Parable of the Vase

Tim Groseclose reviews Garett Jones’ Hive Mind, whose “primary and most important contribution is to document the following empirical regularity: Suppose you could a) improve your own IQ by 10 points, or b) improve the IQs of your countrymen (but not your own) by 10 points. Which would do more to increase your income? The answer is (b), and it’s not even close. The latter choice improves your income by about 6 times more than the former choice.”

The Parable of the Vase, which it employs to explain the point, is an instantly canonical illustration, Groseclose argues. (“I do not think it is an exaggeration to say that the parable ranks as one of the all-time great examples in economics.”)

The parable begins with a simplifying assumption. This is that it takes exactly two workers to make a vase: one to blow it from molten glass and another to pack it for delivery. Now suppose that two workers, A1 and A2, are highly skilled—if they are assigned to either task they are guaranteed not to break the vase. Suppose two other workers, B1 and B2, are less skilled—specifically, for either task each has a 50% probability of breaking the vase.

Now suppose you are worker A1. If you team up with A2, you produce a vase every attempt. However, if you team up with B1 or B2, then only 50% of your attempts will produce a vase. Thus, your productivity is higher when you team up with A2 than with one of the B workers. Something similar happens with the B workers. They are more productive when they are paired with an A worker than with a fellow B worker.

So far, everything I’ve said is probably pretty intuitive. But here’s what’s not so intuitive. Suppose you’re the manager of the vase company and you want to produce as many vases as possible. Are you better off by (i) pairing A1 with A2 and B1 with B2, or (ii) pairing A1 with one of the B workers and A2 with the other B worker?

If you do the math, it’s clear that the first strategy works best. Here, the team with two A workers produces a vase with 100% probability, and the team with the two B workers produces a vase with 25% probability. Thus, in expectation, the company produces 1.25 vases per time period. With the second strategy, both teams produce a vase with 50% probability. Thus, in expectation, the company produces only one vase per time period.

The example illustrates how workers’ productivity is often interdependent—specifically, how your own productivity increases when your co-workers are skilled.

The example generates an even more remarkable implication. It says that, if you are a manager of a company (or the central planner of an entire economy), then your optimal strategy is to clump your best workers together on the same project rather than spreading them out amongst your less-able workers.

Leave a Reply