Tag Archives: Most Insightful Articles

A Difficulty in the Concept of Social Welfare

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Welcome to the third installment in our series of discussions of the Most Insightful Articles in economics. Today we are discussing Ken Arrows’s 1950 article A Difficulty in the Concept of Social Welfare.

If you’re interested in politics, you may have done the following thought experiment. Suppose there are three voters—1, 2, and 3—and three alternatives—A, B, and C. Voter 1 prefers A to B to C. Voter 2 prefers B to C to A. Voter 3 prefers C to A to B. By a vote of 2-1, “society” prefers A to B. It also prefers B to C. If a rational person prefers A to B and B to C, then that person prefers A to C. But in this example, “society” prefers C to A! Is society irrational? Is this just a problem with majority rule? To cut to the chase, in this paper Arrow shows that it is a general problem. Any method of aggregating individual preferences is either irrational or has some other properties that are arguably undesirable.

One can envision collective decision-making as selecting a social welfare function and then using it to compare states of the world. Arrow defines five conditions to which a social welfare function ought to hold:

  1. The function is universally defined. There are not certain preferences that people can have that cause the function to be indeterminate (though the function is allowed to express indifference).
  2. If someone decides that X is more desirable than he initially thought, and nothing else changes, the social welfare function cannot penalize X.
  3. The function should provide the same ranking for a subset of options as it would for that subset within a complete set of options. Adding or removing an option should not affect the ranking of other options.
  4. No preferences are taboo. Any social preference ordering is possible if people have the right individual preferences.
  5. The function must be collective in the sense that it does not simply mimic one person’s preferences.

Seems reasonable, no? Arrow’s proof proceeds by contradiction. He assumes that there are two individuals, three alternatives, and a social welfare function that satisfies the above conditions. These assumptions lead to three consequences:

  1. If both individuals prefer one outcome to another, then the social welfare function prefers it as well.
  2. “[I]f in a given choice, the will of individual 1 prevails against the will of individual 2, then individual 1′s views will certainly prevail if 2 is indifferent or if he agrees with 1.”
  3. If individual 1 prefers X to Y and individual 2 prefers Y to X, then the social welfare function must be indifferent between X and Y.

Now, suppose that individual 1 prefers X to Y to Z and individual 2 prefers Z to X to Y. By consequence 1, the social welfare function prefers X to Y. By consequence 3, the function is indifferent between Y and Z. Since the function prefers X to Y and is indifferent between Y and Z, the function must prefer X to Z. However, also by consequence 3, the function must be indifferent between X and Z. This is a contradiction, which means that one of our assumptions cannot hold. In Arrow’s words:

If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial.

What does this mean? There is no “will of the people,” at least not if that phrase is to encompass what we normally think of as rationality. Rousseau is incoherent. Democracy can be manipulated by agenda control, as Levine and Plott show in a hilarious article in Virginia Law Review.

How can we get around this conclusion? One way is if preferences are unidimensional and single-peaked. If all voters think in terms of a single liberal-to-conservative spectrum and prefer candidates that are closer to some optimum point, then you can no longer demonstrate the contradiction. Another way is if you allow some way of expressing intensity of values (interpersonal comparisons of utility), such as by bidding with dollars, though this may undermine some of Arrow’s conditions.

For discussion: Voter preferences are shockingly unidimensional, are they not? People who favor high taxes tend also to be pro-choice on abortion. What do these have to do with each other? Does this correspondence save democracy from the charge of irrationality? Or is it further evidence of it? Does Arrow’s result explain why everyone is so dissatisfied with the government basically all of the time? In light of Arrow’s result, are some voting systems better than others? Does the fact that collective choice is incoherent mean that collective morality is also incoherent?

Next time, we will discuss Ronald Coase’s 1960 paper The Problem of Social Cost. If Arrow had read Coase, he would not have made the errors that he made on p. 334. See you in the comments!

The Use of Knowledge in Society

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Welcome to the second installment in our series of discussions of the Most Insightful Articles in economics. This post is going up a little later than I had planned, but hopefully you have stuck around. Today we are discussing Friedrich Hayek’s 1945 article The Use of Knowledge in Society.

Whereas Coase invites us to consider (and dismiss) a world without transaction costs, Hayek invites us to consider (and dismiss) a world in which all information is known to a single mind. In this world, Hayek points out, allocating resources in the most rational or efficient way is strictly a math problem, a more complicated version of some of the problems I make my Intermediate Micro students do. “This, however, is emphatically not the economic problem which society faces.” In the real world, information is dispersed, incomplete, and frequently contradictory. How can we use all this dispersed, incomplete, and contradictory information to make the best use of the resources we have?

When we engage in decision-making about resource allocation—whether collectively or individually—we are engaging in what Hayek calls “planning.” This raises two questions. First, how can those who possess some fragments of information communicate them in a useful way to the planner? Second, who should do the planning—one person or many people—and should it be centralized or decentralized? Under what arrangement can we make the best use of all the knowledge that is dispersed in society?

Most of the knowledge that exists in society is not universal, like F=ma. Instead, it is local; in Hayek’s words, “the knowledge of the particular circumstances of time and place.” Everyone knows at least something that no one else knows. For instance, I need a new holder for my EZ Pass because my old one melted in the sun. How likely is it that anyone else would know that? For society to make the best use of its resources, it must develop a method to collect and exploit local knowledge, not just universal knowledge.

It is essential that this method be robust in the sense of being able to withstand constant change. The world is not static. Statistical aggregates hide the innumerable small changes that occur. For instance, if my demand for eggs rises and my neighbor’s demand for eggs decreases by the same amount, my neighborhood’s demand for eggs has not changed. Nevertheless, the optimal allocation of eggs has changed; this suggests that statistical aggregates are not an appropriate basis for allocating resources.

“[T]he economic problem of society is mainly one of rapid adaptation to changes in the particular circumstances of time and place.” To solve the problem, we need some form of decentralization. Decentralized actors need to be able to 1) exploit their local knowledge while 2) making use of some sort of summary of the local knowledge possessed by others that is relevant to their decisions. This summary can strip out a lot of “why” questions. The actor does not need to know why some resource is more or less scarce than before, but he does need to know if it becomes more or less scarce.

The problem is solved by the price system. “[P]rices can act to coördinate the separate actions of different people in the same way as subjective values help the individual to coördinate the parts of his plan.” If there is some new and valuable use for tin, the price of tin will rise and people will economize on tin without even knowing why they are doing it. “The whole acts as one market, not because any of its members survey the whole field, but because their limited individual fields of vision sufficiently overlap so that through many intermediaries the relevant information is communicated to all.”

“We must look at the price system as such a mechanism for communicating information if we want to understand its real function…The most significant fact about this system is the economy of knowledge with which it operates, or how little the individual participants need to know in order to be able to take the right action.” This is not to say that the system operates with 100% efficiency. But it is nevertheless a marvel that changes occur and tens of thousands of people adapt by moving in the right direction, without any orders being issued. “I have deliberately used the word ‘marvel’ to shock the reader out of the complacency with which we often take the working of this mechanism for granted. I am convinced that if it were the result of deliberate human design…this mechanism would have been acclaimed as one of the greatest triumphs of the human mind.”

Hayek was more aware than most intellectuals of the extent and significance of our ignorance, and of the importance of extending the range of human cooperation beyond that which could be imagined by a single mind. The idea of a spontaneous order, that some phenomenon could be the product of human action, but not of human design, has been around since at least Adam Ferguson of the Scottish Enlightenment. It is striking that so many people persist in attributing both omniscience and deliberate design to society. We will discuss something else that people erroneously attribute to society next time when we review Ken Arrow’s 1950 paper, A Difficulty in the Concept of Social Welfare.

Suggestions for discussion: I have quoted extensively from this paper because it is very quotable. What are the best quotations that I have left out? Approximately how many bytes of local knowledge are there? Is it conceivable that a very powerful computer could solve the economic problem society faces? Are there other difficulties beyond the sheer quantity of information? What is it about undesigned phenomena that makes people uneasy? What is the greatest deliberately-designed triumph of the human mind and how does it compare in importance to the discovery of the price system? Is there any value at all to the math problems I make my Intermediate Micro students do? Does Hayek’s way of thinking about prices yield any insight into what happens when relative prices are distorted by taxes and subsidies? I look forward to your comments!

The Nature of the Firm

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Welcome to the first installment of our series of discussions of the Most Insightful Articles in economics. Today we are discussing Ronald Coase’s 1937 article The Nature of the Firm.

Ronald Coase wrote only a handful of academic journal articles—nearly every one is a blockbuster. He won the Nobel Prize in 1991 “for his discovery and clarification of the significance of transaction costs and property rights for the institutional structure and functioning of the economy.” He is still alive at the ripe old age of 99; if you do the math, that means he wrote the article we are discussing today when he was 26. This gives me the sneaking suspicion that I am “behind.”

One useful way of thinking about the market is as a coordinating system. The price mechanism serves as a means for directing the flow of every resource to its highest valued use. Suppose that a hurricane hits New Orleans, and as a result the price of plywood increases. That increase in price performs an important coordinating function. As a Virginia resident, when I observe the price of plywood going up, I am induced to delay my plans to build a shed in my backyard. That is, I conserve plywood. This leaves more plywood available to go to New Orleans, where it is most needed. The price system is impersonal, meaning that I don’t even have to know or care about the people in New Orleans in order to behave in a way that is beneficial to them. We will talk much more about the role of prices in the next installment.

However, the market is only one of two main ways that resources are directed. The other mechanism is command and control. Within firms, the autonomous impersonal coordination of the price system is replaced by a conscious interpersonal coordination mechanism. The boss has to gauge or guess if employees are pulling their weight, and to figure out if there are enough computers and office space and coffee and so on. The whole purpose of a firm is to engage in production without the coordinating assistance of the market mechanism. Why should this be? Why would anyone want to avoid a system that sends resources to their highest valued use?

It must be the case that there are costs intrinsic to using the price system. These “transaction costs” include the cost of discovering what the relevant prices are and the cost of negotiating complete contracts that plan for all contingencies and eliminate opportunism. When an entrepreneur starts a firm, she is making a bet that she can direct resources within the firm with enough efficiency so as to produce at a lower cost than the market could produce. That is, she is betting that she can economize on transaction costs. This, Coase argues, is the raison d’être of a firm.

Coase then asks, “[W]hy, if by organising one can eliminate certain costs and in fact reduce the cost of production, are there any market transactions at all? Why is not all production carried on by one big firm?” There must be some countervailing cost that increases with firm size that makes it uneconomical for firms to continue increasing their “insourcing” forever. The main answer that Coase gives is that it gets harder for the entrepreneur to direct resources as the number of resources increases. At some point, the firm is directing so many resources internally that the cost of directing one more resource is equal to the cost of just relying on the market to direct it, transactions costs and all.

The theory can now be used to discuss what affects firm size. Factors that decrease transaction costs or increase organizing costs will tend to make firms smaller. Factors that do the opposite will tend to make firms larger. One factor that increases transaction costs is taxes on market exchange. If it costs firms extra money in taxes to buy furniture, they may decide to make their own furniture in-house. (For discussion: how does the income tax affect the household’s decision to have a second partner go to work or stay home? Hint: households are firms!) A second factor is technology. As communications technology improves, it becomes cheaper to organize over a wider spatial area, increasing firm size. On the other hand, technology also reduces the cost of using the market, e.g. locating prices, and therefore would tend to reduce firm size.

We can keep going with this. Here are some issues that Coase did not discuss. Another factor is bankruptcy and contract law. The fact that there are default rules for contracts lowers the costs of creating contracts (assuming the law is reasonably efficient). Fewer contingencies need to be specified in advance. This makes the cost of using the market lower, decreasing firm size. Next, consider employment regulations. These tend to make it more expensive to direct resources (at least human resources) internally, and therefore firms will be smaller when there is extensive employment regulation. Finally, what if there is a complete breakdown in law and order? This will tend to increase transaction costs, making markets less attractive. Firms will increase in size, and in fact, humans might revert to a tribal existence (tribes are firms!). Law and order, and markets generally, are what enable us to live our lives in a reasonably individualistic way.

Coase also spends a fair bit of space contrasting his theory with Frank Knight’s theory of the firm. I won’t spend a lot of time on this, but we can discuss it in the comments if people are interested. If you want food for thought on this, how plausible is Knight’s view if there are insurance markets and no transaction costs?

To sum up, using the price system is not free. The fact that there are transaction costs means that people will attempt to limit the number of their transactions to economize on these costs. This implies that they will seek alternative methods of directing resources, which we find in firms. The other method, command and control, does not scale well forever. Therefore, there are natural economic limits to the firm’s size.

I’ve raised a few questions above, but here are a few more. How does Coase’s notion of what it means for a firm to be large or small differ from our usual metrics? What is the role of market discipline (profits and losses) in ensuring that firms do not become inefficiently large? If you were an inventor with strong humanitarian impulses, would you want to invent a technology that lowers the cost of transactions or of organization? In a world with no transaction costs, would there still be unemployment? How does the existence of the concept of morality affect transaction costs?

The discussion is not limited to my questions, of course. Feel free to raise whatever issues in the paper you want to discuss. Our next article will be Friedrich Hayek’s 1945 piece The Use of Knowledge in Society. I will be in Las Vegas at a conference early next week, so our next discussion will not be until the latter part of the week. See you in the comments!

What are the Most Insightful Economics Articles?

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Which economics articles teach us the most about how to think about the world? Over the next few weeks, I plan to write about the articles that I think belong in this group. I am hoping that some readers will want to follow along and discuss the articles in the comments.

Here is what I propose. I will select an article and give anyone who wishes to some time to read it (optional). A few days later, I will write a post in which I give a framing summary and explanation of the article, and perhaps some questions for discussion. I will conclude each post with a link to the next article on the list.

I am shooting for ten articles. I haven’t fully decided on the list yet; suggestions, especially from my economics colleagues, are welcome. I will try to go in chronological order by publication date, though because I have not yet decided on the full list, there may be a little backtracking. The articles I am interested in are not necessarily those with the most citations or the ones that have had the most influence on the profession. I assume no one is interested in Heckman selection. I am looking for articles that provide the greatest insight into the world we live in.

If this sounds like something you’d be interested in, I encourage you to participate. I only ask that you keep the discussion in the comments civil and on topic. If you want to be uncivil, you can always post on your own blog about what an idiot I am. And of course feel free to pass this link around to other people who might be interested.

I will aim the discussion to be at the level of an intelligent and educated general reader with no prior background in economics (trained economists are of course welcome to participate as well). My hope is that this exercise will be helpful to many of you. I believe that studying and discussing these articles is a way to get a lot smarter very quickly. I also hope that by blogging about them, I will organize my own thoughts about them and their importance.

The first article in the series will be Ronald Coase’s 1937 article The Nature of the Firm. See you in a couple days.