If I take a course in Barnard that is listed in the economics section of the bulletin, do I need to get approval from the department?

No. However, any remaining seats are open to general registration, and that there are some overlaps between Barnard and Columbia College courses. If you take two courses that the department deems too similar, then only one of those courses will count towards your major or concentration. Below is a list of pairs of courses offered in the department and Barnard that cover essentially the same material so only one of them may be taken to fulfill the major requirements:
i. GU4321 and BC3029: Economic Development
ii. GU4329 and BC3039: Economics of the Environment
iii. GU4400 and BC3019: Labor Economics
iv. GU4505 and BC3038: International Money
v. GU4235 and BC3041: Historical Foundations of Modern Economics
The department may add courses to the list above should other courses seem too similar.