A hypothetical university in Illinois, in the middle of corn fields, has a policy that education should be free for all and that students shouldn't have to take loans. The prerequisite for getting in the university is that students sign a contract stating that they can't take loans. State of Illinois, welcomes this policy and agrees to help each student with $200 scholarship every week. In addition to this scholarship, students also receive a credit amounting to 50% of their labor income from university if they work up to 20 hours in a week. All jobs available at the university offer a wage rate of $20 per hour. However, the university also believes that working more than 20 hours in a week adversely affects student's educational attainment and thus taxes labor earnings at 50% beyond 20 hours of work. Consider a student at this university with a utility function given by U(C, L) = [(C 200)(L 20) + 1, 000] and the student has a total of 100 hours in a week to allocate to work and leisure. The remaining time is allocated to sleep, classes and assignments.

1. How many hours will this student choose to work while in college? Provide a step by step solution.
2. If the policy only involved free tuition and a scholarship of $200 (no tax or credit on labor income), how many hours will this student choose to work?
3. In which case is the student better-off? Part (a) or part (b)?