The effect of risk aversion and demand uncertainty in inventory system is studied. The monotonicities of the
optimal order quantity and optimal profit on penalty cost and risk level are obtained. By using stochastic comparison, larger
demand leads to high optimal order quantity, and larger demand leads to higher optimal profit when the penalty cost is set
to zero. It is proved that the profit will decrease when the demand variability increases, and the corresponding sufficient
conditions and/or necessary and sufficient conditions are given. Furthermore, a class of distributions exist such that larger
demand variability leads to higher optimal profit. Several examples are provided to illustrate the obtained results.