We can denote the solution by the consumption demand functions c1(r, m) and c2(r, m). Both goods here are normal goods. (Note that r is sufficient to capture the price ratio (1 + r)/1 and we can treat m as being measured in units of good 2.

The savings function is simply 1 c1(r, m). Demonstrate that the consumer could actually save less - or could save more - if the return to savings (the price r) increases. We cannot tell. [Note: yes, I am essentially asking about the sign of a derivative of a function you don't know, so you cannot just take the derivative. Yet, the question has a short and simple answer of maybe 4 or 5 lines. But how to get it?]