Answer

Solution

1. 1

   Diminishing MU concerns own second derivatives $u_{ii} < 0$, while diminishing MRS concerns

2. 2

   the convexity of indifference curves, which depends on $u_{11}, u_{22}$ and the cross

3. 3

   partial $u_{12}$. Standard counterexamples (e.g., $u(x,y) = xy$ has constant or non-diminishing

4. 4

   MU in $x$ alone but diminishing MRS; conversely, suitable utilities can exhibit diminishing

5. 5

   MU but increasing MRS once the cross effect is hostile). Therefore diminishing MU of

6. 6

   at least one good is neither necessary nor sufficient for diminishing MRS.

Answer structure / marking notes

Content note