posted by Brett on .
Suppose Fred and Ethel need to divide 20 pizza slices and 10 cans of beverage. Fred's utility function is given by the equation U=Min(Z,B), where Z is the amount of pizza and B is the amount of beverage. Ethel's utility is given by the equation U=Min(1/2Z,B). What are the efficient allocation of Pizza and Beverage?
So for Fred, Z and B are efficiently allocated when Z=B. Further, there are no diminishing returns. That is MU at Z0=B0 is the same as MU at Z1=B1. For Ethel, like Fred, there are no diminishing returns. However, efficient allocation calls for 2Z=B.
So, it may not be equitable, but one efficient allocation is to give everything to Ethel.