Yes, we will generally be able to tell the difference, esp if the course catalog is on-line.
My school is a top 10 which also houses a business economics PhD program. The version of PhD micro that undergrads most commonly take is the business school PhD micro, which according to the professor is less deep and mathematical than the econ PhD micro (although it still uses MWG as the primary text so I'm not sure of the magnitude of this difference).
My question is, are adcoms likely to know that this is lower level than standard PhD micro? (I've read on this forum that the primary means of gauging rigor is to ask for the prescribed textbook, which is MWG) Is that likely to diminish the signalling value of the class?
Even if the pure econ course has higher signaling value, it may be more sensible to take the less demanding business school course. If you can do well in the first year sequence of a business econ PhD at a top 10 univ - I'm assuming something like Stern or Wharton - you can probably get admitted to an equally or higher ranked PhD econ/bus-ec program. Which means there's diminishing returns to investing in admissions-related signaling. Taking a hard grad micro couse is a particularly costly signal because you'll almost certainly have to take a comparable course again. IMO, conditional on being able to do well in the business econ PhD micro course, your additional time next semester is probably better spent on research assistance or supervised thesis writing.
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