Does creating functions consume more memory

Yes, creating functions uses more memory.

... and, no, interpreters don't optimize Case A down to a single function.

The reason is the JS scope chain requires each instance of a function to capture the variables available to it at the time it's created. That said, modern interpreters are better about Case A than they used to be, but largely because the performance of closure functions was a known issue a couple years ago.

Mozilla says to avoid unnecessary closures for this reason, but closures are one of the most powerful and often used tools in a JS developer's toolkit.

Update: Just ran this test that creates 1M 'instances' of Constructor, using node.js (which is V8, the JS interpreter in Chrome). With caseA = true I get this memory usage:

{
    rss: 212291584,       //212 MB
    vsize: 3279040512,    //3279 MB
    heapTotal: 203424416, //203 MB
    heapUsed: 180715856   //180 MB
}

And with caseA = false I get this memory usage:

{
    rss: 73535488,       //73 MB
    vsize: 3149352960,   //3149 MB
    heapTotal: 74908960, //74 MB
    heapUsed: 56308008   //56 MB
}

So the closure functions are definitely consuming significantly more memory, by almost 3X. But in the absolute sense, we're only talking about a difference of ~140-150 bytes per instance. (However that will likely increase depending on the number of in-scope variables you have when the function is created).

I believe, after some brief testing in node, that in both Case A and B there is only one copy of the actual code for the function foo in memory.

Case A - there is a function object created for each execution of the Constructor() storing a reference to the functions code, and its current execution scope.

Case B - there is only one scope, one function object, shared via prototype.