Mormons and Markets, II.A: Information and the Failure of the United Order, an Addendum

May 23, 2005 | 6 comments
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Consider this an addendum to Nate’s post on the catastrophically large amounts of information needed to plan an economy.

Suppose that you are in charge of allocating a set of goods and services among a group of people, and you wish to do so in a way that is best, whatever definition of best you wish to use. God, for example, acts so as to bring about joy and eternal life. And so let us take that as our goal; we wish to allocate resources in a way that maximizes the number of people in the group who will be exalted and joyful. So, for example, we give them food because eating makes people happy, and we give them land so they can avoid idleness, and we give them extra stuff so they can choose to give it to the poor and they can consume it. Now imagine a function that takes as input how many goods a person is given, and then delivers a number that, for example, indicates the propensity of that person to achieve exaltation and happiness. We’ll call this function J(X), where the X is the list of stuff we gave them. Our goal is to maximize these J(X)’s across people. So now we’re ready for the fun stuff:


“It’s fun to have fun, but you have to know how!”

J(X) takes as input a huge list of possible goods. Thus for each of those goods we wish to give someone, we need to know how giving more or less of it affects their joy function J(X). So let’s index the function so that each good has an assigned index number from 1 to N. If I write J'(2), let that be the amount that one unit of “good 2″ increases my propensity to exaltation or happiness. We also need to keep track of the fact that this function varies by person. So now J'(2,Frank) is the added benefit from good 2 for Frank. Now consider a simple version where my wife and I are allocating household resources. To achieve a maximum in an economy composed of just Frank and Carrie only, where I simply am trying to sum their propensities to exaltation and happiness*, I need to pick an allocation such that the following is true:

J'(1, Frank)/J'(2, Frank) = J'(1, Carrie)/J'(2,Carrie)

Essentially it says that at the maximum, the relative benefit of good 1 to good 2 has to be equal across Frank and Carrie. That must be true, not just for goods 1 and 2, but for every pair of goods. And, for a real economy, this needs to hold not just for Frank and Carrie, but for every pair of people. And, by the way, the numbers in this equality are not constants that can be learned once, they change every time you change the set of goods you give a person. So there is a tremendous amount of information required here. For those of you who are married, imagine the difficulties of allocating family resources, multiplied by, for the U.S. economy, 300 million. Then square it.

So far I have ignored where these goods came from. There is a symmetric allocation problem on the production side, where you must know how each input affects each plant’s productive capacity and they must each fall into a ratio similar to the one above in order to achieve the most production at the least cost.

Well, obviously, no mortal has anywhere close to that much information about everybody else. It is just pie in the sky theory to think that one could ever get this to all work, right? For a mortal social planner, that is absolutely right.

The Price Genie
But it turns out that if each firm knows their own cost structure and each person knows their own J(X) function and seeks to maximize it, then one can achieve the theoretical optimum just by establishing a market and enforcing contracts. Because Frank’s attempts to make himself happy are equivalent to him finding a point where J'(1,Frank)/J'(2,Frank) equals the ratio of prices for goods one and two. And so on for each other person. And since each person moves to the price ratio, they all equal each other, and one achieves the optimal allocation. This is true across all goods and, on the production side, it is true for all production decisions.

Thus prices are the information signal that move society as close as possible to the best of all possible worlds. The information requirements, though still large, are clearly way less than before; because now you only need to know about yourself and the prices. True, people make mistakes and there are cases where this doesn’t work, but mistakes and problems happen under any system. The information requirements of a free market are orders of magnitude smaller than in a planned economy simply because the prices naturally keep track of all the information about other people for us.

Consequently anything we do to mess with the prices, like taxes or minimum wages or price subsidies, will mess this relation up and move us away from the optimum, by corrupting the information signal available in prices. There are all sorts of problems that one has to deal with in a competitive market, but the advantages of having informative prices are so huge that it really is worth a lot of effort to (very carefully!) tweak the system into working well, before trying to reinvent the wheel and do central planning.

Agency
Speaking of mistakes, some people are lousy at choosing what makes them happy and exalts them. That is pretty much the basis fo the missionary program. But God lets them make their own choices anyway. A market economy has the nice feature that it encourages individual accountability in a parallel way to how God does. In this sense it is similar to Mosiah’s teachings about the evils of a monarchy, given the possibility of a wicked king. It means we receive wages of him whom we listeth to obey. And each man is rewarded according to the desires of his heart; not the desires his heart should have.

Retreating to simplicity
Could this information problem be solved by retreating to simplicity, as Nate discusses? A retreat to simplicity is essentially saying that some set of goods will just not be offered, and thus they carry an infinite price. This lowers the information hurdle of pricing the other goods, but arbitrarily setting the price of some goods to infinite does not change the fact that those goods would have made people happy. It just means that those participating in the planned economy have to give up those goods from day one. Thus you will still have problems of black market entry or those who abandon the faith because the price of membership is so high. Or, if there is no competition from the outside world, this means that one is giving up higher J(X)’s in exchange for the rather dubious benefits of having a central authority run people’s economic lives. If that is God’s will, I’m fine with that. But there is little evidence that it is.

The Amish presumably face this modernization problem all the time. They know those modern goods are available, and the price of those goods is relinquishing membership in their congregation. I would guess that this issue is never far from their minds, and leads to a fair amount of membership loss. On the other hand, barriers to entry in religion can be quite important for maintaining group solidarity

To maintain those infinite prices we would have to expend a tremendous amount of energy in preaching and doctrine, for a decidedly uncertain benefit. In the early days of Utah, when the economy did not function well due to lack of currency and no access to capital, and there were only a few goods to deal with, it is possible to imagine real gains from the centralization of the economy. But as we got our feet under us, those benefits dissipated pretty fast. Thought about this way, it is quite possible that Brigham Young’s centralized control was not a quirk of Brigham Young so much as what was needed at the time to get things moving, before the market instututions could be developed and put into place. Just as from Nephi to Mosiah there were kings, until the people were ready to take care of themselves and have judges.

It is, therefore, not surprising which direction the Church moved over time.

* Here I am ignoring another set of sticky allocation problems.

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6 Responses to Mormons and Markets, II.A: Information and the Failure of the United Order, an Addendum

  1. greenfrog on May 23, 2005 at 1:24 pm

    I like this analysis. I remember being fascinated the first time I read Milton Friedman unpacking the informational content of price.

    Does the formulation hold if the process of getting goods through markets operates, itself, on the J(X) function?

  2. Nate Oman on May 23, 2005 at 1:24 pm

    A point: Frank it seems to me that J(X) is a welfare function described in theological terms. Fair enough. However, it seems to me that you then make the jump of assuming that J(X) is some sort of idealized utility function that describes the behavior of rational individuals, although you make allowances for poor choices, imperfect information, etc.

    It seems to me, however, that there is not reason that we should assume that a normatively desirable welfare function bears any relationship to a descriptively accurate or useful utility function. Hence, it seems to me that misbehavior, etc. far from imperfect information and the like, may simply be an example of perfect rationality with a different maximand.

    What this means, philosophically, is that in order to justify the market one will either need to (1) conflate welfare functions and utility functions such that what makes a person better off is defined a priori as the maximization of their expressed preferences; or, (2) a moral theory, e.g. the inherent value of agency, that acts as a normative trump to whatever welfare function that we offer.

  3. Frank McIntyre on May 23, 2005 at 2:31 pm

    greenfrog,

    Allowing the markets themselves to act on the utility, or for utility to be a function of prices themselves, is sometimes, but not always, problematic. It depends a great deal on exactly how they affect utility.

    Nate,

    So I mention the agency angle already. But aside from that, yes, we are relying on the notion that people need some concept of what they want. As I noted, God seems to use this concept himself, in that He gives us that which we desire. Thus one could make a case for the idea that we should receive according to our observed choices.

    Alternatively, one can simply say that the J(X) function differs from the function the person maximizes U(X), and that that difference J(X)-U(X) represents an inefficiency that rises as the difference rises. This is a problem for welfare theory types, but I don’t see that it implies much policy action unless one thinks that there are other people (people you trust) that know J(X) better than the individual. I tried to hit that point above. The scriptures seem willing to concede that a righteous tyrant can be better than democracy. I am similarly willing to concede that a rightreous central planner can do better than a free market. The problem is that one cannot a priori restrict central planners to just the good ones.

    And even then you are left with the agency problem, that God knows J(X), but made a big deal out of not imposing outcomes on us. Or, to put it another way, outside action can never maximize J(X) because one of the primary increasers of J(X) is that decisions are self made.

  4. Nate Oman on May 23, 2005 at 2:45 pm

    Frank: I am not trying to offer an argument for central planning. My point is simply that we cannot assume that a maximand that we find normatively attractive is the actual maximand of human behavior. (Notice my reference to maximands of behavior means that I am trying to work within a rational choice paradigm.)

    Suppose that God believes that ultimately each person should maximize their supply of wheat. Now under some circumstances rational individuals will maximize their supply of wheat, but the coincidence is unlikely to be frequent enough that we ought to use utility maximization as a rough and ready proxy for wheat maximization. Put in theological terms, using rational choice as a rough and ready model for the maximization of any theologically desirable maximand runs into the fact that most of the time most of God’s children seem to desire that which is not good.

    It seems to me that in your response you are using efficiency as a way of denoting the maximization of J(x). This, it seems to me, is an idiosyncratic usage, since efficiency seems to be most often associated with the maximization of expressed preferences.

  5. Frank McIntyre on May 23, 2005 at 3:03 pm

    I granted that J(X) and U(X) can differ, explicitly in my last comments and implicitly in the original post. You agree. Is there more to this that I am missing? Are you claiming that they are negatively correlated? Are you saying they are uncorrelated? I think that, except when the scriptures and modern prophets tell us otherwise, we should assume that U(X) and J(X) are as good as anything else we have. Do you disagree?

    “Now under some circumstances rational individuals will maximize their supply of wheat, but the coincidence is unlikely to be frequent enough that we ought to use utility maximization as a rough and ready proxy for wheat maximization.”

    Are you ignoring the fact that God gives us outcomes that are consistent with our wishes? Thus there may be a special place, theologically, for the revealed preference/desires.

    “It seems to me that in your response you are using efficiency as a way of denoting the maximization of J(x). This, it seems to me, is an idiosyncratic usage, since efficiency seems to be most often associated with the maximization of expressed preferences.”

    That is only idiosyncratic because we normally assume U(X)=J(X). Once you let that slide, the obvious move is to associate efficiency with welfare, not revealed behavior. In that way, one preserves the Pareto efficiency meaning of the concept.

  6. Stephen M (Ethesis) on May 24, 2005 at 7:43 am

    Fun stuff. You do know that Tito ran Yugoslavia on a market economy (an interesting concept, communism with a great deal less central planning) for that very reason. Of course in the 1970s, Yugoslavia was the one place you didn’t have to wait in line to buy food in a communist country.