Optimal Breeding Strategy for Livestock with a Dynamic Price

Leishi Wang, Mingtao Li, Xin Pei and Juan Zhang
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Leishi Wang: School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
Mingtao Li: School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
Xin Pei: School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
Juan Zhang: Complex Systems Research Center, Shanxi University, Taiyuan 030006, China

Mathematics, 2022, vol. 10, issue 10, 1-24

Abstract: China’s livestock output has been growing, but domestic livestock products such as beef, mutton and pork have been unable to meet domestic consumers’ demands. The imbalance between supply and demand causes unstable livestock prices and affects profits on livestock. Therefore, the purpose of this paper is to provide the optimal breeding strategy for livestock farmers to maximize profits and adjust the balance between supply and demand. Firstly, when the price changes, livestock farmers will respond in two ways: by not adjusting the scale of livestock with the price or adjusting the scale with the price. Therefore, combining the model of price and the behavior of livestock farmers, two livestock breeding models were established. Secondly, we proposed four optimal breeding strategies based on the previously studied models and the main research method is Pontryagin’s Maximum Principle. Optimal breeding strategies are achieved by controlling the growth and output of livestock. Further, their existence was verified. Finally, we simulated two situations and found the most suitable strategy for both situations by comparing profits of four strategies. From that, we obtained several conclusions: The optimal strategy under constant prices is not always reasonable. The effect of price on livestock can promote a faster balance. To get more profits, the livestock farmers should adjust the farm’s productivity reasonably. It is necessary to calculate the optimal strategy results under different behaviors.

Keywords: optimal breeding strategy; dynamic price; profit maximization; Pontryagin maximum principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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