Westward magazine publishers are thinking of launching a new fashion magazine for women in the under-25 age group, their original plans were to launch in April of next year but information has been received that a rival publisher is planning a similar magazine. Westward now have to decide whether to bring their launch forward to January of next year, through this would cost an additional $500000. If the launch brought forward it is estimated that the chances of launching before the rival are about 80%. However, if the launch is not brought forward it is thought that there is only a 30% chance of launching before the rival.
For simplicity, the management of Westward have assumed that the circulation of the magazine throughout its life will be either high or low. If Westward launch before the rival, it is thought that there is a 75% chance of a high circulation. However if the rival launches first, this probability is estimated to be only 50%.
If the rival does launch first then Westward could try to boost sales by increasing their level of advertising. This would cost an extra $200000, but it is thought that it would increase the probability of a high circulation by 70%. This increased advertising expenditure would not be considered if Westward's magazine was launched first. Westward's accountants have estimated that a high circulation would generate a gross profit over the magazine's lifetime of $4 million. A low circulation would bring a gross profit of $1 million. It is important to note, that these gross profits do not take into account additional expenditure caused by bringing the launch forward or by increased advertising.
B) Assuming that Westward's objective is to maximize expected profit, determine the policy that they should choose. (ignore Westwards preference for money over time. )
C) In reality, Westward have little knowledge of the progress which has been made by its rival. This means that the probabilities given above for beating the rival (if the launch is, or is not, brought forward) are very rough estimates. How sensitive is the policy you identified in (part B) to changes in these probabilities?