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Optimal weight based on energy imbalance and utility maximization

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  • Sun, Ruoyan

Abstract

This paper investigates the optimal weight for both male and female using energy imbalance and utility maximization. Based on the difference of energy intake and expenditure, we develop a state equation that reveals the weight gain from this energy gap. We ​construct an objective function considering food consumption, eating habits and survival rate to measure utility. Through applying mathematical tools from optimal control methods and qualitative theory of differential equations, we obtain some results. For both male and female, the optimal weight is larger than the physiologically optimal weight calculated by the Body Mass Index (BMI). We also study the corresponding trajectories to steady state weight respectively. Depending on the value of a few parameters, the steady state can either be a saddle point with a monotonic trajectory or a focus with dampened oscillations.

Suggested Citation

  • Sun, Ruoyan, 2016. "Optimal weight based on energy imbalance and utility maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 429-435.
    • Handle: RePEc:eee:phsmap:v:442:y:2016:i:c:p:429-435
    DOI: 10.1016/j.physa.2015.09.034
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    Cited by:

    1. Barbieri, Paolo Nicola, 2017. "Modelling body weight, dieting and obesity traps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 139-146.

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