You just got a job in Washington, D.C. You move into an apartment with some acquaintances. All your roommates, however, are slackers and do not clean up after themselves. You, on the other hand, can clean faster than each of them. You determine that you are 70% faster at dishes and 10% faster with vacuuming. All of these tasks have to be done daily. Which jobs should you assign to your roommates to get the most free time overall? Assume you have the same number of hours to devote to cleaning. Now, since you are faster, you seem to get done quicker than your roommate. What sorts of problems may this create? Can you imagine a trade-related analogy to this problem?

We know that we can clean 70% faster at dishes and 10% faster at vacuuming compared to our roommates. Let's find out how much time each person spends on each task. Suppose a roommate takes 1 hour to do the dishes; since we are 70% faster, we take 1 - 0.7 = 0.3 hours (or 18 minutes). Similarly, if a roommate takes 1 hour for vacuuming, we take 1 - 0.1 = 0.9 hours (or 54 minutes).

Now let's find out the time saved by assigning each task: - Time saved with dishes: 1 hour (roommate) - 0.3 hours (us) = 0.7 hours - Time saved with vacuuming: 1 hour (roommate) - 0.9 hours (us) = 0.1 hours

Comparing the time saved, it's clear that we save more time overall by assigning the dishes task to our roommates, while we handle vacuuming. By doing this, we are ensuring that we have the most amount of free time.

A possible problem may arise when roommates notice that we are completing tasks faster than them, and they might be demotivated or feel less responsible for the cleaning tasks. This could result in roommates slacking even more in their duties. A trade-related analogy to this problem would be the concept of comparative advantage in economics. In international trade, countries produce and export goods for which they have a comparative advantage (lower opportunity cost) and import goods in which they have a comparative disadvantage. In our case, we have a comparative advantage in both tasks; however, the opportunity cost of doing the dishes ourselves is greater than vacuuming. So, by specializing and trading (here, dividing household chores), we maximize overall efficiency and free time.