Final answer:
To maximize free time, the individual should do dishes themselves since they are significantly faster at it, applying the principle of comparative advantage. Problems that may arise include resentment and coordination issues. A trade analogy is a country that specializes and trades based on efficiency and opportunity cost.
Step-by-step explanation:
To maximize free time and ensure efficient task allocation among roommates, an individual who is 70% faster at doing dishes and 10% faster at vacuuming should take on the task of dishes themselves, as this is the task with the greatest time-saving potential due to the higher relative speed increase. By assigning the task at which you're relatively more efficient, you reduce the overall time spent on that task. It is a principle similar to comparative advantage in trade, where each party specializes in the production of goods for which they have a lower opportunity cost, resulting in more efficient outcomes.
Problems that may arise from you consistently finishing tasks quicker than your roommates include potential resentment or a lack of responsibility from them. Furthermore, if task completion times impact other shared responsibilities or plans, this discrepancy could lead to coordination issues.
In a trade-related analogy, this situation is akin to a country that can produce certain goods more efficiently (with lower opportunity cost) than others, and thus specializes in producing those goods while trading for other goods that it produces less efficiently. If one country consistently benefits more from trade, it may lead to trading partners feeling taken advantage of or deciding not to engage in trade at all due to perceived inequality.