If the age at which students can dropout of high school is increased from 16 to 18, what happens to production possibilities and unemployment rates?
You can argue that your production possibilities curve would move left. You can say that this is because you have all these people who could have been working but are now back in school.
However, you can argue that your PPC would actually move right in the long term because more education will make your work force more productive. I'd take either answer if I were asking that question.
Unemployment rates would likely fall because you would have fewer teens in the labor force -- teens who are likely to have high rates of unemployment because they lack skills.
Increasing the age for allowing students to drop out from school from 16 to 18, will definitely mean that people can start seeking regular full employment at the age of 16 rather than at 18. This is assuming that thee are no other legal constraints on employment of people under 18 as a part of child labour or any other law. Thus number of people seeking employments with this will definitely tend to increase by this change.
The impact of this increased availability of people depend on the extent to which production of goods and services in the economy was constrained by shortage of this kind of manpower. If an economy is already facing a situationof high employment rate, it is quite likely that the production is being constrained by factors of production other than manpower. In such there may not be any significant extension in production possibility frontier.
The impact of rate of unemployment will also, similarly, depend on the impact of increased availability of manpower in increasing production. An economy constrained by manpower shortage may be able to increase its total production with the availability of added manpower. Under favourable conditions, this may create a multiplier effect which could actually reduce the unemployment rate. But in adverse conditions, the economy may not be able to provide jobs to the increased number of job seekers, and the unemployment rates may increase.