You just got a job in Washington, D.C. You move into an...

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?

Key Concepts

Trade and Specialization Analogy

Analogous to international trade, where countries specialize in what they produce most efficiently and then trade to mutual benefit, this problem highlights how individuals can gain from specializing in tasks where they have a significant performance advantage. However, just as in trade where disparities in productivity can lead to negotiation imbalances or fairness concerns, differences in inherent efficiency may create issues of perceived inequity or imbalance in the distribution of work.

Opportunity Cost

Opportunity cost refers to the benefits that are forgone by choosing one option over another. In the context of task assignment, it means evaluating what is lost (in terms of time or efficiency) when a faster individual performs a task that a slower individual could handle with less relative inefficiency, thus informing better strategic choices on task distribution.

Comparative Advantage

This concept involves identifying which party is relatively more efficient at a given task, rather than simply who is more efficient overall. It suggests that even if one individual is faster at every task, they should focus on tasks where their efficiency gain is greatest relative to others, allowing everyone to contribute most effectively to the overall workload.

Division of Labor

Division of labor is about assigning different tasks to different individuals based on their strengths and relative efficiencies. By allocating tasks so that each person performs the type of work they do best, total productivity increases and overall time spent on tasks is minimized, leading to greater collective free time.

Transcript

00:01 So in this problem, we know that you clean dishes 70% faster, um, than your roommates.

00:06 So i'm just going to sign random numbers to these are not really random.

00:09 They're kind of thought out.

00:10 So for the roommates, i'm just going to say that they can in one hour.

00:15 So our quote unquote labor equals one hour.

00:21 And, um, in one hour, your roommate can do 10 dishes and can vacuum 10 square feet, which is not a lot at all.

00:32 But let's just suppose.

00:34 And now you can clean dishes 70% faster than your roommate.

00:38 So 70% of 10 would be seven.

00:41 So 10 plus seven would be 17.

00:45 Another way of calculating that would be, um, by using the following formula.

00:52 It would be the observed, minus the expected over the expected.

01:00 In this situation, the expected are both 10.

01:04 And you know, this equals 0.7, but this represents is the percent difference.

01:10 Um, so yeah, you can do, um, and then your observation would be whatever whatever this comes out to be.

01:18 And we get 17 when we do that.

01:20 Um, so that's just the example.

01:23 Formula i used if you guys are doing this on a test.

01:25 I'm pretty sure that will work too.

01:26 So i have 17, and now i know that i vacuum, uh, 10% faster than my roommate.

01:33 So 10% of 10 is one.

01:35 So i know that i can do 11 square feet in one hour again.

01:41 Not a lot, but just imagine so.

01:44 Now we have to figure.

01:45 So what we have here is basically a comparative advantage matrix kind of thing, right? um, we have to figure out who has what now it's pretty obvious to see that in both situations, dishes and vacuuming, i have the absolute advantage.

01:57 So here's where the problem can come up.

02:00 I can do everything more quickly, but i only have so much time.

02:03 So we have to.

02:04 We can come up with a trade situation if, um, there's a comparative advantage involved.

02:10 So to figure out the comparative advantage, we have to figure out the trade ratio for the opportunity cost of each thing.

02:17 So for you, one dish is equal to 11/17 square feet, right? and we get this because we have 17 dishes equals one hour, one hour, and we have that 11 square feet equals one hour.

02:39 And because they both equal one hour, we can set them equal to each other.

02:42 17 dishes equals 11 square feet.

02:46 And when we divide to just get one dish, we have to divide both sides by 17.

02:50 18 equals 11 square feet over 17...

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