Question

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?

Short answer

To maximize overall free time, you should assign the dishes task to your roommates and handle vacuuming yourself. This is because you save more time by doing dishes faster (0.7 hours saved) compared to vacuuming (0.1 hours saved). However, this may create problems such as demotivation or less responsibility among roommates. A trade-related analogy to this situation is the concept of comparative advantage in economics, where specializing and trading tasks based on comparative advantage maximizes efficiency and free time.

Step-by-step solution

Compare Speed in Tasks

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).

Calculate Time Saved for Each Task

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

Assign Tasks for Maximum Free Time

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.

Problems Created and Trade-Related Analogy

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.

Key concepts

Opportunity Cost

Opportunity cost refers to the benefits or value of something that one has to give up to choose or obtain something else. In simple terms, it reflects the trade-offs involved in any situation where a decision must be made. For example, by choosing to do one task well, you give up the opportunity to do another task.

In our household cleaning scenario, even though you are faster at both dishes and vacuuming, your opportunity cost differs for each task. By focusing on the vacuuming (where you have a lesser advantage), your opportunity cost is lower because you allow your roommates to handle the dishes, where they are markedly slower.

This means you make the most of your time. You efficiently "spend" your effort on vacuuming, and in doing so, you gain more free time by allowing others to handle the slower task. Understanding opportunity costs helps in knowing which sacrifices lead to better outcomes.

Specialization

Specialization involves focusing on a specific task that you are relatively best at, in order to maximize production or efficiency. When applied to our cleaning example, this concept suggests that each person should undertake tasks in which they have a relative advantage.

Although you are faster at both cleaning tasks, if you specialize in vacuuming, where your advantage is only 10%, you can alleviate the heavier workload from the dishes, where your roommates are significantly slower.

This specialization is analogous to how countries operate in the global market. Countries often specialize in producing goods where they have benefits of lower opportunity costs. They then trade these goods with others, just like dividing household chores efficiently. Specialization helps in increasing productivity and sparking cooperation among entities involved.

Efficiency

Efficiency refers to making the most of resources and achieving the maximum output with the least waste of time, effort, or materials. In terms of household chores, efficiency is reached when tasks are completed in the shortest time possible with the highest amount of free time available afterward.

By assigning tasks based on each person's comparative advantage, you enhance the overall efficiency. You take on vacuuming, which you can do swiftly. By leaving the longer task of doing dishes to your roommates, even if they aren’t as quick, you ensure time is used better collectively.

Being efficient means not just getting work done quickly but discerning how each person's time and skills can be best utilized. Similarly, in economics, achieving efficiency allows economies to grow and resources to be conserved, resulting in satisfying different needs effectively and swiftly.