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It appears the math professor couldn't handle the fact that in economics:
We have models, wherein all the rules and mechanisms are clearly defined;
We have the real world, where it's a lot harder to boil things down to a few transparent mechanisms.
We use the former to clarify our thinking about the latter.
Models are fully-articulated artificial economies where the researcher has full control over the preferences, the production functions, and the trading arrangements. We then figure out properties of those model economies, identify key transmission mechanisms, and poke them to see how they react.
Then we reason by analogy to the real world.
And if you think the assumptions don't reflect the real world along some first-order dimension, you build a competing model where you have different trading arrangements, or different utility functions, or different production functions, or whatever. Then you see how far from the benchmark your model takes you.
This guy gets it. Now if he would only get why she's raising these concerns.
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