A Trivial Economics Question

Here is the story. I have an object X that I wish to assign (gift or give away) to one of three: A, B, or C. How do I determine whom to give it to if I am concerned about allocative efficiency? Assume that A, B, and C have different preferences and abilities to pay.

To put a nice twist to the story, what if I am also concerned about equity? That is, although I have only one object X, I don’t want to be unfair to the other two who will not get the object X. What is the best way—the mechanism—to resolve this issue?

Of course, the answer changes if I don’t wish to give more than just the object X, as opposed to the case where I am willing to give more than X just for the sake of being fair to all three.

Finally, a real world situation. My siblings and I have inherited our parents’ property. The eldest occupies it, but the other three (including me), are waiting for our share. What is the most economically efficient way to distribute the value of the property if the property itself is indivisible?

Your views are solicited. Let’s see if we can find answers to the questions that we find satisfactory. And if we do, perhaps we will understand a little more about the question of how economies work. That is the beauty of economics. From seemingly trivial—though interesting—questions, one can gain insight into larger questions.

POST SCRIPT: I made the mistake of putting two entirely different scenarios on the same post. So there is much confusion. I wish to clarify that the “efficient allocation of an object X” is a seperate matter from the “fair and efficient distribution of an indivisible inherited property.” Conflating the two was not my intention.