A business school offers an MBA program with two areas of specialization: finance and marketing. For simplicity, suppose that the school is facing only two potential students: one who is interested only in finance and his utility from studying in the school is 2_sF - p and the other who is interested only in marketing and his utility is s_M - p, where sF is the quality of the finance courses, s_M is the quality of the marketing courses and p is the tuition. If either one of the two students decides not to enroll his utility is 0. (We can easily extend the problem and consider many students of each kind but this will not change any of the results). Suppose that the business school can choose the quality of the finance and the marketing courses, but the cost is increasing with the quality of the courses: The cost of finance courses for the school is (s_F)² / 2 and the cost of the marketing courses is (sM)² / 2. For simplicity, assume that the tuition, p, is determined by the government (the school cannot choose it) and is equal to 2. The objective of the school is to choose the quality of the finance and the quality of the marketing courses in order to maximize its income from tuition minus the cost of providing courses.

1. Suppose the students can tell the quality of the courses before they enroll. What is the quality above which each student will decide to enroll.

2. Given your answer to (1), compute the quality of the courses that the school will offer and the school’s profit. Explain what will happen if p > 2.

3. Which courses will have higher quality: finance or marketing? Which student cares more about quality? Does the school provide efficient level of quality or not?

4. Now suppose that the students cannot observe the quality of the courses before they enroll. Compute once again the quality of the courses that the school will offer and the school’s profit (note that the school chooses the quality although the students cannot observe it before they enroll).

5. Now suppose that the students can only observe the average quality of the courses provided by the school. That it, students only observe s ≡ (s_F + s_M) = 2 but they cannot observe s_F alone and sM alone. Suppose that the students observe an average quality s and both enroll. What will  be the qualities s_F and s_M that the school would like to choose? 

6. Now suppose that the students anticipate the quality choices that the school makes. What is the value of s for which both students will enroll?

7. Are the students better-off when they observe both s_F and s_M or are they better off when they only observe s? What about the school: is the school better off when the students observe both s_F and s_M or when they only observe s? Explain the intuition for your answer in detail.