Tuesday, February 7, 2017

A brief theory of goods and prices

Economics is the study human action in light of a budget constraint. It observes action in terms of means and ends. The agent perceives her environment and is able to imagine how she may acquire some end. We assume that the agent values any end that she seeks to realize. Traditionally, this valuation reflects utility that the agent expects to receive. By hypothesizing that the agent measures value in terms of homogeneous units of utility, we have been able to employ the metaphor of calculus to understand rationality in the economic system. No such units exist in reality. Rather, the agent ranks ends in light of the magnitude of desire, which reflects the benefit that the agents expects to receive from the good in light of its cost. Monetary prices, however, reinforce the metaphor of an optimizing calculus as agents are forced to compare valuations of goods by allocating wealth in terms of monetary prices.

We observe action by agents who are attempting to realize states that they prefer more over those they prefer less. Those are state-goods. State-goods include goods that are discrete objects and functions. If I decide to join a friend for an early morning coffee, I have acted to attain a state-good. I forgo spending the morning in bed as well as the monetary cost of coffee and transportation.

All valuations occur in the present. If I act to attain a candy bar, the candy bar is a good as I attain it. I assume that I am be better off with the candy bar than without it. It is possible that the candy bar will be a link in a long chain of consumption that degrades my health, but in the moment of action, I choose the candy bar who utility from consumption is realized for me in the short term over good health that I would receive in the long term if I choose to abstain from these habits.

Goods can also be functions or, in other words, a service or a process. Some men will pay to talk to a woman on the phone who is a complete stranger simply to alleviate their loneliness. They have paid for a good that exists only at the time of consumption. Others pay significant amounts of money to play videogames and may even buy artifacts in the game that have no existence outside of the game. Others will pay for characters in the game that have been matured by another player. Still others, when able, will pay for a surrogate mother (Kuchar 2016). All of these are things that the consumer prefers over other options that they might otherwise choose.

Agent preferences for goods comprise an ordering. At any moment, the agent must choose one good over another. When he receives his pay for the week, he must choose which food to buy. Over the course of a year he knows that he must purchase some new clothes and determine which he shall purchase. He must choose a means of transportation to facilitate other actions. Ludwig von Mises argues that these choices evidence a preference ordering. Only action can evidence preferences. Ordering is itself a challenge. On a week to week basis, a typical preference may include food and energy. On a month to month basis, we may add housing to the list. On a yearly basis clothes and vehicle repairs. Those goods that are not typically purchased in a shorter period must be accounted for by savings or debt. It is in this sense that we think of an agent’s planned expenditures. They can only purchase goods for which they have the wealth necessary to acquire them.

Concepts from programming languages can inform our modeling of the agent. We may create an agent in a program who has a list of goods that he purchases every day. Another list of goods that he purchases every week. Another that he purchases every month and so on. The agent could systematically purchase certain goods at particular times during each cycle. Or perhaps there is a 1 in 30 chance, for example, that the agent buys a good on his monthly list on any given day. Any goods not purchased on a given day but purchased at a later point exist either in the form of savings or future income, that latter of which includes loans.

These economic goods are all subject to scarcity. That is, not everyone who wants to use them is able to use them. A standard example of a non-economic (free) good is air. While it is true that air is available to anyone who would like to take a breath, the quality of air will be priced into land values much as parking that is supposedly free is priced into the value of commercial real estate (Demsetz 1964). Air is free to anyone who is willing to suffer the cost of living without a claim to a warm bed, but for others, free goods become an attribute of value attached to the other goods for which they pay, as we observe in a theory of hedonic pricing.

Property, ownership, and prices
In order to deal with scarcity, some form of ownership must exist. An economic good require the assignment of right of use over it. An agent’s scope of action is delimited by her property rights. The extent of her property rights will determine her preferred course of action. How long can she expect to control a piece of property? Can she sell the property? What are legitimate uses of the property? Any economic system must define the possible space of terms of ownership if any order is to arise at all in the economic system. If they are not already known, they are discovered through a process of trial error in the legal system.

In absence of property rights allocated to an individual, the political structure governs the use of resources. In this case, ownership is nominally in the hands of the state or some other political apparatus and practically shared by bureaucrats and managers. The value they can extract from this ownership is a rent. A man who manages farmland for the state may allocate use to an agent who will later reciprocate the manager’s actions. Systems that disallow for personal ownership make planning for use of property more difficult. One cannot be certain whether he will have access to property and revenues generated from it in year or decade’s time. Rather, personal relationships centered around power become the dominant mode of economic planning for individuals. These relationships are not subject to contract, but rather the continuance of goodwill which is itself dependent upon incentives embedded in the economic system. They fall under the category of reciprocal relationships, which economists so often disregard in their analysis but which are integral to any description of institutions.

Under a system of private property, agents are able to make better use of their resources. Owners of property are allowed to collect revenue from some use or sale of the property. This alienability of property rights is fundamental in the formation of expectations, which include market prices that reflect the value of the land according to its estimation of its most profitable use. If the owner is allowed to sell the land, buyers will only be willing to buy the land if it is offered at a price that is lower than the value they expect to derive from its purchase. Competition among buyers will tend to move prices more quickly toward the value given existing economic conditions. If I am a landowner who is not generating the highest possible value from the use of my property, I have incentive to sell it for the value it will fetch in the market. If I so value the land that I am willing to offer it for sale, I value the proceeds more greatly than I value maintaining control over the particular asset.

Under a system of alienable property rights and competition, prices play a fundamental role in communicating to users and potential users the scarcity of a good in light of the cost of the good’s supply. By cost we refer to the value of the opportunity cost of the good’s use. If the current owner of a good derives value from the good that is higher than the monetary value of the next best use, we expect that the current owner will not relinquish control. It is possible that the current use actually generates less revenue than the next most valuable use. The owner could be made to have greater material wealth as valued by the market – other men and women. If he fails to sell it at this price, then he values his ownership and use of it more than the extra revenue he would receive by the property’s sale.

Prices operate in a fractal manner. A person may be willing to pay a certain price for a good. That person offers some amount and is successful in purchasing the good. If the seller notices that buyers are usually willing to pay prices that are relatively higher than he had been selling, he may increase his asking price. If he has correctly sensed that consumers are willing to pay a higher price, he will earn higher revenues for his sale. If consumers are not willing to pay a higher price, then the entrepreneur will come to regret his decision. Assuming that he has not raised price due to an increase in costs, he earns a profit. This increase in price will encourage the producer to produce more than he had before at the lower price. He and others like him will provide a greater quantity of the product to market, producing to the extent that the producers expect will be profitable.

Understanding prices with supply and demand curves
A price may rise for two reasons and only two reasons. Either, there has been an increase in demand for the product, as in the case of the discussion above. Price may also increase if the cost of supply increases. This may occur if the price of an input for the goods production increases.

A rise in price of a good systematically leads to a decrease in the quantity consumed. If the government implements a 5% tax on oil revenues in effort to reduce consumption of oil, it will likely be successful in the goal as less oil will be produced in the area subject to the tax. Similarly, if the price of oils falls as a result of the introduction of cost reducing technology, more oil will be consumed.

To say that there has been an increase in demand (Figure 1) is to say that there is an increase in the consumer’s willingness to pay for a product. Likewise, a drop in demand is a lowering of a consumer’s willingness to pay. As sentiment of consumers tend to move together, on average, we often refer to an increase in demand in the market for the good. When smart phones first became available, not everybody was interested in owning one. The value to early users was likely novelty and status, in addition to convenience. But as the use of this technology spread, those who lacked the ability to be more accessible found advantage in using this technology to communicate with friends, family, and coworkers. Utility gained from the use of these phones increased due to a network effect, and demand thus increased (Figure 3).

In the case of supply, we refer to movements in the price that suppliers are willing to accept for sale of a good. In a competitive market, this price tends toward the cost of provision, as the lowest cost suppliers will be able to undercut less efficient providers of a good. Competition in an environment with relatively free flow of information will tend to remove suppliers who fail to adopt cost saving technologies adopted by the most innovative competitors. Producers who decided that they will only provide landline phones when cell phones first came into use are likely struggling if they have managed to survive the last decade. The cost of supply may fall, and therefor the supply increase (Figure 2), due to an improvement of conditions. For example, if an area occupied by corn farmers becomes more rainy, farmers will be able to produce more corn at the same cost.

Figure 1

Figure 2

To better understand supply and demand, we employ supply and demand curves. We say that demand curves slope downward and supply curves slope upward. As the price of a good falls relative to other goods, consumers are willing to purchase more of the good. We explain this phenomenon in two ways. Agents always have a limited budget constraint. A decision to purchase one good is necessarily a decision to go without another good. Therefore, as the price of a good rises, our agent’s real income falls. Of course it is possible that a single agent will always buy a certain good if the price is not too high. At some point, the quantity the agent is capable of purchasing may fall to zero if the price rises too high. Acting in light of a budget constraint, agents must choose to purchases goods that they believe will provide more value to them, as opposed to less. This is a necessary condition for the downward sloping demand curve. The agent will eventually reach a point of consumption where an increase in consumption of the desired good will be accompanied by relatively less utility with each unit consumed. This is the principle of decreasing marginal utility. As an agent’s budget constraint shrinks, or in other words as the relative price expenditure increases, those goods that provide relatively less utility per dollar spent will be forgone for those that provide more.

Supply curves are upward sloping. This is derived from the fundamental concepts of opportunity cost and action. Tautologically, action attempts to create the greatest value for the agent. Agents take action that will bring him to a state of being that he prefers over other possible states. This means that, given the agent’s wealth, he will attempt to trade things that are less valuable for those that are more valuable. Likewise, production of goods come at some cost. The highest cost producers tend to produce at the market price. If consumer demand for a good increases, then the price consumers are willing to pay increases. Higher cost suppliers can therefore enter the market profitably.

Figure 3

Figure 4

We assume that supply and demand are independent of one another, but it is possible to show their interaction via the price mechanism. That is, it is possible that demand affects supply over time. Much modern technology has shown this pattern. Smartphones, which were relatively expensive when they were first introduced have proliferated in industry and can be purchased for relatively cheap, so long as the phone desired is not the newest and fastest model available (Figure 4). We see a general description of this phenomenon with Moore’s law: the speed of processors tends to double every one to two years (Figure 5).[1] Thus, we increasing processor speeds and a continual fall in the price of processing power and memory for a computer. Producers respond to technological demand from business who are willing to pay a high price for the fastest and best functioning computers. These businesses must remain competitive or else be removed from the market through bankruptcy. The same principle holds for tech savvy consumers who find value in using the latest technology. Demand from these agents push up the price of new technology so as to make innovation profitable and thus incentivize reduction in the cost for a unit of memory or processing power.

Figure 5

The Law of One Price
Movement toward an equilibrium price in a market is implied by the principle of human action. Humans act to move the world toward a state they prefer. They do this subject to a budget constraint, which represents the resource at their disposal. From this we surmise that if there are gains from trade potentiated by discrepancies between prices of some like goods, these discrepancies will be offset so long as they are profitable. We call the act of exploiting gains that arise from price discrepancies, arbitrage.

If the price of an ounce of gold in England is $1500 and the price of an ounce of gold the U.S. is $1505, there exist an opportunity to profit by buying gold from England and selling it in the United States. If the cost of buying an ounce of gold in the U.S. and selling it in England is less than five dollars, we expect that the final price in either country will lie somewhere between $1500 and $1505. If the cost of buying and selling and ounce of gold is zero dollars, then we expect that both countries will reach exactly the same price.

A similar process occurs when shares are bought on an exchange, however, a layer of complexity is added. Imagine that instead of the price of an ounce of gold, we observe the price of a share of gold worth one ounce from a gold exchange trade fund (ETF) is worth $1505 in the U.S. and that a share in Britain is worth $1500. The shares from Britain cannot be bought in the United States, however, investors will shift demand instead of moving supply. Those invested in the ETF in the U.S. will sell shares and can reinvest them in Britain. Demand for shares of the U.S. based ETF falls and demand for the ETF based in Britain rises.

There are cases where the law of one price appears to be violated, however, this is always due either to transaction costs or subjective valuations of acquiring a good. Consider two apartments that are identical in every way except location. If the apartment in New York is worth four times the value of the price in Omaha, it is not because the law of one price has been violated. The goods are commonly referred to as being non-tradable. One good cannot be used for the same purpose of another. Not only are transportation costs especially high for real estate, the conditions that exist in one area, including scarcity, cannot be transported to another area.

There also exists discrepancies between observed prices. A gas station on one street corner may charge a higher price than one on the opposite corner and still not lose customers. Often, this may occur because the price discrepancy is small and drivers are willing to pay this cost in order to stay in the comfortable zone delineated by their habits. But if the price of gas at one station increases high enough, its profits will shrink as drivers choose to purchase gas at the station across the street.

The profit mechanism, driven by the desire of human agents to improve the state of the world that they inherit – most patently when the choice is between having more or having less of something for the same cost – drives the market process. This drive when in operation in a competitive environment at least approximately subject to the rule of law promotes the convergence of expectations, allowing for a high level of coordination where plans of economic actors come to fit together. This is Adam Smith’s invisible hand and what Daniel Klein refers to as concatenate coordination.

Good – An object or state toward which an agent attributes positive value.

Scarcity – A state in which an agent must choose between ends due to there being limited quantities of goods desired.

Opportunity cost – The next best use of a good or action. In a market, agents are able to measure the value of an opportunity cost in terms of a currency unity.

Economic good – A good that can that is subject to scarcity and that can be bought and sold. Economic goods are sold for a positive price.

Price – That which is given up by an agent in exchange for something that he believes is more valuable.

Monetary prices – Prices denominated in a currency. An agent must give up an amount of currency equal to the monetary price in order to attain a good desired.

Human action – Action by a man or woman is always aimed at replacing an incumbent future state with an expected state that the agent values more highly.

Property rights – Property rights serve to legitimate ownership of an object and delineate the use that is allowed by such ownership. Rights over a property may be divided, such as the case where ownership of a piece of land is maintained by one owner and the rights to minerals beneath the property are sold to another.

Preference ordering – At any given time, an agent prefers to spend his wealth on some goods as compared to others. Those goods that an agent chooses to purchase during a finite span of time are represent those goods toward which he attributes the greatest value.

Budget constraint – An agent has only a finite amount of wealth. The value of this wealth, whether it exists in currency or assets that may be sold, represents the agent’s budget constraint.

Demand – An agent’s willingness (and ability) to pay for some good represents his demand for the good. If the agent experiences diminishing marginal utility from consumption of the good, the price he is willing to pay for each addition unit of the good falls.

Supply – Production of a good always implies opportunity cost. The value of opportunity cost tends to increase with the quantity of the good produced once efficiency increases from mass production have been exhausted.

Endogenous – As being generated within a model. If an increase in demand for a good raises its price such that it promotes new investment in cost reducing technology, the increase in supply that results is an endogenous increase in supply.

Law of one price – The observation that the price of like goods tend toward equality in light of transaction costs.

Expectations – Predictions of agents concerning the future. Expectations is a broad category that includes both price expectations – predictions of future price – along with plans and strategies that agents use to adapt to a changing environment, and institutions whose logic help coordinate agent interaction and plan execution.

Invisible hand – The observed tendency for competitive markets to make efficient use of resources and promote the dovetailing of plans acted on by disparate actors.

[1] Moore's law refers to an observation made by Intel co-founder Gordon Moore in 1965. He noticed that the number of transistors per square inch on integrated circuits had doubled every year since their invention. Moore's law predicts that this trend will continue into the foreseeable future (From  Wikipedia).

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