and timing has roots in early economic thinking, and kernels of it can be found in the discussion between D. Ricardo (1895) and one of his disciples, that time by itself does not bear any "fruits." As an example, he considers two barrels of wine: the first contains "unfinished" wine, though the treading process is finished, and the second "fin-ished" wine which will not be improved by additional time. After one year, the first barrel will have increased its value, but the second will have not, though time "operated" equally on both barrels ! His conclusion: time itself cannot produce any effect. He strengthens this argument by another example from plantations. In growing trees, even though all factors of production were implemented, the production is not finished additional time is needed. And he explains this phenomenon in an illustrative way. There is a "machine" in the tree that needs time to operate. Applying this to the wine example, the unfinished wine is like a machine for producing wine. Ricardo refutes McCul-loch's argument by raising the question: How come the same machine in …