@NerdyChica obviously has some sort of agenda to steer you towards Duke.
Regarding LAC’s:
My sister teaches at a USNWR top 25 university. She’s chaired two departments during her time there. She loves her school, but she’d readily tell you that a major part of the school’s mission of elite universities is to do research and publish new information. Therefore faculty are recruited on that basis, and not at all on their ability to teach. There are many wonderful teachers at these schools, but there are also a significant number of faculty who view teaching simply as something that gets in the way of their research.
My sister, who is familiar with Amherst, would back up Amherst’s claim that their mission, first and foremost, is to educate their students. Not denigrating Duke, but I am confident that at Amherst your professors will take a much greater personal interest in you and will do more to see that you succeed. Similarly, I think that if you have a problem, e.g., a personal crisis or extenuating circumstances of any sort, you’ll get more help at Amherst, both from the faculty and/or the admisinistration. This is in my mind the biggest difference you’ll find between LAC’s and major universities.
Regarding finding jobs in the market? I think that if you do an apples to apples comparison, the schools come out pretty even. There may (or may not) be more philosophy majors proportionally at small LAC’s than at Duke, so maybe more LAC kids don’t have a readily marketable skill when they graduate. I don’t really know. I guess the main point is that if you don’t have marketable knowledge or skill and/or haven’t demonstrated in college that you’re able to succeed in a rigorous course of study that it doesn’t matter if you graduated from Amherst or from Duke. My guess is that @NerdyChica has little direct knowledge about Amherst or about the job prospects for math/econ majors who graduate schools like Amherst, Williams, Pomona, etc.
I posted this link in another thread, but I think that it’s helpful:
https://www.amherst.edu/system/files/media/69th%2520SSR%2520in%25202015%2520%2528Class%2520of%25202019%2529.pdf
Scroll down to the next to last page that shows all of the majors of last year’s graduating class. I think that it’s instructive. Note how many Economics and something else double majors are there. And note that there are 12 Econ/Math double majors (of 450ish graduates). I can almost guarantee you that any of these kids, if they graduated with good academic records, who wanted a job in finance found a job in finance. You are in a much more select group graduating with this degree from Amherst than you’d be at Duke.
Also, without question Amherst is held in very high esteem by folks who do admissions at graduate schools.
But honestly, I have no dog in this hunt. You should go to the school that’s the best ‘fit’ for you. As I wrote in the prior note if I were you I’d look at factors other than post-graduate job opportunities. Most importantly I’d look for where you think you’d connect best with the other students and where you’d most feel at home. But if you’re a good student who won’t get lost in distractions when you’re in college I don’t think you need to base your decision on which school will give you a leg up on a job or graduate school. You’ll not be limited in those opportunities if you choose Amherst.