6.8 separable utility A utility function is called separable if it can be written as U (x, y) = U1(x) + U2(y), where U ′i > 0, U i

″ < 0, and U1, U2 need not be the same function.

a. What does reparability assume about the crosspartial derivative Uxy? Give an intuitive discussion of what word this condition means and in what situations it might be plausible.

b. Show that if utility is separable then neither good can be inferior.

c. Does the assumption of reparability allow you to conclude deinitively whether x and y are gross substitutes or gross complements? Explain.

d. Use the Cobb–Douglas utility function to show that reparability is not invariant with respect to monotonic transformations.