Friday, May 23, 2008

天譴論 -- An Economic Exploration

天譴論最近在報刋鬧得火紅。

From my very limited understanding (for all those who know the theory better than I do, educate me please), the theory goes something like this:

Let A be God, B be the secular ruler, and C be the ruled.

The theory suggests, again my understanding might be incorrect here, that when B performs poorly, there will come a point where A will do something nasty, NOT to B, but to C instead as a signal of A's indignation towards B's acts. That is, the bad things happening to C serve as a red flag for B in the hope that B will cut back on his harmful acts targted at C.

But the question is, why B will do less of the bad acts when some of the costs of his bad actions are not borne by B himself or hershelf but shifted to C instead?

10 comments:

said...

I think the theory works, at least in the ancient world, because C or its productivity is viewed as the property of B.

Wai Hong said...

The hidden agenda is this: When enough of C are hurt, they will rise up and overthrow B; so it is in B's best interest to do good deeds. It is a more costly form of checks and balances. Separation of power as we know it in the West is by no means free either.

Gary M C Shiu said...

Dear Ming:

Yes, I am aware of the private property constraint ie. what is C's belongs to B's as well.

But what I have in mind is this:

A dollar in the safe of the ruler (B)is different from the dollar in the vault of the subjects (C).

While it does not cost B much to go to his or her own safe to get the dollar stored there, it is not the same if B wants to get his or her hand on the dollar stored at C's vault. C would have the incentive to hide wealth away so B would not be able to steal it. In other words, it is costly for B to get that dollar stored away at C's vault.

Taken that costs into account, if A takes away a dollar's worth of wealth from B, that would cost B less than a dollar.

Let's have a concrete example here. Say it would cost B 50 cents for each dollar grabbed from C. So on net, a dollar from C is only worth 50 cents to B.

Now suppose A takes away a dollar from C in bid to punish B, the actual costs borne by B is only 50 cents! That is definitely a cost lower than if A takes a dollar directly away from B! And my argument will still go through.

said...

Hi Gary,

I am not saying that A should punish B by doing bad things to C. However, I think we have an interesting topic here (much much more interesting than my thesis, at least) and let's see whether I can defend my argument.

First of all, I agree that "it is costly for B to get that dollar stored away at C's vault". Thus, punishing B through C is less effectively than punishing B directly, but in per unit sense only.

In those cases that A want to punish B, wealth of the royal family (i.e. B) is normally very tiny when comparing with the tax revenue from the people (i.e. C). In this sense, a bad thing on C will result in a greater wealth reduction of B than a direct bad thing on B.

To incorporate Yeung's idea, I will say that B's finances collapse when the wealth reduction reaches certain level and C will rise up due to higher taxes/insufficient relief.

Gary M C Shiu said...

Dear Ming:

Thanks for your kind words.

You see, the argument that I am trying to make is simply this:

To examine the effectiveness of A's (God) policy tool in dissuading B (secular ruler) from doing bad things to C (the subjects)by taking stuff away from C through disasters, one has to put oneself into the shoes of B, yes the bad guy.

Once you imagine yourself to be B, then what matters to you when deciding whether to perform an extra unit of bad indeeds is doing your own cost-benefit analysis. The key word here is marginal.

My example given in my earlier comment shows that A will be far more effective if A wants to dissuade B from doing one less unit of bad things by directing taking stuff away from B than through destroying stuff stored away in C's safe.

That is the down-sloping demand curve at work again, you do less of something when the cost of doing that something is high. In this particular case, that something is doing bad things to C.

You mentioned;

In those cases that A want to punish B, wealth of the royal family (i.e. B) is normally very tiny when comparing with the tax revenue from the people (i.e. C). In this sense, a bad thing on C will result in a greater wealth reduction of B than a direct bad thing on B.

Here you are basically saying that the discounted present value of C's productive potential is far higher than whatever is stored away in B's vault at this moment in time. I am not disputing that and would simply point out that you are thinking in total not marginal terms here.

B, when contemplating whether to do one more bad thing or not, thinks in marginal terms, and for A to punish B indirectly through C would render it less costly for B to do so, hence more bad deeds would come along than if A punishes B directly. That cost-benefit calculation at the margin holds even if what you say is true ie total discounted present value of C's productive potential far outweighs the value locked up in B's safe at this moment in time.

said...

Dear Gary,

You know, I am sure that I will have much more interesting thesis topic if we have met earlier.

Let me fight for another round.

Yes, agree that marginal cost is the key. However, I am going to have my defense by arguing the definition of the marginal cost of B's bad deed.

It is true that direct punishment on B is more effective to reduce B's bad deed if marginal cost is defined as one unit of wealth taken away by A.

If marginal cost is defined as one disaster, however, it is clear that disaster happened on C is more effective. Of course, I implicitly assume that A's cost for inducing a disaster is fixed regardless of its scale.

Gary M C Shiu said...

Dear Ming:

Thanks for spending time on this seemingly trivial matter.

My sense is that re-defining the definition of MC would not help here.

A numerical example may help illustrate what I have in mind here:

Say at this moment in time, B(the secular ruler) has 5 dollars in wealth stored away in his vault while C (the subjects) has 20 dollars (in discounted present value terms).

All I am arguing is that, 5 dollars taken away from B directly would stop B at a lower level of bad behaviour than imposing that same costs on C (remember 5 dollars taken from C would translate into 2.5 dollars for B because of extraction costs, I assume it in my earlier example anyway).

In the indirect punishment scheme, to match the effect of taking stuff directly away from B (in terms of the level of bad things done by B), A(the GOD) would have to do more, punish C more harshly by destroying 10 dollars worth of valuable belongs owned by C.

Hence, you would need to destroy more stuff owned by C, if punishment is indirect, in order to get the same level of bad behaviour. That is not very effective eh?

said...

Hi Gary,

Let me follow your numercial example, but assume that it requires 10 dollars to stop B at a lower level of bad behaviour this time. Due to B's endowment limitation(i.e. 5 dollars), it seems that A has no alternative but to punish C indirectly in order to reduce B's bad baheviour.

So, I would say that it is the endowment limitation makes A to use the indirect punishment scheme even though punishing B directly is more effective.

To extend the example, I can further assume that B would transfer part of C's wealth to its own once its wealth is taken away from A.

Therefore, A needs to punish B twice (of course, B needs to know it in advance. Otherwise, the first punishment will become sunk cost) to stop B's bad behaviour. (i.e. 5 dollars in the first disaster and another 5 dollars in the second one).

In this case, A may choose to take two disasters on B (take away 5 dollars each time) or one disaster on C (take away 10 dollars at one time) to stop B's bad behaviour.

As assumed in my last argument, there is a cost for A to induce a disaster each time, but the cost is independent of the disaster's scale (i.e. size of wealth taken from the disaster).

Taking A's cost into consideration(e.g. 6 dollars per disaster), I think it is still possible that indirect punishment is more effective.

Just forgive me if I keep making stupid argument :)

Gary M C Shiu said...

Hi Ming:

Again thanks for spending time in debating with me.

You said "So, I would say that it is the endowment limitation makes A to use the indirect punishment scheme even though punishing B directly is more effective"

My argument is invariant to the numbers used in my example, but yours do not. You are trying to add an additional constraint (endowment)to make the case while the numbers I have in the example merely serve to illustrate my point. If you like, you can assume B's wealth to be 10 dollars while C has 20 dollars stored separately at their respective vaults.

Your additional assumption of transfer of wealth from C to B once A sanctions B does not alter my analysis, I think.

In addition, in the last paragraph of your most recent comment, you are assuming that the costs of A in dispensing punishment would alter the result I have. Again I do not think it does.

In addition, it is important for you to see how, instead of confronting my argument head on by going through its internal logic, you keep on adding new assumptions to make you case. Just be aware of that.

said...

Hi Gary,

Can I put it in following way?

It is always true that "5 dollars taken away from B directly would stop B at a lower level of bad behaviour than imposing that same costs on C".

However, the endowment of B and A's cost make it possible (possible only) for A to reduce B's bad acts by punishing C instead of B.