Fashion Buyers I A buyer for a department store must decide on which designs the stores will carry before he knows what the demand will be in the coming season. Choosing a poorly demanded design means lots of unsold merchandise and losses that are

$200,000 on average. Passing on a highly demanded design means unsold merchandise and missing out on profits that are $300,000 on average. What probability of a design's success should he be in order to choose to carry it?

Under the hypothesis that a given design will be profitable, the cost of a Type I Error (false positive) is $300,000 and the cost of a Type II Error (false negative) is $200,000 of passing. If p is the probability that the hypothesis is true, the expected costs of both decision errors are equal if:
p×$300,000 = (1-p)×(200,000)
or
p×$300,000 = 200,000-p×200,000
or
p×($300,000+200,000) = 200,000
or
p = 200,000/($300,000+200,000) = 40%.
So long as he is more than 40% confident that the design will be successful, carrying the design will minimize expected decision error costs.