Suppose a firm's customers consist of two segments, A and B. B's demand is more price elastic than A's. Assume the firm can price discriminate between these two groups

1. Who should be charged a higher price? Explain.
2. Assume that separating these two groups is costless (for example, if group B are college students, the firm doesn't have to pay anything to verify their student status). Will it always be more profitable to price discriminate than charge a single price to groups A and B? Explain.