Re: Callahan on Axtell: Artifact Origins and Increase

Last month, Gene Callahan brought to my attention an error that is present in Robert Axtell’s paper “Why Agents?” Before I respond to his post, I encourage readers to familiarize themselves with not only this paper, but Axtell’s work and other research representative of the growing agent-based paradigm. While I don’t expect that equilibrium models that employ systems of linear equations will disappear any time soon, agent-based and complexity economics are here to stay. The paradigm will only grow more influential over the next decade or two.

The error itself exists in what appears to be a tangential discussion within Axtell’s paper. He identifies “bugs” that arise in the program as “artifiacts”. These artifacts produce output that typically produce results that are not robust to small parameter changes. Axtell writes,

This architecture, in which very little source code effectively controls a much larger amount of execution code, is the basis for the highly scalable nature of agent-based models. The number of agents or commodities, for instance, are conveniently specified as user-defined constants in the source code or read in from the command line, and thus the scale of the model can be specified at compile or run-time. Typically, no significant rewriting of the code is needed in order to change the scale of the model.

It is also the case that the “small source, large execution code” character of agent computing is partially responsible for the production of artifacts, an important class of systematic problems that can arise in agent models, as alluded to above. When a small amount of code — say a single commodity exchange rule, for example — controls so much other code, then it will sometimes be the case that an idiosyncrasy in the rule code will produce output that one might erroneously take to be a significant result of the model. A common route to phenomena of this type occurs when the agent interaction methods impose some spurious correlation structure on the overall population — for instance, agents are interacting with their neighbors more than with the population overall in what is supposed to be a “soup” or "mean field" interaction model — then an ostensibly systematic result — large price variance, say — is clearly artifactual.8 There is no real solution to this problem, aside from careful programming. One can, however, look for the existence of such artifacts by making many distinct realizations of an agent model, perturbing parameters and rules. When small perturbations in the code produce large changes in the model output, then artifacts may be present. Sometimes, large changes in output are realistic and not signatures of artifacts. For example, imagine that a small change to a threshold parameter makes an agent die earlier than it otherwise would, and therefore induces at first a small change in agent exchange histories (i.e., who trades with who), that over time is magnified into a wholesale change in the networks of agent exchange. Perhaps this is not unrealistic. But when such large scale changes have origins that are unrealistic empirically, then one should be instantly on guard for undiscovered flaws in the source code.

Gene Callahan identified as a causal error in his post,

Rob Axtell, in his 2000 paper "Why agents? On the Varied Motivations for Agent Computing in the Social Sciences," attributes the existence of what he calls "artifacts" (program behavior that is not a part of the model being created, but a byproduct of a coding decision which was intended only to implement the model, but actually did something else as well) "partially" to the fact that, in agent models, a small amount of source code controls a large amount of "execution" code. As an example, he offers a system where millions of agents may be created and which might occupy up to a gigabyte of memory, even though the source code for the program is only hundreds of lines long.

But this explanation cannot be right, because the causal factor he is talking about does not exist. In any reasonable programming language, only the data for each object will be copied as you create multiple instances of a class. The functions in the agent-object are not copied around again and again: they sit in one place where each agent "knows" how to get to them. What causes the huge expansion in memory usage from the program as it sits on disk to the program running in RAM is the large amount of data involved with these millions of agents: each one has to maintain its own state: its goal, its resources, its age: whatever is relevant to the model being executed.

So what we really have is a small amount of code controlling a large amount of data. But that situation exists in all sorts of conventional data-processing applications: A program to email a special promotional offer to everyone in a customer database who has purchased over four items in the last year may control gigabytes of data while consisting of only a few lines of source code. So this fact cannot be the source of any additional frequency of artifacts in agent-based models.

The code itself is not copied. Rather, the same code is used to instantiate some number of agents. Each of these agents has objects of its own. These objects, as opposed to the code itself, occupy memory. So the error here is mostly identified by Gene, but it can be investigated further.

What we have is an increase in the number of interactions which occurs as a result of having numerous agents, as compared to a single program. It just so happens that the objects that are instantiated along with the agent take up space. However, even if they took up no space, the problem of "artifacts" / bugs would exist. The more agents there are, and the more they interact, the more opportunities there are for bugs to arise. The problem is a combinatorial one. All else equal, the increase in the number of agents and their objects grow the behavior space of an ABM program at an increasing rate.

To demonstrate, consider a simple combinatorial problem where we want to find the number of possible permutations (ordering matters). How many ways can a line of 5 people be arranged? The answer: they can be arranged in 5! possible states, 5 * 4 * 3 * 2 * 1 = 120. The problem is simple to think through. If agent 1 stands at the front of the line, the other four agents can be arranged in 4! (= 24) different states. Repeat this process with agents 2 through 5. I could continue to break the problem down iteratively, start with agent 1 in front and 2 second in line. The others could reorganize in 3! (= 6) different states. Replace agent 2 with agents 3, 4, and 5 and now we have 4! different states with agent 1 in front. Replace agent 1 with agents 2, 3, 4, and 5 and, voila, we’ve arrived back at my earliest formulation of the answer. Increase the number of agents to 6, and now the number of possible permutations grows from 120 to 720. Increase to 7 and now there are 5760 possible permutations.

Now imagine growing the number of agents to something in the range of 100,000 or 1,000,000 agents. Let’s say that each of these agents own 10 different objects. If all of these objects can potentially interact with one another due as part of pairwise agent interactions, then the model represents a behavior space that is vast. Within that behavior space is likely a large number of “artifacts” that cannot be detected until runtime.

Axtell is correct that “artifacts” might arise due to emergent patterns not accounted for by the programmer. He mentions one example:

A common route to phenomena of this type occurs when the agent interaction methods impose some spurious correlation structure on the overall population — for instance, agents are interacting with their neighbors more than with the population overall in what is supposed to be a “soup” or "mean field" interaction model — then an ostensibly systematic result — large price variance, say — is clearly artifactual.

Also note that in the first quite, Axtell does recognize that "A common route to phenomena of this type occurs when the agent interaction methods impose some spurious correlation structure on the overall population." He intuitively, even if not explicitly, sees that the problem is combinatorial. 

Axtell is pointing to an effect of a bug in the code. This effect – in this case, a higher than expected rate of local interactions - is what skews the data and may make a spurious result appear to be significant. However, this does not capture the full extent of the problem. The combinatorial growth of interacting agents and the objects associated with them implies that the behavior space is growing at an increasing rate. With every increase in memory, the rate of growth of the behavior space is increasing! But in this analysis, memory is only a stand-in for the objects that occupy it. What Axtell appears to be calling execution code are the objects instantiated by that code. The amount of memory occupied by these objects - as opposed to the growth rate - has no bearing on the combinatorial problem. It is the number of objects that is of interest. These objects, whose content are transformed by the processes associated with them, promote massive growth of the behavior space as population increases. It is the job of the scientist to identify and categorize different types of states and progressions. One of those types is the “artifactual.” 

Prices, Information, and Coordination of Disparate Agents

In the last post, I listed 9 classes of objects that are pertinent to the study of economics. I stopped short of describing all 9 classes. Left are prices, expectations, and entrepreneurship. Each of these deserve their own post. Today I start with investigating prices, their place within economic analysis, and the system that they form.

As I mentioned previously, the price of a good is equal to the thing given up in order to attain it. If I give a dollar to a gas station attendant in exchange for a candy bar, the price that I pay is $1. However, not all prices are denominated in currency. Let’s say that the ladies and gents at a "free hugs" booth decide to start paying to give hugs because they have found zero willing participants at zero price. They set a price of 1 mini candy (you know… those candies that you give out during Halloween and put in the bowl at Christmas). The price paid implies an opportunity cost. We assume that the agent giving the hug expects this strategy to yield an outcome better than the next best outcome that could have been attained by some alternate use of the candy. This next best use may be consumption of the candy or its exchange for something. Or maybe one “hugger” would enjoy throwing out a candy onto the sidewalk just to see a passerby pick it up. This is known as opportunity cost. The agent imagines alternate uses for the object exchanged and places some value on these uses. We cannot know what these exact values are, or if they can even be represented by exact values. All we know is that the huggers prefer to use the candy to pay for a hug from a passerby compared to all other uses recognized by the hugger.

Typically in economics, when the word price is thrown around the author is referring to a market price. I might ask, “What is the price of one share of “Apple” stock?” For an answer, I check the stock price on the financial TV station or on a financial website. There is thought to be one price, at least during trading hours, as the vast majority of trades take place on the exchange. But does this hold for a commodity that can be bought or sold anywhere? Consider a scenario where two gas stations within proximity of one another charge different prices. Can we say that there is a single market price? Clearly these gas stations are charging different prices. How can we say that the law of one price [1] holds? Remember, price may be objectively represented by a value denominated in currency. Notice that the value of currency is not the only price paid by an agent. If he or she prefers to act out of habit, going to the cheaper gas station across the street may be a cost incurred in addition to the nominal price. Or maybe the agent prefers to not check prices. Whatever the reason, you are willing to incur the higher price. This does not disprove the law of one price as there must be some point at which the size of the discrepancy between prices motivates you to go the station with cheaper gas. The perceived cost of switching stations is equal to whatever that difference is to the agent and that perceived cost may not remain constant across time. Or put another way, if the agent is aware of the discrepancy and still shops at the more expensive station, the additional cost of purchasing gas from the apparently less expensive station, as perceived by the agent, is greater than the price discrepancy. This explanation can be made clear by an extreme case. Let’s say that one gas station decides to charge a dollar more than the other gas station across the street. While there may be some buyers that do not switch to the cheaper gas station, enough will switch as to promote a state where the station that charges a higher price lowers it and/or where the gas station charging the lower price will raise it. If neither of these occur, we can expect the station charging a dollar more for gas to go out of business. There are bounds within which notional prices are free to move as a result to subjective interpretations of price. In competitive markets, this range tends to be relatively narrow.

It is by this tendency toward convergence for prices of like goods that a constellation of relative prices can arise. Agents do not need prices to perfectly represent information about market conditions. Rather, price need only approximate market conditions in order for agents to make economic decisions that coalesce with one another. With this standard met, agents can interpret nominal prices of different goods as relative prices. In this way, an agents can compare the price of substitutes for inputs and outputs and make decisions about what products to make and what inputs to use. It is the consumer who provides information to producers concerning whether or not their choice of products to produce and inputs used to produce them were “correct”. Negative feedback – AKA, a growing stock of unsold goods or realized losses – helps the producer to decided whether or not to continue producing a particular good in a particular manner.

In the above case, prices convey information of which producers may have no knowledge. In what is perhaps his best known academic work, “The Use of Knowledge in Society”, Hayek tells a story about the price of tin to this effect:

Fundamentally, in a system in which the knowledge of the relevant facts is dispersed among many people, prices can act to coordinate separate actions of different people in the same way as subjective values help the individual to coordinate the parts of his plan. . . Assume that somewhere in the world a new opportunity for the use of some raw material, say, tin, has arisen, or that one of the sources of supply of tin has been eliminated. It does not matter for our purpose – and it is very significant that it does not matter – which of these two causes has made tin more scarce. All that the users of tin need to know is that some of the tin they consume is not more profitably employed elsewhere and that, in consequence, they must economize on tin. There is no need for the great majority of them even to know where the more urgent need has arisen [emphasis mine], or in favor of what other needs they ought to husband the supply. If only some of them know directly of the new demand, and switch resources over to it, and if the people who are aware of the new gap thus created in turn fill it from still other sources, the effect will rapidly spread throughout the whole economic system and influence not only all the uses of tin, but also its substitutes and the substitutes of these substitutes, the supply of all things made of tin, and their substitutes and so on.; and all this without the great majority of those instrumental in bringing about these substitutions knowing anything at all about the original cause. 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. (1945)

It is by this process that social economies appear to be auto-poetic, or self-organizing. Neither of these is too strong of a term to describe markets where autonomous agents are free to make and enact plans and engage in a process of trial-and-error where they bear the costs – and benefits – of their actions. It is the ability of agents to organize their plans in accordance with current relative prices and expectations of relative prices that allow markets to function. Thus the price system is “not the product of [any single] human design and … the people guided by it usually do not know why they are made to do what they do (Hayek 1945).” Of course, not all social institutions can be defined within this paradigm, nor do markets exist in isolation of political influence. These are interesting and important arrangements to analyze, but they are outside of the purview of a pure analysis of the price system.

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[1] The “law of one price” is a concept that falls out of classical economics where, in the long-run, price discrepancies for like goods in different markets will be eliminated by arbitrageurs who buy low and sell high. The profit motive guides the market toward a single price, though we cannot say what that exact price is any given moment. In the modern world, financial markets tend to quicken this process.

Formulating a Framework for Economic Analysis (with Agent-based Modeling in Mind)

What is economics? In his Principles of Economics, Carl Menger tells us that his goal is to “reduce the complex phenomena of human economic activity to the simplest elements that can still be subjected to accurate observation, to apply to these elements the measure corresponding to their nature, and constantly adhering to this measure, to investigate the manner in which the more complex economic phenomena evolve from their elements according to definite principles (46-7).” Economics is about the relationships that arise between elements, and those new elements that come into existence within the market order. These cannot be studied with Cartesian causation, with what Menger referred to as “a natural-scientific orientation,” if the goal of the study is to understand the economic processes and complex relationships of diverse economic elements. Emphasis must be on structure and process as opposed to simple input-outputs processes defined by parameters. This requires greater emphasis on the elements of economic analysis than is embodied by the modern paradigm.

What are the objects of study in economics? Before, we considered the example of a husband pleasing his wife within a general economic framework, but we did not identify systematically the objects of interest to the study of economics. These include:

1. Agents
2. Preferences
3. Goods
4. Capital Structure
5. Money
6. Property Rights
7. Prices
8. Expectations
9. Entrepreneurship

I will review these one at a time.

1.  Agents

The economy is comprised of real life human beings. These agents are ecologically rational, meaning they do not reason only by means of internal objects. They relate their thought processes to the webs of objects that comprise their reality (Gigerenzer 2008). While agents can adopt technically advanced methods of decision making, most decisions are made using heuristics – rules of thumb. Those that reduce decision making down to the attributes of one or a few elements in their environment have been shown to be efficient (Gigerenzer and Goldstein 1996). The common practice in economics has been to assume that agents have perfect information. This assumes away the process that economics, at its core, seeks to analyze.

Marshall referred to supply and demand as a pair of scissors. One blade requires the other for successful analysis. Herbert Simon and Gerd Gigerenzer suggest that a new pair of scissors to motivate analysis:

The structure of natural environments, however, is ecological rather than logical. In Simon’s words: “Human rational behavior is shaped by a scissors whose two blades are the structure of task environments and the computational capabilities of the actor [emphasis mine]” (Simon, 1990: 7). Just as one cannot understand how scissors cut by looking only at one blade, one will not understand human behavior by studying either cognition or the environment alone. (Gigerenzer 2008, 7)

Agents offload computational work by using objects that they have identified from the environment. This is why doctors don’t understand how to apply Bayesian statistics when information is couched in statistical jargon and formalization, but can apply simple math to the structures they already use to interpret reality, and thereby arrive at a more accurate survey of the data. The information that agents access is typically not purely abstract. The habit of academia is to assume that all reasoning must take place in formless models. This has been true in economics as a consequence of the growth of rational expectations as the dominant mode of analysis.

The problem here discussed is well represented by analysis of the real world. Gerd Gigerenzer notes:

When physicians try to draw a conclusion from conditional probabilities, their minds tend to cloud over (chap. 9). What can be done to correct this? From an internalist perspective, one might recommend training physicians how to insert the probabilities into Bayes’s rule. Yet this proposal is doomed to failure. When we taught students statistics in this way, their performance dropped by 50 percent just one week after they successfully passed the exam and continued to fade away week by week (Sedlmeier & Gigerenzer, 2001). Moreover, the chance of convincing physicians to take a statistics course in the first place is almost nil; most have no time, little motivation, or believe they are incurably innumerate. Are innumerate physicians inevitable? No. In the ecological view, thinking does not happen simply in the mind, but in interaction between the mind and its environment. This opens up a second more efficient way to solve the problem: to change the environment. The relevant part of the environment is the representation of the information, because the representation does part of the Bayesian computation [emphasis mine].”(17)

This efficient form of computation – let’s call it ecological Bayesian computation – has no analog in typical models. Luckily, an agent-based computational framework allows for this sort of representation and decision making. This paradigm of analysis has an obvious medium for modeling!

2. Preferences

In our model of the economy, preferences are the ultimate given. I (implicitly) spent enough time last post describing preferences. Preferences are observed directly from the actions of agents. If an agent chooses to take a particular action, it is because she believes the results of the action, given its expected cost, to be better than the other options she can imagine. Traditional models abstract away from decision-making processes and make decisions dependent upon expected utility. This measure is typically treated like a cardinal value, which might be useful for conveying the nature of economic action. From the perspective of “pure” theory, preferences are ranked ordinally, not cardinally. We can only observe what an agent does. If in a model, an agent’s preferences are assigned utility values, the states that arise from the interaction of the agent with her environment are the objects of interest to the study of preferences. Any sort of optimization of utility derived from calculus is a convenient tool for arriving at ordered preferences. Cardinal utility has no bearing on these real life processes.

3. Goods

Carl Menger clearly defines a good in his Principles. He writes:

Things that can be placed in a causal connection with the satisfaction of human needs we term useful things. If, however, we both recognize this causal connection, and have the power actually to direct the useful things to the satisfaction of our needs we call them goods (52).

A thing is a good if the following prerequisites are met:

1.     A human need

2.     Such properties as render the thing capable of being brought into a causal connection with the satisfaction of this need.

3.     Human knowledge of this causal connection.

4.     Command of the thing sufficient to direct it to the satisfaction of the need. (52)

Not only must these prerequisite be met, but they must also appear to be achievable by the agent in question (Note criteria from #2).

A thing ­­loses its good character if:

1.     Owing to a change in human needs, the particular needs disappear that the thing is capable of satisfying

2.     Whenever the capacity of the thing to be placed in a causal connection with the satisfaction of human needs is lost as the result of a change in its own properties

3.     If knowledge of the causal connection between the thing and the satisfaction of human needs disappears

4.     If men lose command of it so completely that they can no longer apply it directly to the satisfaction of their needs and have no means of reestablishing their power to do so. (52-53)

But a good that loses its goods character may still be treated like a good:

1.     When attributes, and therefore capacities, are erroneously ascribed to things that do not really possess them

2.     When non-existent human needs are mistakenly assumed existent. (53)

Last time, I described a good with a simple story about a husband seeking to please his wife. While a story is a nice way to remember a concept, it is important for the sake of study this more general definition. Remember that a good can only exist if some agent expects that attainment of the good will improve his position. Thus, the definition and type of good requires context.

4. Capital Structure

a.       Orders

Capital structure is a formal description of the arrangement of economic goods. A good can be described by its order: its position in the process of production. If a good is employed to produce a higher order good (say machinery), the good is itself a higher order good. But if that same good is consumed with expectation that consumption will improve the welfare of the agent consuming it, then the good is a first order good. Thus, there is nothing intrinsic about the order of a good. It is a description relative position in the structure of production.

5. Money

Money serves several roles. It is:

 1. A medium of exchange.

 2. A store of value.

 3. A common unit of account.

a.       A standard of deferred payment.

Historically, money has arisen when agents in a community begin to accept one a small number of commodities as a medium of exchange. Consider the first oat farmer who realized that he was not only growing food, but money! Under such a standard, exchanges are measured in terms of volume of wheat. Oats have a finite lifespan, which does not serve well for functioning as a store of value. Eventually, a money that is durable and easily divisible will be commonly accepted.

6.  Property Rights

Assumed in our analysis is an organization of ownership described as private property. Menger describes property rights as:

              

The entire sum of goods at an economizing individual’s command for the satisfaction of his needs, we call his property. His property is not, however, an arbitrarily combined quantity of goods, but a direct reflection of his needs, an integrated whole, no essential part of which can be diminished or increased without affecting realization of the end it serves.” (76)

In our model of the economy, as well as in real life, agents are empowered by their ownership of goods. When an agent owns a good, that good is under his control. Thus, property ownership provides a social space for a property owner to experiment with the allocation of goods at his disposal. When property rights are considered alongside the existence of money and money prices, the scheme serves to account for all of society’s available resources, assuming that property rights are secure.

Property rights, however, are not perennial. While ownership may be a natural habit of humankind, formal property rights, guarded by the legitimated use of violence – historically from the state – must be developed. Security of property rights has fluctuated overtime, and has seen its greatest development since the Glorious Revolution with the ascension of a government that served a broader array of interests than those of the aristocracy (North, Wallace, and Weingast 2012). This is not to suggest that property rights did not exist elsewhere, or that they were perfected at that time. Rather, this era marks a turning point in the representation of group interests in the edifice of government. It is no coincidence that since that time, society has flourished in a manner never before observed in history. It is also no coincidence that this move toward well-defined property rights has tended, even if imperfectly, to shift responsibility of ownership to those who are best able to maintain valued resources.

Thus, we have explored a large part of the general economic framework. In future posts, I will spend more time investigating prices, expectations, and entrepreneurship as each of these elements merit thorough description.

Economic Action: Subjectivity, Value, and the Price System

Unlike in other fields of study, in economics we do not study objective reality. We study agents functioning subjectively within a given objective reality. As Kant argued in his Critique of Pure Reason, “Let us then make the experiment whether we may not be more successful in metaphysics, if we assume that the objects must conform to our cognition (13).” Whether in search of a metaphysic, or a daily meal, humans do not experience the world as it actually is. We interpret it through the black box of cognition. The manner in which an agent employs reason will manifests innumerable issues of interpretation of the world and its objects that the agent confronts daily. It is only by interpretation of reality, no matter how imperfect that interpretation, that agents can act with expectation of influencing that reality.

               

So we arrive at the subject of economics: man in all his fallibility. The amazing fact is that, even within mundane limitations of cognition, humans are able to extract enough information to form reasonably accurate expectations of the future. These expectations, in the least, allow them to survive, and when they are well formed, allow persons and the communities they form to prosper. How is it that, in a world of over 7 billion conscious actors, disorder is not the primary result? Why should we expect an orderly social economy to emerge?

               

Here, we must seek the motivations of men and women in their most general form: means and ends. Humans, perceive the world in its present state. They choose actions based upon their interpretation of the data of the world. Action is chosen with expectation of attaining some end state. Whether this state is to appear immediately, or it is to arrive at some point in the future is left to the discretion of the acting agent. Consider a husband he seeks to please his wife. He might plan a surprise dinner in effort to romance his wife. The expectation being that he and she will feel closer to one another than if the dinner was not prepared and enjoyed together.

               

Of course, the creation and implementation of a plan do not guarantee any degree of success. The husband mentioned above might be too selfish to plan such an event. Or his wife might not like romantic dinners. Beforehand, and the husband will employ his knowledge so that future actions pleases his wife. Ex ante, a plan is made. Only ex post – after the fact – can the husband judge whether or not he took correct action. If he is not pleased the result of the dinner, he can adjust his actions in the future. Still, this process of trial and error does not guarantee that the husband will correct his actions. If he is unable to please his wife, whether for reason of her being unpleasable or him being incompetent, she may elect to leave him, resulting in the ultimate failure if his goal is for her to be pleased with the relationship.

               

In the above example, a few descriptive terms will help to convey the point. The husband seeks an end which we identify as a good. For the sake of exposition, let’s say that he values his wife’s companionship. Or that he places a high degree of importance on maintaining a pleasant, loving relationship with his wife where both partners feel assured of each other’s passion and commitment. This thing, no matter how intangible, is a good. In its final state of being experienced, it is a good of the first order. The husband must find means to secure this good. The dinner itself, if viewed as a means to that end, is a good of higher order. Of course, one might also consider the dinner as part of the end, in which case we can abstract away from it and call the plan for dinner a good of higher order. Planning the dinner is itself a good because the husband expects that it will help him to achieve his desired end state. From this light, we can see that the dinner acquires value that is derived from the husband’s desire to be part of a fulfilling relationship, his ultimate end.

               

Value, always and everywhere, is an outgrowth of human desire. If a woman desires some object or end, she values it. In the tumult of desire, something must often be sacrificed in order for a particular end to be achieved. That thing sacrificed in exchange for the desired end state is the price paid for the end state. The price paid is not to be confused with the value of the object. Ideally, a woman exchanges an object that she values less than her desired end. When this is done successfully, she has attained a profit. The state achieved is valued more greatly than the state that was sacrificed. This does not always have to be the case. Again, the discrepancy between ex ante and ex post arises. The intended end state is not always the realized end state. It is possible that the state arrived at is less pleasant for the agent than expected. In such a case, the profit is smaller than expected. If the state is perceived as being worse than the previous state, this is considered a loss. Notice, that this definition is entirely subjective. It is possible that the pessimist finds himself facing incessant loss. It is not for the economist to argue that the pessimist is perceiving incorrectly and has actually earned a profit. Welfare improvement, like value, exists in the mind of the agent with respect to her reality.

               

Agent valuations, by the actions of those agents, eventually lead to something approaching market prices. An individual price is what an agent gives up for a transaction. Over time, prices tend to converge toward a narrow range of prices (Gintis 2005; Axtell and Epstein 1996). These prices reflect scarcities perceived within the economic system by at least some agents. Three situations are possible. 1) The available quantity of a good or service are insufficient to meet the quantity demanded at current prices, 2) the available quantity of a good or service are exactly equal to the quantity demanded at given prices, and 3) the available quantity of a good or service is greater than the quantity demanded at given prices. In the first case, the narrow range of prices will tend to increase. Otherwise, suppliers will face a situation where they cannot meet all consumer demands at the given price. In the second case, the corridor of prices will tend not to change. Finally, in the third situation, suppliers will find themselves with excess supplies of goods. In order to alleviate the excess, prices must tend to fall.

               

Consider the following example:

When there is a hurricane that causes power to fail and demand for ice rises, one of two things can happen. The stores and gas stations can raise the price of a bag of ice or else they will soon find that they have sold all available ice. Is the price increase bad? Economics cannot answer that question. However, if the price of ice is too high, the inventories at the store will fail to clear. On the other hand, if price rise sufficiently to prevent a shortage, ice will go to the most willing buyers. You might ask, doesn’t this only benefit the rich? While those who are relatively more wealthy can more easily purchase the ice than those who are not wealthy, anyone who is willing and able to pay the temporarily elevated price can assume ownership of the ice. The increase in price will encourage only those who need ice immediately to purchase it. Furthermore, an elevated price will encourage ice producers to send their ice to the stricken area, thus increasing the quantity available. The increase in the available quantity of ice will help alleviate what would otherwise be a shortage of ice.

In sum, humans experience the world subjectively. This subjective experience includes agent values and their evaluation of means toward attaining more highly valued end states. These values are reflected in the prices that agents pay in order to attain those end states. Within a competitive market, there is a tendency for prices to become constrained to a relatively narrow corridor. Thus, something approaching a market price of a good or service emerges and helps to coordinate resources toward uses valued relatively more highly.

*Late note: I draw the form of this lecture largely from Mises's "First Analysis of the Category of Action" in Human Action.

"I, Pencil", Complexity, and Economic Coordination

How is a pencil created? This question was posited by Leonard Read in his popular story, “I, Pencil”. A pencil is a relatively simple product – relatively meaning, “in comparison to other products.” Still, it would be difficult for any one person to oversee the entire process of producing a pencil. Where does the wood for the pencil come from? How is it processed? How do the lumberjacks acquire sustenance? Where does the graphite lead come from? How is it processed? Who makes the lacquer? Where does the rubber for the eraser come from? Who brings all of these elements together? While it may seem like an obvious process, the problem of creating a pencil is a foray into the profound world of economic complexity.

How might we conceive of complexity in the economy? Economist Bryan Arthur describes the complexity paradigm as an accounting of continual emergence in an economy as plans of agents are constantly upset and readjusted (2013). Compare this to the equilibrium paradigm where agents have static preferences, only interact through price and quantity vectors, and do not affect one another even in the process of altering one’s own array of commodity holdings. The latter view is nonsense. It is clear that, if I acquire a particular good and other agents desire that good, that they cannot have the same good. With fungible – essentially identical – goods, this is not so obvious. Instead, consider a house that is for sale. If I and another person both desire the house, we will both have to guess at the bid price that will secure the house. One of us will earn claim to the house with a high bid, the other will not. In a world of scarcity, agents constantly face this sort of problem.

            

The problem does not stop with wealth allocation. If this was the case, perhaps the economy could be “solved” by computer programs that can emulate human preferences as Oscar Lange had hoped, though I doubt that this solution is workable. Beyond the problem of allocation is the abstraction that is necessary for individuals to engage in trade. What is necessary? Property rights. A common medium of exchange (money). Legal and accounting systems. Communication between parties. Can you think of any more? What do all of these institutions have in common? Before a trade can occur, individuals must develop the expectation that a trade can occur. Why should I, party A, expect that party B will want to trade with me, or that they even can? There is no reason to expect this a priori, but somehow, humans successfully engage in trades every day. What enables this? We must consider how institutions develop.

If I were to drive on the left side of the road in Fairfax, VA,  I might receive more than a few obtuse looks from oncoming drivers. I will probably wreck my vehicle. In the United States, drivers have developed a habit of driving on the right side of the road, a habit that has been ingrained to the point of becoming law. In the same way, if I attempted to make purchases in Chinese yuan rather than American dollars, most vendors would likely turn away my business. Why? While dollars are legal tender within the United States, dollars were originally accepted as currency because gold and silver were commonly accepted media of exchange. Dollars (the word is actually derived from the German Thaler) are simply a measure of a particular amount of gold (~1/20 of an ounce). The common measure, formally adopted in the constitution, was consistent with the practices and expectations of the day. Ever since, Americans have used dollars to engage in commerce. So far, agents in the U.S. have continued to successfully integrate the exchange of dollars into their expectations. I could go on with examples, but I presume the reader understands the general argument: successful interaction between agents requires coordination that is only possible with a sufficiently high level of mutually compatible expectations. While some types of expectations help guide agents toward mutually beneficial interactions, other expectations are constantly upset. We think of upset expectations as "loss" that occurs within a system of profit and loss.

               

This brings us back to the question, how is a pencil created? How is it that loggers are fed and have access to coffee? Where do their saws come from? Where does the lacquer come from? Who makes the strips of metal that hold the eraser and connect it to the pencil? In the most basic sense, prices help coordinate this activity. Each agent having a finite budget must choose what he will and will not consume. He must plan accordingly so that his flow of income at least offsets expenditures. Agents all follow some form of this rule, and must change their approach if the rule is violated. Otherwise, they will go bankrupt.

We can imagine firms as forming a network that is the structure of production. Each node in the network – structure of production – employs are particular dollar value of resources. In order to be maintained, the structure of production must contain nodes whose revenues exceed their expenditures. This picture can be nuanced further by discounting revenue with respect the time period that resources are held. While this is not necessary in the short-run, the long-run tendency will be for the structure of production to lose any nodes/firms that are not at least earning the average (market) rate of return. This implicitly accounts for the cost of holding an asset. So we have a simple rule that organizes production without a single overseer. TR => TC. Firms do not have the privilege of attempting to guarantee that MR => MC except in discrete periods where they reevaluate their actions at the end of each period. A firm must choose a strategy for production and reevaluate at some later date (Alchian and Demsetz, 1972). At the end of each period, a firm can continue employing its previous strategy, revise its plans, or exit the pool of competing firms. We can extend this logic to labor as well. A laborer will compare the costs incurred for work with the revenue earned from working. If she can earn a greater wage elsewhere, she has incentive to change positions, though the change in position is not guaranteed for any individual agent.

In short, common expectations that facilitate agent interaction provide a medium by which production and exchange can occur. With common expectations regarding interactions sufficiently realized, profit and loss guide agents in the system. Those who have foresight will quickly adjust to changing agent preferences, technologies, and flows of revenue and capital in order to increase the likelihood of earning a profit. Those who don't will likely incur economic losses. The production of the pencil follows this general process. The firm that processes the timber, like the firm that creates rubber erasers or that produces yellow paint, will continue to produce as long as revenues remain sufficiently high. As long as entrepreneurs find a way to profit from each step of production, they will, in piecemeal fashion, successfully coordinate the resources and labor necessary to produce the final good that is a pencil.