The risk averse and prudent newsboy: changes in risk and fixed costs

The classic single-period inventory problem (newsboy model) has been analysed to determine the qualitative effects of increases in the demand riskiness and of changes in fixed costs. This paper provides a sufficient condition for an increase in fixed costs to reduce orders. It has been shown that when the demand experiences a single spread around the optimal order or a restricted mean-preserving spread, the newsvendor reduces orders if he is risk averse, or prudent respectively. This paper advances such results by showing that the relation runs in both directions. That is, whenever the uncertain demand undergoes a risk increase characterised by a single spread, the newsboy will reduce orders if and only if he is risk averse; and that prudence is both necessary and sufficient condition for the newsboy to reduce orders whenever he is faced with a restricted mean-preserving spread of the random demand.