The symbol on the left is the caduceus or a herald's staff. In Greek mythology, it is an attribute of Hermes, the god of messengers, economists, merchants and - pure coincidence, I suppose - gamblers, liars and thieves. Hermes is the closest Olympian god to economics and business, that's why the caduceus shows up on this website - and in many places related to commerce, for example:

How the caduceus ended up as a symbol for medical institutions in the U.S., I don't know. Maybe it got confused with the Rod of Asclepios?