Question: George Walls, president of Bradley School, is concerned about declining enrollments. Bradley School is a technical college that specializes in training computer programmers and computer operators. Over the years, there has been of competition among Bradley School, International Technology, and Career Academy. The three schools compete in providing education in the areas of programming, computer operations, and basic secretarial skills.
To gain a better understanding of which of these schools is emerging as a leader, George decided to conduct a survey. His survey looked at the number of students who transferred from one school to the other during their academic careers. On the average, Bradley School was able to retain 65% of those students it originally enrolled. Twenty percent of the students originally enrolled transferred to Career Academy, and 15% transferred to International Technology. Career Academy had the highest retention rate: 90% of its students remained at Career Academy for their full academic program. George estimated that about half the students who left Career Academy went to Bradley School, and the other half went to International Technology. International Technology was able to retain 80% of its students after they enrolled. Ten percent of the originally enrolled students transferred to Career Academy, and the other 10% enrolled in Bradley School.
Currently, Bradley School has 40% of the market. Career Academy, a much newer school, has 35% of the market. The remaining market share-25%-consists of students attending International Technology. George would like to determine the market share for Bradley for the next year. What are the equilibrium market shares for Bardley School, International Technology, and Career Academy.