I have come across the following problem:
Determine the marginal rate of substitution MRS(x1, x2) at point (x1, x2) = (5,1) for the following function:
u(x1, x2) = min(x1, x2).
The solution is that the MRS is undefined at that point.
However, I don't understand why that is. With this utility function, we get an income expansion path that goes exactly 45 degrees from the origin, because the two goods are alway consumed in equal quantities. And as far as I know, the MRS of such a function (u(x1, x2) = min(αx1, βx2)) is only undefined at the exact angles of these curves, i.e. where x2 = (α/β)x1. In the problem at hand, however, we have x2 < (α/β)x1, i.e. 1 < 5. Shouldn't this mean that the MRS at the point (5, 1) is actually 0 and not undefined?