理性住宅需求者效用極大化之最適房價

OPTIMAL HOUSING PRICE TO MAXIMIZE THE UTILITY OF RATIONAL HOUSING BUYERS

在房地產景氣循環中，大家都普遍認為房價早已偏離正常價格，非一般受薪階級可以負荷的，但影響房地產價格的因素眾多，且房地產又兼具消費功能及投資動機，合適房價要如何界定，本研究認為是最適房價。本研究以理性住宅需求者效用極大化的模型為基礎，在取得影響理性住宅需求者之最適房價的幾個重要參數後，將參數量化並把模型以相對數值模擬。我們的模型摸擬結果是對數房價成長率、住宅消費偏好、實質報酬率、風險規避係數對最適房價的影響為正向，貸款價值比（LTV）及遺贈動機（bequest motives）的影響為負向，而房貸利率則在低利率時影響為負向，在高利率時影響為正向。最適房價隨著住宅消費偏好或實質報酬率提高導致住宅消費增加，或因實質房價成長及風險規避的提高驅動住宅投資增加而上升。

When housing prices deviate from normal prices during a housing boom, salaried workers cannot afford the higher prices. However, housing prices are affected by many factors, and housing has both a consumption function and investment motives. This paper argues that an appropriate house price can be best defined by the optimal housing price. Based on a model of the maximal utility of a rational consumer, this study takes several important parameters that affect the optimal housing price of a rational buyer, quantifies the parameters, and simulates the model with relative values. The results of the model indicate the positive impact in terms of the real growth rate of housing prices, the housing consumption preference, the real rate of return, and the risk aversion coefficient on the optimal housing price. Thus, the loan value ratio (LTV) and the bequest motives all show negative impact. However, the impacts of mortgage rates at lower rates are negative, while those at higher interest rates are positive. The optimal price increases with housing consumption preferences or the real rate of return on investment, resulting in an increase in housing consumption, or an increase in housing investment due to increased real estate prices and risk aversion.