In a way, the theory of supply and demand explains prices. But in another, more accurate way, bargaining theory explains prices.
The idea that the prices of commodities are determined by the bargaining power of the buying and selling parties is not new, having been raised in the nineteenth century, but it does not play a major role in left political analysis. It is seen in discussions of collective bargaining, and is sometimes mentioned as an account of exploitation by those who reject the labor theory of value. But to my knowledge, this bargaining theory of prices has not been much developed, and advances made in the last few decades by game theorists who study bargaining games have not been incorporated into the political economic discussion.
I will argue for the adoption of the bargaining theory of price as a useful analytical tool that has several advantages over the theory of supply and demand: it requires fewer idealizing assumptions; it is methodologically individualistic; it clarifies rather than obscuring how exploitation works; and it helps to avoid a trap that caused Bohm-Bawerk to overstate the efficiency of markets and miss the “poverty among plenty” phenomenon.
Supply and Demand: Reactions to Sanyazi and Carson
The correctness and usefulness of the theory of supply and demand is debated in a couple of recent articles. At the Hampton Institute, Shi Sanyazi published an article with its thesis statement as the title, “Housing is determined by class power and profit, not ‘supply and demand’.” Sanyazi points out that even in cities like Austin, where rental housing supply increased at a faster rate than the population in the 2010s, rental prices have gone up. Addressing the neoliberal position that the solution to the housing crisis is building more housing, Sanyazi writes, “The ‘supply crisis’ narrative is deficient because it makes no attempt to reckon with the class relationships which define the housing market.” Sanyazi presents various methods by which different capitalist subclasses – landlords, real estate developers, and financiers – exert their power. Among others, these include police violence, concentration and professionalization of property ownership, and advances in information technology that help landlords determine optimal pricing (optimal for landlords, that is; suboptimal for tenants). This kind of analysis is exactly what organized working-class tenants need to understand and develop in order to avoid the traps set for them by neoliberal and Austrian economics.
Sanyazi’s article prompted a half-defense of the theory of supply and demand by Kevin Carson in C4SS. Carson defends supply and demand as technically correct, while agreeing with Sanyazi that it is not a source of insight into how the power relations figure into pricing. For Carson, the supply and demand theory is not in conflict with the class power factors, but stands alongside them as a different form of analysis. His point, as I understand it, is that the supply and demand curves all have the same general shape, and intersect at equilibrium, regardless of what values the curves reflect or what factors determine the values. The theory of supply and demand does not need money or freedom to be true; in a prisoner-of-war camp in which contraband cigarettes are exchanged for food rations, there are still supply and demand curves that intersect at an equilibrium, and the quantity of cigarettes and food rations exchanged, as well as their prices in terms of each other, can be predicted to occur at equilibrium. This is true regardless of power factors such as who is favored by the guards, who has outside connections that can sneak in cigarettes, and what the regime for cracking down on contraband cigarettes looks like.
Carson calls the applicability of supply and demand “nearly a tautology.” I don’t agree with “nearly”. In the Bohm-Bawerkian form of the theory that Carson uses, it’s a mathematical equivalence. The theory describes a function which, given a type of commodity and a set of inputs, and given some assumptions about its operations, produces an output in the form of a price range. The inputs for Bohm-Bawerk are the number of buyers and sellers of the commodity and the intensity of each buyer or seller’s desire for the commodity, compared to the money or other commodity being exchanged for it. To make it simple, the theory of supply and demand can determine the price range of a type of thing given how many people want the thing, how many of the thing are for sale, and how much each person values the thing . The theory needs to make some idealizing assumptions in order to work, such as: nobody ever pays more than they need to for a commodity; buyers have complete knowledge of what’s for sale and sellers have complete knowledge of who is interested in buying; and there are no transaction costs.
The fact that the theory of supply and demand is tautological does not mean that it is not useful. It may be an equation, but there is value in understanding the components of the equation, just as one can learn a lot about a company by looking at its books, even if they are perfectly balanced. The theory of supply and demand can predict changes in price based on changes in the quantity and intensity of people’s desires for different commodities. If people start valuing horses less because cars become affordable, then the reduction in the amount that people would pay for horses predicts a drop in price, if all else remains equal. The new price of horses, and the reduction in the number of horses sold, can be quantified based on the changes in the input factors.
The Bargaining Theory of Price
The fact that the theory of supply and demand is a mathematically correct analysis of price does not preclude other, equally mathematically valid price equations based on different types of input.
It is perfectly possible to analyze prices in terms of bargaining power and other bargaining factors. The bargaining theory of price was recognized at least as far back as 1898, when the Scottish-Canadian economist John Davidson published The Bargain Theory of Wages. Davidson argued that wages of individual workers are determined by factors such as the disutility of the work, competition for labor among employers, knowledge of the market, frequency of pay, method of pay (money vs. company scrip or credit), mobility of labor (which Davidson characterized as “the crowning disability of labor”), collective bargaining, legislation and public policy.
Wages are not metaphysically unique, and other prices can be accounted for in terms of bargaining power as well. It is intuitively obvious that bargaining factors play a role in price formation. No reasonable person would doubt that if workers formerly restricted to work in one small town are now given the ability to move freely in search of employment opportunities, their wages would rise, if all other factors are kept equal. Or that if the seller of a product would pay a significant transaction if a potential buyer walked away, while the buyer would not face any such cost for walking away, then the price of the product would be lower than if the situation was reversed (all else being equal). Or that if a party has a much more thorough knowledge of the product and the market than the party on the other side of the transaction, it will get a better deal than otherwise (all else being equal); or that a buyer of a common product for which there are many sellers will pay less than she would pay for the same product if it was unique or available only from that seller (all else being equal).
This sort of reasoning is orthogonal to the (Bohm-Bawerkian) theory of supply and demand, which does not deal with such bargaining factors explicitly. The bargaining factors are, at best, in the background. If they are not assumed away, they are treated as incorporated into the inputs, namely the quantity and intensity of supply and demand. The supply and demand theory’s idealizing assumptions that transactions are frictionless, and that buyers and sellers have complete information about the market, simply disregards these bargaining factors. The level of a buyer’s knowledge of a product is baked into her valuation of the product, which the supply and demand theory treats as a basic input.
The development of the theory of sequential bargaining games, starting in the 1970s, has made it possible to formalize the bargaining theory of price in a way that permits quantitative precision. In such games, two players take turns making moves. After the initial move in which the first player makes an offer, each player on their turn can either accept the offer that is on the table, or reject it and make a counteroffer. There is no preset limit on the number of moves. It is assumed that the parties have complete information and bargain optimally. (For those unfamiliar with sequential bargaining theory or game theory, William Spaniel’s video series on bargaining theory and game theory are highly recommended.)
Classically, the parties are bargaining over the division of a definite sum, where each party prefers a larger share over a smaller share. For example, if the sum is 1, then it could be divided so that each party gets 0.5, or so that one gets 0.6 and one gets 0.4, or that one party gets 1 and one gets 0, and so on, with each party preferring to get as close to 1 as possible. Formally, this is equivalent to the buying and selling of a good with one party having a reservation price of 0 and the other having a reservation price of 1. A sale of the item for 0.5 is equivalent to a splitting of the sum so that each party gets 0.5.
This formalism is therefore a fairly good simulation of what takes place in a market, in which people are generally free to make offers to buy or sell, to accept or reject offers, and to make counteroffers. The fact that the game is modeled as a back-and-forth negotiation does not mean that the determination of prices requires such a back-and-forth. Rather, as a famous 1982 proof by Ariel Rubinstein shows, transactional friction, represented formally by a discount factor, causes rational bargainers to determine the price in the first round in order to avoid the discount. The calculation of the price requires the possibility of a multi-round negotiation, and the existence of that possibility, with its associated discount, incentivizes the buyer and the seller to settle in the first round of negotiations.
Sequential bargaining with discounts: an example
Here is an illustration of a sequential bargaining game with a discount factor, adapted from Spaniel’s video. Let’s call our seller Ariel (or A) and our buyer Bohm-Bawerk (or B). A is trying to get rid of his copy of The Complete Works of Ayn Rand and has a reservation price of 0. This means that he would accept $0 for it, but hopes to find a buyer who will give him some money for it, the more the better. A approaches B, who is interested in the complete works and would pay up to $1 for it, but hopes to pay as little as possible. Both men are strangely fixated on the insight that time is valuable, so each of them considers the value of the transaction to be 10% less to them after each move. That is, if B rejects A’s first offer and makes a counteroffer that is accepted, each party is now 10% worse off, and in effect, they are bargaining over 0.9 worth of value instead of 1.
The solution for this game is that A offers 1/1.9, which is about 0.526, and B accepts. That means the price of the books in this transaction is 52.6 cents. If A insisted on more, B would be better off rejecting it and making an optimal counteroffer to A that he would accept. A and B both know this, so A would not make such an offer on his first move. But 52.6 cents is low enough that B would be worse off insisting on making a counteroffer, because of the discount that would affect both parties. Again, both parties would know this. For this reason, A makes the optimal offer, and B accepts it. The combination of valuations and optimal bargaining has determined the price.
The general formula for this kind of game, in which the discount factor is equal for both parties, is that the offeror offers 1/(1+d) and the offeree accepts it, where d is the value after a single discount. In our example, where the discount is 10% per round, d equals 0.9. The less patient the parties are, the higher the discount, and therefore the greater the advantage for the person making the offer. The lower the discount, the closer the split gets to 50/50. In this way, the price of a commodity is impacted by the patience of the parties, as well as which party gets to make the first move.
If the parties have different discount factors, reflecting different levels of patience, then an advantage accrues to the more patient party. If A’s discount is 10% per round while B’s is 50%, the price would be 90.9 cents, a huge advantage to A. In general, if da is the value to A after one round and db is the value to B after one round, then the price will be 1 – db(1-da)/(1-(da)(db)). In short, more patient market participants get better prices than less patient ones.
This demonstrates the impact of patience on prices. Patience is a form of friction that is assumed out of existence in Bohm-Bawerk’s supply and demand theory of prices, but as this example shows, is a bargaining factor that helps to determine prices. If an economic class of people could systematize advantage in a bargaining factor like patience, it could exploit other classes by systematically getting more favorable prices in transactions with them.
There are other bargaining factors that could be shown to impact prices by modeling them in the sequential bargaining theory. These include each party’s understanding of the value of the thing being exchanged to itself and the other party; understanding the other party’s understanding of the value to all parties of the thing being exchanged; each party’s understanding of its best alternative to reaching an agreement, including transaction costs associated with walking away from a negotiation; each party’s understanding of the other party’s understanding of its best alternative to reaching an agreement; each party’s (or its agent’s) bargaining skill; whether any party has monopoly power; and if negotiating through an agent, the faithfulness of the agent negotiating the agreement. Spaniel’s series on bargaining theory includes several videos showing the operations of some of these factors.
One feature of the bargaining theory is that it is possible to completely specify the price in terms of the bargaining factors. This is not an empirical result, but is true by definition. If a set of bargaining factors, expressed as quantities, is found not to predict the correct price, then either the numbers assigned were incorrect, the calculation was incorrect, a bargaining factor was missed, or someone failed to bargain optimally. As with the theory of supply and demand, the fact of the tautology is not a failing of the theory, because the interesting part of the analysis is how the bargaining factors fit together to yield the result.
It should be apparent from the foregoing that the bargaining theory is a legitimate way of analyzing prices. One advantage that it has over the theory of supply and demand is methodological individualism. The bargaining theory determines the particular price of a particular thing in a particular negotiation. Since prices are features of individual transactions, this makes it a more precise mechanism than the theory of supply and demand, which applies to general prices of types of things.
Supply and demand has to assume that buyers are indifferent between tokens of the same type. In Bohm-Bawerk’s example, where the buyer is a peasant in need of a horse, the peasant does not discriminate between the options available for sale – to him, a horse is a horse. Of course, in the real world some types of commodities are fungible, while others are not. New cars of a given model, style and year are completely interchangeable to the buyer, but houses are usually sui generis. The theory of supply and demand would have to be used at a high level of generality to be of any help in accounting for housing prices, but it can be useful for accounting for the price of new Honda Civics. The bargaining theory of price would have to generalize the price of a typical new Honda Civic from the individual prices determined between individual buyers and sellers of new Honda Civics.
An advantage of bargaining theory is that it makes analysis of market exploitation relatively straightforward. By exploitation, I mean unfairly making use of an advantage one has over another person to make oneself better off, and the other person worse off, than if the exploiter had acted fairly. This is roughly the approach to exploitation found in the work of Alan Wertheimer and Matt Zwolinski. Since the price of a commodity is determined by how the bargaining factors operate on a negotiation between market participants, exploitation in market transactions must be the result of unfair bargaining advantages helping to determine prices that are favorable to the person holding the unfair advantage, and less favorable to the person with the unfair disadvantage.
Unfair bargaining advantage does not have to mean unequal bargaining power – that depends on your beliefs about fairness. Most people would probably accept some forms of bargaining inequalities as fair and others not. Zwolinski’s Exploitation and Freedom distinguishes between an accidental rescuer and a professional rescuer demanding a large sum of money as a condition of rescue. The accidental rescuer – a person who happened to be in a boat for her own purposes, and came across a drowning person, who she could easily save – would be seen as engaging in extortion if she insisted on being paid for the rescue. The professional rescuer, who patrols the waters at her own expense, providing a valuable service when she could be doing a different job, would be seen justified in charging for the rescue, or at least more justified. The bargaining inequality between the drowner and the saver are the same in both situations, but it is only seen as unfair for the accidental rescuer to use this inequality to extract a lot of money from the drowner.
I mentioned a trap at the beginning of the article concerning the efficiency of markets. Bohm-Bawerk, working from his theory of supply and demand, argues that market pricing is efficient, directing goods to the people who value them the most. In fact, market pricing directs goods away from those who value them most, in one critically important respect.
Bohm-Bawerk’s supply and demand analysis uses a special definition of “value” (or “desire” – I will stick with “value”) that causes the argument for market efficiency to fail, and masks the actual counterefficiency of markets. For Bohm-Bawerk, a person’s valuation of a type of commodity is not measured by her psychological attitude or physiological need for it, nor by how much she is willing to exchange for it, but by how much she is willing and able to exchange for it. “Value” thus factors in the wealth of the valuer. In the common usage of the word, a person dying of thirst in a desert would place an enormously high value on a bottle of water, but in Bohm-Bawerk’s theory, if such a person came across a convenience store in the desert but had no money to buy a bottle of water with, he would not “value” it at all. The upshot is that two people who want or need a commodity to an identical degree can “value” it differently, based on their ability to pay.
As a result, the people who “value” basic necessities like food and drinking water the most in Bohm-Bawerk’s special sense tend to be the well-off people who already have plenty of it. Food and drinking water are produced in overabundance, but the market fails to allocate them in adequate amounts to billions of people, because these people do not have enough money to “value” them. In the ordinary sense of the word, people who lack sufficient food and drinking water value them very highly in the objective sense that life, health, and wellbeing depend on them. Poorer people also highly value such basic necessities in the subjective, but basically universal, sense that people would forego other, less fundamental goods to get these necessities, whereas wealthier people whose basic needs have been met would pass up food and water at the margin for more luxurious goods. Because markets allocate such necessities away from those who value them the most in the ordinary sense of the word, which is also the more morally compelling sense of the word, markets are counterefficient, creating poverty amidst plenty, when wealth concentration is high. This counterefficiency is obscured by the theory of supply and demand, which bakes market power into its definition of demand.
Bringing the discussion back to Shi Sanyazi’s article: it seems likely that lack of market power is a major factor in rising rental prices and rising homelessness. The amount of rental housing might be increasing faster than the number of people who need housing in some places. But market prices are not affected by those who need housing and can’t afford to pay enough for it. If the supply is taken up by some combination of people with higher income – tenants, homeowners living in potential rental units, purchasers of second homes, and landlords who wish to strategically keep the homes empty – then the benefits of increased supply fails to trickle down to those with less market power. Like the victims of famine and starvation documented in Amartya Sen and Jean Drèze’s work, they are not the victims of inadequate production, but of market distribution in unequal societies.