You'd need a bigger hard drive rather than more memory: dynamically shared libraries are paged-in to be used just as statically linked libraries are and are also paged-out when not in use, in just the same way.
Thus, to run a dynamically linked program you need to use the same amount of memory as you would a statically linked program.
However, if you are lucky (or have enough RAM), there is a chance that you won't have to load the page containing the library as it may already be in memory.
So there is a valid argument that to take full advantage of dynamically linked libraries you need more memory than for statically linked libraries.
Thus, to run a dynamically linked program you need to use the same amount of memory as you would a statically linked program.
However, if you are lucky (or have enough RAM), there is a chance that you won't have to load the page containing the library as it may already be in memory.
So there is a valid argument that to take full advantage of dynamically linked libraries you need more memory than for statically linked libraries.