[6 points each]

A coffee shop manager realizes that demand for coffee is more elastic among students, and is trying to determine the optimal pricing schedule. Specifically, she estimates the following average demands:

\fThe two groups visit the coffee shop in equal numbers on average. Assume that the marginal cost for coffee is $2 and there is no xed cost. 1, Assume that students can buy a cup of coffee at a discounted price p3 by showing their student ID card and non-students can buy it at a normal price pN . What price should be set for each group? 2, If the coffee shop cannot distinguish whether customers are students or not, what is the optimal single price pU