本研究旨在人們理性控制體重的行為中，探討最適體重的決定因素與調整方式。本文援用Becker and Murphy (1988)的研究途徑及Levy (2002)的效用函數作為基礎，加入個人預算限制式，建立食物攝取與體重和健康之關係的最適控制模型，求解食物消費和體重間的關係。
我們發現均衡體重和食物價格、基礎代謝率及時間折扣率為負相關;而與所得、食物的邊際效用及理想體重呈現正相關；尤其是理想體重之調整具有引導實際體重的力量，使得均衡體重的變動幅度遠高於理想體重的調整幅度。在動態過程分析上，我們亦發現，不管均衡體重增加或降低，兩種調整方向的動態模式均顯示出，食物消費的動態調整過程具有「過度調整」的現象。也就是說，在均衡體重變重(輕)時，消費者首先大幅度的增加(減少)消費，隨著時間經過再逐漸減少(增加)食物消費；然因消費量高(低)於身體代謝所需，所以體重乃逐漸提高(降低)而趨於均衡。

The thesis studies determinants and adjustment paths of the people's weight from the view point of rational behavior.It followes the research approach of Becker and Murphy (1988), makes use of the utility function from Levy (2002), and corporates a budget constraint so as to establish an optimal control model for food consumption and weight, and to find out the relationship between them.

Negative correlations are found between the steady-state weight and food prices, basal metabolic rate, and time discount rate.Positive correlations are found between the steady-state weight and income, marginal utility of food, and desirable weight. There is a tendancy to guide the actual steady-state weight to a much higher fluctuation margin than that of the desirable weight.In the dynamic analysis, it is also found that, regardless of an increase or decrease of the steady-state weight, both directions of adjustment show that the process of food consumption is always ``overshooting."In other words, when the steady-state weight becomes heavier (lighter), consumers first increase (decrease) their food consumption substantially. And, as the time goes by, there is a gradual decrease (increase) in food consumption owing to the fact that the food consumption is still higher (lower) than what is required for metabolism of the body that makes the weight getting to increase (decrease) till the new equilibrium is arrived.

1 緒論 6
1.1 研究動機 6
1.2 文獻回顧 7
1.3 研究方法 8
2 最適體重的恆定均衡 10
2.1 基本模型 10
2.2 最適解的必要條件12
2.3 恆定均衡13
2.4 之合理參數空間 17
2.5 比較靜態均衡分析 18
3 最適體重的動態分析22
3.1 動態調整系統的安定條件22
3.2 調整路線的方程式解25
3.3 動態調整路徑的安定鞍臂 26
3.3.1 安定鞍臂方程式 26
3.3.2 安定鞍臂與 的關係27
3.3.3 安定鞍臂與 及 的關係 28
3.4 體重調整途徑的動態分析. 30
3.4.1 食物價格變動引發的動態調整過程30
3.4.2 貨幣邊際貢獻引發的動態調整過程 32
3.4.3 食物邊際效用引發的動態調整過程 32
3.4.4 減肥引發的動態調整過程 32
理想體重 引發的調整 32
基礎代謝率 引發的調整33
3.4.5 時間折扣率引發的動態調整過程. 34
4 結論35
參考文獻 37

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