by Filip Palda
These are weighty matters so let us end on a mischievous note. If the history of the past can be illuminated by the economics of chance, is there anything to be said about the history of the future? To answer this question we should pose another one. Can manifestations of chance in stock market returns tell us if time travel exists? If you can start to formulate an answer then you are well into your apprenticeship as an economist.
References
Eliade, Mircea. 1954. The Myth of the Eternal Return: Cosmos and History. Willard R. Trask in the Bollingen Series, number 46.
Friedman, Milton. 1968. “The Role Of Monetary Policy.” The American Economic Review, volume 58: 1-17.
Grossman, Sanford J. 1975. “Rational Expectations and the Econometric Modelling of Markets Subject to Uncertainty.” Journal of Econometrics, volume 3: 255-272.
Lucas, Robert E., Jr. (1972), “Expectations and the Neutrality of Money,” Journal of Economic Theory, volume 4: 103–124.
Marshal, Alfred, 1895. Principles of Economics, 3rd Edition. MacMillan and Company.
Markowitz, Harry M. 1952. “Portfolio Selection.” Journal of Finance, volume 7: 77-91.
Markowitz, Harry M. 1991. “Foundations of Portfolio Theory.” The Journal of Finance, volume 46: 469-477.
Muth, John R. 1961. “Rational Expectations and the Theory of Price Movements.” Econometrica, volume 24: 315-335.
Nerlove, Marc. 1958. “Adaptive Expectations and Cobweb Phenomena.” Quarterly Journal of Economics, volume 72: 227-240.
Sharpe, William F. 1964. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, volume 19: 425-442.
Tobin, James. 1958. “Liquidity Preference as Behavior Towards Risk.” The Review of Economic Studies, volume 25: 65-86.
Varian, Hal. 1984. Microeconomic Analysis, 2nd Edition. W.W. Norton
SPACE 5
WE BEGIN WITH A STORY about space as most people understand it. In the 1970s letters in the US were delivered by the government mail company. It had an official monopoly that extended only to first class mail and not to packages. The US Postal Service was not worried about competition from package mail because so few people sent anything that way. Then came the Boeing 727 and other airplanes that made it possible to deliver cargo rapidly and economically by air. A bright young entrepreneur figured out that a private company could deliver packages at reasonable prices, overnight to and from anywhere in the US provided its hub was properly situated. That did not mean putting the hub in the geographic center of the US but rather in the demographic center. To find this center you first had to cut a sheet of plywood in the shape of the US. Then you drew a fine grid on the sheet. Then you calculated what proportion of the population inhabited each grid. Then you took a hundred weight of metal ringers and placed them on the tiles of the grid in proportion to the populations of each tile. Finally you found the demographic center by finding the point upon which the sheet could be balanced on a pole. That center happened to be Memphis, Tennessee.
It did not take an economist to figure out the best place to locate to satisfy customers, but economists had been thinking along these lines for some time. Their goal had not been to find new means of transportation but rather to study how new discoveries lowered the costs of transportation and spurred development. The innovations they studied were varied and fascinating. The invention of multi-modal containers lowered the cost of transporting goods across the world and led to an explosion of trade in the late 20th century. Teleconferencing eliminated distance as a factor in business negotiations. Before the mid-19th century livestock had to be consumed where it was slaughtered because transporting meat over even small distances led to rapid wastage. The invention of refrigeration in the mid-19th century allowed frozen meat to be transported from Chicago to New York and then around the world, leading to a boom in world protein and caloric intake. In each case changes in the cost of overcoming distance led to changes in production and consumption. Cataloguing such costs, looking at how they change, and then seeing how this has influenced market relations became the subject matter a field known as economic geography.
Somehow economic geography became the preserve of geographers. Economists felt there was insufficient challenge in the field. Little room to push economic reasoning further. An economic geographer was an intellectual clock-puncher applying the same thoughts to different situations in a productive but mundane manner. Then came successive insights that made space a topic worthy of being studied by the best minds in the field of economics.
The first insight was to notice that space was not just a barrier to moving goods around, but rather a field upon which competitors jostled to be nearest to their customers. Harald Hotelling, perhaps one of the top five economists of all time, came up with the idea and showed how it transformed the theory of competition.
The second insight lay in realizing that space was not just a span in the physical world, but also a span in abstract dimensions that mattered to consumers, workers, and voters among others. Kelvin Lancaster, one of the best economists never to be anointed with a Nobel Prize, showed that a good such as a house was made up of many different characteristics, such as proximity to parks and amenities, age, and size. Each of these characteristics could be visualized along an axis. Each could be measured in “characteristics space”. Different goods containing many characteristics could be combined with the other to “span characteristics space”, meaning to reach combinations of characteristics not possible by consuming single goods alone. His realization launched the field of home economics and sensitized economists to the reality beneath the appearance of products. A computer looks much the same as it did 30 years ago but its deeper characteristics have changed. This insight has had crucial ramifications for how we should measure economic progress and calculate price indices.
The third insight came with Sherwin Rosen. He warned that people can become trapped in characteristics space because of who they are. Before Rosen the standard view was that people weigh alternatives in the face of material constraints. The fallout is a shower of prices that equilibrate what people want with what others supply to them. All that matters is price. The identity of the buyer and seller do not matter to this outcome. The used-car dealer does not care whether a buyer is of noble ancestry or a vagrant. All that matters is what the buyer is willing to pay for his “pre-owned” vehicle. Similarly, the buyer does not care if the dealer walks to work, or rides a Bactrian camel. All he or she wants is a good deal.
Rosen showed that in some cases considerations of who the seller and buyer are become pivotal to whether a trade takes place and to the price. The importance of identity arises from the “tied” nature of exchanges in characteristics space. A tied exchange is one that implicates each party as a seller and a buyer at the same time. The young worker seeking a first job is not just selling his labor but also receiving on-the-job training from this employer. The sale of his labor is “tied” to his simultaneous receipt of training. The wage adjusts to compensate the employer for providing this service and by means of this “equalizing difference” the market clears. A government policy such as the minimum wage may not allow the worker to sufficiently compensate his employer through a lower wage. The result could be that either the employer seeks out people with previous experience or, if possible she simply reduces the level of on-the-job training she provides to the employee. Such an insight is not possible in the standard analysis of labor markets.
Another example of a tied sale is marriage. Both parties each desire a list of features in the other. Each feature is measured on a subjective scale and the set of such features situates the candidate as a “point” in characteristics space. If the points of the man and woman are too far apart (in traditional marriage), a money transfer such as a dowry or bride price may be the equalizing factor that closes the deal and leads to marriage.
The language may appear contrived, but the concept applies to disparate situations. Employers and employee
s also seek the right fit with each other; in that case, salary acts as a monetary equalizer that leads to an employment contract. Identity assumes importance in transactions because of the inability of the parties involved to “unbundle” the features that are important in the exchange. Cash then may overcome the distance and a deal is made. Sometimes though the list of tied characteristics is so long that no financial compensation can clear the market. Rosen’s insight has surprising implications for government policies such as the minimum wage and anti-discrimination law, as well as for certain laws governing divorce.
I would be less than frank with you if I tried to pretend that all economists have enthusiastically made space an essential tool of their craft. They have not. The role of space in economics is recent. Despite some early enthusiasm, it has struggled to find a large following, though like an underground Pennsylvania coal fire it continues to smolder and threaten to erupt. Space, especially in the case of tied-sales, adds a complexity to models that many economists would rather not have to be bothered with. Yet in some cases it is the best way we have of understanding why people behave as they do and what the consequences of government intervention may be. For these reasons an understanding of space is necessary for anyone seeking to attain a mastery of economics. Let us examine how Hotelling, Lancaster, and Rosen essentially created the field.
Hotelling and the competitive continuum
IN HIS 1929 essay, “On the Stability of Competition”, which is easy to read and as full of relevant insights today as it was nearly a hundred years ago, Harald Hotelling sought to understand why markets were far more stable than economists thought they should be.
According to accepted thinking the ability of consumers to switch brands posed a problem to the theory of collusion between small numbers of firms. If firms fixed prices then such price fixing could not be stable. Even the smallest price reduction by one firm cheating on the collusive agreement would instantly attract all consumers to the thrifty product. Other firms would lower the price until prices finally collapsed back to their free market level. Then collusion would raise them up again and price instability would plunge them down again, and so on. You see this sort of thing happening every day at rival gas pumps.
Hotelling wanted to understand why markets showed more stability in reality than in theory. His answer lay in the money it costs to travel to a market. Suppose you live in a one-street town where Grandpa’s Grocery is located half-way between the center and the east side of the town, and Farmgirl’s Grocery is half-way between the center and the west side. If you buy from either grocery then your time-cost of traveling has to be added to the market price of what you buy to come up with the full price. Some consumers live closer to Grandpa’s than do others, so that their total costs are lower than those who live further away. Grandpa’s has to be careful not to set prices too high. If Grandpa’s price is greater than what it would cost his nearest consumer on the side of Farmgirl’s to travel to Farmgirl’s and bring back the rival product then Grandpa’s would lose all its customers to the west of it. Grandpa’s could gradually regain customers by lowering price and attracting those within a span where produce price plus travel cost to Grandpa’s is lower than produce price and travel to Farmgirl’s. The crucial insight here is that gradual changes in prices do not precipitate mass movements of consumers, but rather gradual movements. Hotelling saw in this inertia of consumer allegiance a source of stability in competition between firms. From this simple basis he was able to calculate the different prices that differently situated firms would charge for the same product.
These were not exactly earth-shaking discoveries. But Hotelling was just warming up. What if instead of being fixed in one place and varying price, firms could change their location? He showed that for a wide variety of scenarios, firms selling similar products would tend to cluster close to each other in order to protect themselves from “spatial competition” by other firms. If Grandpa’s moves west to the center of the one-street town not only will it get all the business back eastward to its original destination, but also will attract half the customers who lie between Grandpa’s new location and Farmgirl’s location. To regain these businesses Farmgirl’s must also set up shop in the center.
Here was a more interesting discovery, not only because it predicted how businesses would behave but also because it pointed to an inefficient aspect of competition. Consumers would save on travel costs if businesses selling the same product were uniformly spread out over the city. But if this were the case, any company, no matter where it was located, could always snatch away business by moving to the center. Hotelling proved mathematically, but it is not hard to intuit, that forcing all consumers to travel to the center makes the sum of travel costs exceed what it would be if businesses were uniformly distributed along the street. Perhaps this is why property developers do more than build houses. They also lobby municipalities for zoning laws that prevent businesses from excessive clustering.
Yet Hotelling’s idea ran deeper than this. He conceived of space not simply in geographic terms but also as encompassing the features of a product. As he explained, “distance, as we have used it for illustration, is only a figurative term for a great congeries of qualities. Instead of sellers of an identical commodity separated geographically we might have considered two competing cider merchants side by side, one selling a sweeter liquid than the other” (1929, 54). He used his model to infer that competition in “sweetness space” would force both sellers to offer ciders of a sweetness situated such that half the number of consumers preferred a more sour product and half a sweeter product. This “median” sweet product might be to few people’s liking, especially if tastes were evenly bunched up at extremes where many people enjoyed very sweet ciders and many enjoyed very sour ciders, with a sprinkling of people in between. The bulk of consumers would be best served by a sweet cider producer and a sour producer, but to capture the sprinkling of consumers between these extremes both producers would converge towards providing a product situated at the median of consumer tastes.
Hotelling lamented (1929, 54) that, “The tremendous standardization of our furniture, our houses, our clothing, our automobiles and our education are due in part to the economies of large-scale production, in part to fashion and imitation. But over and above these forces is the effect we have been discussing, the tendency to make only slight deviations in order to have for the new commodity as many buyers of the old as possible, to get, so to speak, between one’s competitors and a mass of customers.”
Had he been less busy railing against markets Hotelling might have extended his model just a little bit further to consider why, if consumers were being left high-and-dry by the inefficiencies of spatial competition, did not some clever businesses come up with a solution? The answer, which was within Hotelling’s grasp, was that if the costs permitted, producers would differentiate their products into “lines” which spanned the characteristics space. So instead of choosing a point in characteristics space, the producer would spawn a variety of products to cover that space.
One should not take this as a critique of Hotelling. How much can we ask of a man who in an article of a few pages creates a new field in economics? I mention the example of product differentiation to illustrate how great economic models create insights. Often these models find some failing in the market. Then the model can be extended by asking how markets would react to correct the inefficiency. A good model will confirm what we see happening in the real world, something which Hotelling’s model certainly does.
Hotelling’s model not only clarified how people would compete in a spatial setting, but also challenged us to be creative in our conception of space. As an example of such creativity Hotelling mentioned in his article, almost as an afterthought, that his model could also be applied to political competition in “policy space”. He thus was the first to propose a mathematical model of political equilibrium. Duncan Black (1948) and later Anthony Downs (1957) would elaborate on this insight to cr
eate the famous median voter model of politics. It was Hotelling’s idea. And it really was just all about space.
Lancaster and characteristics space
THE SECOND EVOLUTION in spatial economics was due to Kelvin Lancaster. His insight was that the basic qualities that consumers seek could be manipulated by combining different products. Hotelling had not considered this possibility. He had been content to accept that one good provided one underlying feature that could be measured in characteristics space. Lancaster saw the matter in greater breadth. Dinner was not just food on a table. It was an attempt to manipulate the basic constituents of flavor and nutrition into a satisfying gastronomic experience. Being a good cook meant knowing that taste had several dimensions including sweet, salty, sour, and savory.
For a meal to be agreeable, it had to combine these elements of flavor and it also had to be easily digested, suggesting that nutritional dimensions such as greasiness, protein content, and temperature had to figure into the cook’s understanding. These basic culinary entities could each be thought of as lying on a left-right scale, or space. The ideal meal, then, sought to combine these features by varying each one as precisely as possible. The challenge, though, is that the kitchen is not a laboratory where atoms and molecules can be precisely combined into new structures. In the kitchen you must combine ingredients that may each contain many of the features you are trying to fine tune. The tomatoes that go into pasta sauce give nutrition, but are acidic. Sugar must be added to moderate the sourness that comes with acid. The more ingredients at your disposal, the better able you are to fine-tune the six or seven basic characteristics of a good meal.
