by Filip Palda
Market equilibrium
MARKET EQUILIBRIUM IS the result of two distinct groups reacting in opposite ways to the shared stimulus of the same prices. Opposites may attract but in equilibrium it is more precise to say that people with opposite reactions can be driven in the same direction depending on where they stand. Suppose buyers of some product find its price to be too high. “Too high” means that at the going price those buyers will not buy and suppliers are stuck with unsold stock. To empty their warehouses suppliers must drop the price of this product. As prices fall some consumers buy more. Meanwhile, at the other end of the market, as prices fall some suppliers become less inclined to offer for sale large quantities of the product. For a few, selling the product even becomes unprofitable. The fall in price drives consumers and producers from the opposite sides of too little demand and too much supply towards a fixed point at which there is no further shortage in demand nor excess of supply.
The fixed point towards which markets gravitate is what economists call market equilibrium. It unites consumers who are most willing to pay for a product in an exchange with the most efficient (meaning lowest-cost) producers. If the situation were otherwise the market would not be in equilibrium. If, at the going price, a high-cost producer is selling while a lower-cost producer sits idle, something is wrong. The lower-cost producer should be able to out-compete and oust from the market the less efficient rival. On the other side of this market divide something is wrong if a consumer willing to pay only a little buys the product while a consumer willing to pay more is kept from making a transaction. Here the consumer with greater willingness to pay should be able to express his or her superior willingness to pay with money and displace the less enthusiastic buyer. As we can see, markets tend toward equilibrium because they are sorting devices; they match up people who have the greatest ability to satisfy each other.
By uniting consumers willing to pay the most cash with producers able to offer the product at the lowest cost, markets move to an equilibrium which is Pareto efficient. A market attains Pareto efficiency if no further shuffling of resources between people would raise the well-being of at least one person without violating the use, right to revenues from, and right to modify features of their own property. At the equilibrium price there is no potential buyer willing to pay sufficiently more to make an actual buyer part with his purchase. Nor is there a firm outside of those presently producing with sufficiently low costs to entice new buyers at the equilibrium price.
Pareto efficiency does not mean markets produce the greatest good for the greatest number of people. It does not conform to utopian notions of who should get the spoils of life. Pareto efficiency in market exchange is simply the result of people being allowed to buy, sell, or barter their property under the rule of law. It is efficient in the sense that each person seeks to sell or buy in a way that brings him or her the most benefit without violating anyone else’s right to property and people continue buying and selling until there are no further possible mutual gains from exchange. There are no “big bills” left on the pavement.
The efficiency of equilibrium
THE ASSERTION THAT market equilibrium is Pareto efficient initially relied on verbal explanations. Pareto was among the first of a long line of economists who were not satisfied with describing the situation in words. Proof had to come from mathematics. Market relations were amenable to mathematics because they could be summarized neatly in equations generally described as “reaction functions”. These functions are more popularly known as supply and demand equations.
Demand shows the quantity consumers will want of something at a given price. Supply shows the quantity of something that producers will make. By using the high-school technique of solving two linear equations in two unknowns (demand and supply, quantity and price), economists can find the price at which demand and supply equal each other. Even for non-linear curves the exercise is not usually more complicated.
The simplicity of finding the theoretical price that equilibrates the supply and demand equations hides how broad yet compact this form of social accounting is. Thousands of people, each with varying means and desires and abilities, make up an economy. Yet demand and supply equations completely compress or “encapsulate”, to use the expression coined by Makowski and Ostroy (1992), all this human variety into a few equations. Using encapsulation, economists are able to prove the two “welfare theorems”. We have already worked our way through the first theorem in our discussion of the efficiency of competitive equilibrium. In this first theorem encapsulation gives economists the precise tools for determining how much output will be produced at what cost and also the value people will place on consuming this output. By comparing the equilibrium pattern of production and consumption with other possible non-equilibrium patterns they can produce an elegant mathematical proof that only competitive equilibrium is Pareto efficient. Other patterns of production and consumption are not efficient because they leave some demand unsatisfied and do not fully exploit the mutually beneficial gains people can realize through market exchange.
The conditions under which the first welfare theorem would hold were not clarified until the works of future Nobellists Kenneth Arrow and Gerald Debreu in the 1950s. Their articles are largely impenetrable to most economists due to their mathematical sophistication, but a simplified proof is available in Hal Varian’s 1984 textbook Microeconomic Analysis, (200-203).
Arrow and Debreu discovered the crucial conditions for competitive equilibrium to be efficient: that no exchange should violate the property rights of a third party. Among the “violations” Arrow and Debreu had in mind were pollution and monopoly. Buying paper for your laser printer is not a Pareto-improving exchange if the pulp company pollutes a river to which downstream anglers and farmers have no established riparian rights. In such a case, the market gets the social calculation wrong because the absence of property rights allows costs to be piled on farmers and anglers without any compensation by the pulp company. The mistake may be so profound that the damage from the pollution destroys more value than that generated by making paper. Monopolies violate Pareto efficiency by forbidding potential producers with a better product from offering it to consumers. By thwarting mutually beneficial exchanges monopoly turns the market into a desert with limited possibilities for mutually enhancing trade.
Economists as far back as Adam Smith had long felt confident in the existence of something like the first fundamental theorem and were aware of the threats to it, but the solid mathematical proofs that came out in the 1950s were reassuring.
The second welfare theorem
ARROW AND DEBREU also proved the second welfare theorem, which in some ways is even more remarkable than the first. A very broad statement of the theorem is that it does not matter how resources are distributed in society, eventually the economy will work its way to an efficient equilibrium. The theorem is remarkable in part because it appeals to both socialist and free-market thinkers.
If you believe the distribution of wealth in society is unfair you need just ask government to come up with a new distribution. With their new endowments people will trade their way back to a Pareto efficient state. As Nobellist Joseph Stiglitz explained in a lecture at Glasgow University, “Of course, the distribution of income which emerged from the competitive market may not be to a society’s liking. And this is where the second Welfare Theorem enters. It says that every Pareto efficient allocation of resources can be attained by means of the market. All the government needs to do is to engage in some initial redistributions, and then leave the rest to the market process” (1991, 4).
If you are a fan of free markets, then you might like the theorem for what it says about privatization. When East Bloc countries abandoned Communism there was some confusion about what to do with the vast government holdings of wealth. Free-market believers in the second theorem advised the post-communist governments to carry out “voucher privatization” in which each citizen received a share of government asset
s. Many had no use for shares in factories or lands and sold theirs to people who felt they could better manage those resources. The idea was that an initially inefficient distribution of share ownership would eventually evolve to an efficient competitive equilibrium as ownership moved from the indifferent to those feeling themselves more competent.
Ronald Coase pushed this idea to its limit in his analysis of pollution. In his 1960 article, “On the Problem of Social Cost” he argued it did not matter for efficiency whether a railroad owned the wheat fields which its locomotives set ablaze from time to time by casting sparks, or whether the field belonged to farmers. If farmers owned their fields they could take the railroads to court and be reimbursed for the cost of losing crops to fire. Railroads would have to count this as a cost of using this route to deliver people or goods and might decide that by reducing the number of trips the cost saved would be greater than the revenues lost from foregone passengers and freight.
If instead, the railroad owned the fields, it could set fires without fear of being fined, but in the end, the costs to it would be the same, because the fires it set would end up burning railroad crops grown on railroad land. If it decided not to grow crops and instead rent the land, farmers would reduce their offers by the anticipated cost of crops lost to railway fires. So for the calculations people made who owned the land was a matter of no consequence.
Here then was the celebrated Coase Theorem. The railroads would be faced either with visible fines for scorching someone else’s land, or with less visible but equally tangible “opportunity costs” from putting their own land to the torch. In the end, transport and crop growth would end up being efficient in the sense that farmers and railway operators would produce up to a point where the benefits they received from the last “marginal” unit of production just equalled the cost. There were no lost opportunities for trade because all costs were taken into account, or “internalized”. If farmers owned their land and you imposed a regulation stating that railroads must not set fire to crops, you drove the market away from Pareto efficiency because the sacrifice of a few crops might allow transport that was far more valuable to the railroads than the crops saved. In such a case, farmers would have allowed—and even encouraged—railroads to burn their crops up to the point where the payments just marginally exceeded the value of the lost crops.
Coase’s initial reasons for writing his article may not be known. He never mentioned a theorem in his paper. That moniker was bestowed by a later generation of economists (intellectuals love to label). But what he ended up providing was an intuitive explanation of the second welfare theorem’s claim that ownership patterns are irrelevant for efficiency. Coase argued that efficiency was attained by making people face the full costs of their actions and realize the full benefits. Most critically, efficiency did not depend on how much money you started out with in life with, whether you got a surprise share in a privatized government firm, or whether a sinkhole swallowed your house. Efficiency was always functional and this is what led people back to a Pareto efficient equilibrium.
The deep waters of equilibrium
WHATEVER THEIR POLITICAL beliefs, the second welfare theorem was warmly embraced by economists. It relieved them of needing to worry about criticisms that their profession heartlessly ignored the unequal distribution of wealth in society. In Stiglitz’s words, the second theorem “says that we can separate out issues of economic efficiency from issues of equity. Economists need not concern themselves with value judgments; whatever the government’s distributive objectives, it implements these through initial lump sum taxes and subsidies, and then leaves the market to work for itself” (1991, 4-5).
Stiglitz’s qualification that redistribution must be “lump-sum” is often overlooked by enthusiastic fans of the second theorem, but it is a key factor in both its limitations and its strengths. A lump-sum redistribution is simply a handout with no strings attached. It is also a tax that has nothing to do with how much you work, or consume, or invest. The redistribution is not influenced by any action you might make. A business subsidy tied to how many homeless people you employ is not lump-sum because it can be influenced by, and in turn influence, your behavior.
Non lump-sum, or so-called “tied” transfers, can be the enemies of Pareto efficiency because they can warp people’s behavior away from profitable exchanges based on the true conditions of the economy, such as wants and capabilities. Various real estate bubbles have been attributed to the effect of government aid intended to help prospective homeowners purchase their first dwelling. Housing bubbles grow because banks lend to high risk borrowers, knowing that government will come to their rescue should the market collapse. Without a government safety net, lenders would look before leaping into the high risk mortgage market. A rational calculation balancing future risks against current gains would contain to some extent the degree of any crisis, should it arise. With a government safety net in place people may blithely ignore real market conditions and strike deals that destroy wealth. The second theorem says that provided we do not warp people’s perspective on true wealth with non lump-sum transfers, government transfers can lead to a Pareto efficient market equilibrium. Government mortgage guarantees subvert the second theorem because as anticipated transfers in the case of crisis these entice us to embark upon excessively risky real estate ventures.
Stiglitz saw the lump-sum condition as a fatal flaw of the second theorem. He did not believe that government was able to redistribute money in a lump-sum manner, mainly because people would cheat on their taxes in a manner systematically related to production.
Consider that tax evasion is a form of transfer from the government to the evader. Those businesses best able to cheat would gain a competitive advantage over their rivals and drive them out of the market. You could end up with a market of inept producers who were adept at cheating on their taxes, thereby driving out people who were efficient but honest. The trick to seeing the weakness of the second theorem lies in recognizing that tax evasion is a form of transfer that might be tied to some feature of the person evading.
Stiglitz also believed people would lie about their needs to get government subsidies. On the surface the lump-sum subsidy should not be related to any feature of your environment you can change. But if you can fake being sick you can get subsidies. The inefficiency that arises is that a class of shirkers forms to exploit subsidies. Previously they could have been gainfully employed. The difficulty of implementing lump-sum subsidies was really the story of the disappointing results in the war on poverty and inequality and the collapse of the Soviet empire, where shirking took on such massive proportions that a special term for it was invented: “economic wrecker”.
Yet was this a fatal flaw of the theorem or of the conditions under which it was made to work? Stiglitz’s critique of government intervention was spot-on because it pointed to an inevitable correlation between the transfer and some actions of the recipients or taxpayers. His critique had much less force in the case in which redistribution was due to some chance workings of the market, such as those caused by an unforeseen earthquake, plague, war, revolution, scientific discovery, or just about any other economic “shock” that is the daily reality of markets.
Free market types do not like to hear this, but the free market is constantly bombarded with inefficiencies due to chance redistributions of resources and opportunities. The good news is that, like a self-sealing tire, the market can patch itself up. The discovery of the automobile put the horse-drawn carriage industry out of business. The automobile’s unexpected discovery acted like a reshuffling of the endowments of talent, and thus of wealth, that nature had handed out in a previous generation. The new opportunities for mutual gain between riders and mechanics that the auto’s development presented led to a shift of resources away from the horse and carriage trade to the car trade.
We think of this as a normal market process and maybe that is so. It is also a demonstration of the second fundamental theorem of welfare
economics. Chance redistributions of advantage are like lump-sum redistributions of income. They upset established market relations but eventually the tendency to equilibrium exploits all possible gains from trade and a Pareto efficient state is attained. Put slightly differently, because it is geared towards equilibrium, a market economy will exploit chances for improving economic efficiency as those chances arise. The “slings and arrows of outrageous fortune” may injure us when they strike, but the economy has a first-aid kit. Or more precisely, it is a self-correcting mechanism that takes change as a normal part of its daily routine and translates that change incrementally into a new and efficient system of social accounts.
It is in such novelty that advocates of the free market place their faith. They see in shocks to old wealth the impetus to discover ways of creating new wealth. Certainly the evidence of the last two centuries supports this view, but the first and second welfare theorems are mute on the question of whether a free market will lead to increasing prosperity.
These theorems are static representations of what is, and not of what may be. In a very circumscribed manner the theorems help us to understand that markets are not simplistic vehicles for the creation of wealth. Markets help people recombine resources after the upsets of chance in such a way that they find their most valued use.
Enter Pigou
THE MATHEMATICAL MODELING of free market equilibrium and its Pareto efficient properties captivated economists. It followed that the economy should be left to itself with the occasional correction of imbalances in wealth being the responsibility of government. What government should not do above all was to meddle in the workings of the market. There were dissenting voices however. There always are.
