The above function suggests that you are only evaluated by the measure in which you do the least well. For economists this is simple, it is a perfect compliment arrangement. It is an extreme case. But when you are preparing to appear in a formal setting, you don't want to know how many shoes you have to chose from to wear with your tux, you want to know if you have one right shoe and a left shoe that matches. Having 5 right shoes does not solve the problem.
The opposite case is a perfect substitute. In professorship many people assume you can either teach well and then not do research or research well and not really excel at teaching. This is not the case. I should point out that teaching well is hard to measure, so we proxy with teaching evaluations.
To some extent the idea of perfect compliments can only occur if the supply of people with moderate ratings on both margins is high. As labor is scarce, quality is sacrificed. However, there seem to be many people that would like the job. It is easy to see that someone needs to be a good researcher in order to be effective in the classroom. Who wants to hear a lecture from someone that is still teaching something they were forced to learn in grad school, good teachers update (good researchers update).
Why might it be the case that you need to be a good teacher to be a good researcher? What about the division of labor? Communicating clearly is very helpful in research. Too often people get rewarded for tweaking a tiny aspect of a model or having the only access to a data set. Just like judging students based on one GRE test, judging an article based on access to data or a particular methodological tool fails a robustness check. I can't exactly explain why a good researcher has to be a good teacher, but it seems to make sense to me. Maybe enjoying the classroom means that a good researcher will stay productive over a long period? I am open to thoughts on this.
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