Yesterday I posed a couple of trivial economics questions. The first was: *“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.”*

For allocative efficiency, we have to determine how much each values X. This is straight forward. Ask each separately how much money he or she would be **willing to accept** instead of X. That is, he or she is equally happy to receive the money as receiving X. Suppose A says Rs 100, and B replies Rs 80, and C Rs 60. Clearly, I should give X to A.

But then, B and C receive nothing. To be fair, I should give Rs 80 to B, and Rs 60 to C. This scheme appears to be fair to me, even though it is true that C receives less money than B.

However, if I wish to only give away X, not additional money, and be fair to all three. In that case, I should use another device. The previous device was the “willingness to accept.” This one is called the “willingness to pay.” (Let’s call this the WP scheme to distinguish it from the previous WA scheme.) I would ask each how much they are **willing to pay** to buy X from me. Suppose A says Rs 90, B says Rs 70, and C says Rs 50. Then I will sell X to A, and give each of them Rs 30 from the sale. This way I achieve fairness without actually spending more than what was the cost of X to me.

Could I have done better? Probably yes. There is an important distinction between “willingness to accept” and “willingness to pay.” The former is not limited by the person’s means. Example: if I am shown a Rolls Royce and asked how much I am willing to accept instead of being given the RR, the figure I would name would be bounded only by my private valuation of the RR. I may be willing to accept Rs 50 lakhs. That is, I would be indifferent between getting Rs 50 lakhs cash and getting the RR. But my willingness to pay would be bounded by my wealth, which could be less than Rs 50 lakhs.

Back to X and the WP scheme where A’s WP was Rs 90. They each got Rs 30, as a result. I can probably do better than that by selling X to a third party who has a higher WP. Suppose someone is willing to pay Rs 120 for X. I sell it to him and distribute Rs 40 to each to A, B, and C. A definite improvement over the case where the sale was limited to only the three.

There is an assumption in the above concocted scenario which should be stated explicitly: that there is full information. That is, A, B, and C know what exactly X is and therefore are able to correctly judge what they value it at. If there is information imperfection, then there is economic inefficiency in the proposed schemes. What if C, whose WP was only Rs 50, did not realize that X would help him earn Rs 200. If he knew that, he would have been willing to pay, say, Rs 180. In that case, he would buy it for Rs 180, and each would receive Rs 60 as proceeds of the sale.

Information imperfections really throw a huge spanner in economic machineries. Consider the case of a public service. It has a cost, **c**. The user has a private valuation, **v**. The service is provided at a price, **p** (and **p** can be zero, if the service is provided free.) Assuming that the user has full information, if **v < c**, clearly it is inefficient to provide the service. And that is what happens in the case of “free” government services at times. I say “free” because there is nothing free. Someone has paid for it. By putting a price **p** equal to zero, government actually causes social losses, and if sufficient social losses accumulate, eventually the economy becomes poor.

I am postponing the discussion of the other issue—namely, the division of parental property—until we have explored this issue a bit more. Also, I have been thinking about the IITs and how they cause allocative inefficiencies. I hope to show that simple economic reasoning is sufficient not just to reveal their problems but also the solution.

Thanks to all who have added comments to the previous post. Trust this post has extended the discussion a bit.

Be well, do good work, and keep in touch.

Categories: Random Draws

Aside from information imperfection, the parties may not be equivalent in their ability to use X.

If one of the three parties was a successful builder, s/he could take X, make an amazing apartment building with 50 flats in it (assuming they also have the political connections to change zoning). Suddenly, instead of 90, X can be worth 1000 to this person.

They may be willing to pay 990 for X but is it fair to give 330 to the other two who have no role in making X worth 990?

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Not too much into economics so my first reaction to the second way of giving Rs.30 to each after selling it to A for Rs.90 under WP scenario, haven’t we made A value X at Rs.60 effectively?

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Atanu,

No treatment of inheritence division is complete without considering Randy Waterhouse’s method (in Neal Stephenson’s Crytonomicon).

It’s a whole (irrelevant?) chapter in the book. Here’s a site that has some excerpts.

Valuation is multi-dimensional.

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Firstly, it all depends on the nature and value of the object. If it is non-perishable and of high value, you could start a TRUST and fund the trust with the object X and make all three beneficiary. This would be a viable solution where you do not have to split the object X and do not have to feel bad of not giving it to the other two. The best part, if you want to give beyond X then you can always fund the trust with whatever you wish toâ€¦…

Hope it works ! ! ! ! I feel this as one of the best solutions……

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