商品价格的需求概率和需求风险模型

Probability and Risk Models of Demand for the Price of Commodity

从商品的需求因素出发研究商品价格的概率和风险模型.首先,给出商品价格的需求概率分布和需求概率最大定价公式,证明了需求量最大的价格就是需求概率最大价格,它低于利润最大价格.需求最大价促成了价格和消费的从众性,可理解为商品的平价.其次,借助于金融数学中风险的度量,通过推广方差的定义,得到了价格变量的需求风险函数;在比较5种特殊价格的需求风险之后,得出:期望价格的风险最小,需求概率最大价格和利润最大价格风险次之,最高价和最低价的风险最大;再次,讨论了浮动(折扣)价格的需求概率和需求风险,给出由于调价而产生的需求风险增加或者降低的条件.最后,通过2006年昆明市春运浮动价格乘客选择意向调查对结果进行了验证.

Probability and risk models for the price of commodity are studied from the demanding factor. Firstly, the probability distribution of demand and formula of the price are given with maximal probability of demand. It is proved that the price at which the demand is maximal is that of maximal probability of demand, and that it is lower than the one with maximal profit. The price with maximal demand causes popularity of price and consumption and can be understood as public price of commodity. Secondly, recurring to the measurement of risk in financial mathematics and extending the definition of the variance, a risk function of demand is obtained for the price variable. Furthermore, after comparing the risks of demand for five special prices, it is concluded that the risks are ordered in turn from minimum to maximum for the expectation price, the price with maximal probability of demand and the price with maximal profit, and the lowest and the highest prices. Thirdly, the probability and risks of demand for floating or discounting prices are discussed. Conditions are given for increasing and lowering the risks of demand due to adjusting the prices. Finally, the results are verified by investigating the favor of choices of passengers for the floating prices during the period of spring transportation in Kunming City.