Normative Supply Functions by Linear Programming Procedures

In many analyses of profit maximization, attention is directed to large herds and specialization in milk production. Why then do some farmers persist in keeping small dairy herds even when prices for Grade B milk become quite low? This article shows that even with relatively low prices for milk the inclusion of the small dairy herd in the combination of enterprises may still provide the maximum profit from the resources available on the farm. At higher levels of milk prices, it becomes profitable to increase the number of cows and the consequent quantity of milk produced. The various levels of prices and corresponding production of milk constitute a supply function for the farm. This paper illustrates the supply function by utilizing the resources found on a typical 160-acre farm in northeastern Iowa with the full-time labor of two men and $10,250 in capital available. With the aid of varilt ble-price programming, optimum combinations of nterprises for maximizing profits were computed, starting with milk prices so low (92 cents per hundredweight for grade B milk) that no milk cows would be included in the organization. With the price of milk increased to $1.01, a 13-cow herd would maximize profits while the small poultry enterprise would be dropped. With the price of milk at $2.38, a 24-cow herd would be the most profitable and the fall pig enterprise would be dropped. Thus at each level of milk prices, the farmer would have an optimum organization of cows, hogs, and poultry for profit maximization. This is Journal Paper No. J-3443 of the Iowa Agricultural and Home Economics Experiment Station, Ames, Iowa. Project No. 1277.