How well does a Columbia Undergrad econ major feed into MBA programs and Marketing firms?
As well as any other place that has an extremely high caliber admit criteria into the undergrad program.
MBA programs are going to evaluate various factors in your profile: academic performance, work experience, standardized tests (GMAT/GRE), and community work. They don’t care what you studied in undergrad, as long as you studied well and can show your current passion for business, marketing, etc.
If you want to go to marketing post MBA, that’s another story. If you don’t have any experience in Marketing pre-MBA you would want to make the most out of your time in b-school. You want to find a marketing related internship, take many marketing classes, participate in business competitions, etc. You should build a network in the area and show future companies that you are knowledgeable enough (and smart) to become an expert in this new domain. People do it all the time - most students going into MBA programs seek to change careers post graduation, so you won’t be alone and you’ll have a good support group (and decent career services, if you go to a top school).
Here are some ideas on how to make the most out of your time in b-school, from a recent Harvard Business School alumna http://admit1mba.com/2014/05/making-time-harvard-business-school.html