by Filip Palda
Economist, economist
THIS FEARFUL SYMMETRY of consumption and production burns bright in the minds of economists. It suggests a link between seemingly diverse elements in society. As optimizing consumers we must think as producers, and as producers we must understand that we too have an ultimate goal as do consumers. That goal is to maximize profits. Our search for efficiency is expressed in a similar manner no matter whether we are consuming or producing. In some way, substitution unites us and gives the term “democracy of markets” a Madisonian ring.
Economists found these parallels between consumers and producers important because they simplified and clarified what are the deep forces or “fundamentals” behind economic change. For consumers these fundamentals are their incomes, the price of goods, and the weight they put on each good in their preference “functions”. For businesses the fundamentals are the prices of labor and machines and the production function that combines these two into outputs. Almost all of economics is about understanding how changes in these fundamentals change our behavior and our well-being. At the bottom of it all is the principle of substitution.
As well, an additional part of economics is about understanding the meaning of prices. Of course a price is what you have to pay to get something. But it can have a deeper, systemic meaning. For suppose that all consumers adjust the rate at which they are willing to trade off two goods until the rate at which they are willing to trade off an additional or “marginal” unit of the good equals the relative price. By “equilibrating” relative preferences at the margin with price all consumers attain a state where they all equally value an additional unit of the good in question. Their preferences may be different, but their behavior drives them to a sort of psychological meeting place where consensus reigns on the relative desired rates of tradeoff.
On the production side, firms generate output until their extra costs of producing equal the extra benefit, which is the price. Price is the point of convergence between consumers’ willing rate of tradeoff and producers’ ability to make more of one good while making less of another. So what happens in the market is that everyone adjusts his or her consumption and production until all consumers and producers agree implicitly on the value of an extra unit of output of the good in question. Markets do not change preferences or costs. They change behavior to the point at which marginal preferences and costs converge in the sense that desired relative desired rates of tradeoff between two goods equal the actual possibilities for tradeoff.
These possibilities are determined by the cost functions of firms. If everyone is taking prices as given then firms and consumers adjust their consumption and output to the point where the desire of all in society to give up an extra unit of one good to get more of another good is equal to the technical feasibility of producing less of one good and using the labor and capital freed up to produce more of the other good. In market equilibrium every producer and consumer values an extra unit of output equally. The meaning of this convergence of marginal preferences and production possibilities is that prices tell the economist what the social consensus about the value of a change in resource allocation is.
People sometimes talk about prices “conveying information”. The traditional model of supply and demand makes no mention of information. Prices emerge spontaneously from the equilibrium process. But information is there. A government that wishes to evaluate the benefits of building a football stadium would like to know what people would be willing to pay for an added possibility of attending the games. Provided that there are no negative non-market consequences of holding football games, such as added noise to the neighborhood where the stadium is to be built, the price of tickets in the market is a guide to the consensus view on the added benefit of the circus component of panem et circenses.
Conclusion
WHILE ECONOMISTS SEE substitution as the backbone of their science, not everyone in the real world is as thrilled with the principle as they are. Unions have been engaged for a long time in a battle against the right of businesses to substitute labor for machines. The word “sabotage” comes from an early union movement in France to destroy machines by throwing wooden clogs known as “sabots” into their workings. Big business may also cast a worried eye on substitution. The internet and the possibilities it presents for costless telephony is a constant source of worry to telecommunications giants. Substitution is not simply a principle consumers engage in to maximize their well-being, or which businesses follow to combine inputs so as to minimize the costs of production. Substitution is the engine of market competition.
However, consumers and businesses that are quick on their feet are grateful for the possibilities presented by substitution. People’s preferences are finely divided, while the possibilities they are provided with are coarsely presented. People want to minutely adjust their purchases to squeeze the most out of every dollar. They can only perform these desired substitutions if in the real world such substitutions are technically or legally feasible. There are fortunes waiting for firms that come up with the technical and legal means to refine the opportunities for substitution. The example of the iPod encompasses both these dimensions. The iPod was a technological breakthrough allowing users to purchase tunes individually. It was also made possible by legal innovations that protected the sale of individual songs from pirates who would have offered these songs free of charge on peer-to-peer networks such as the Napster network of the late 1990s.
Attention must be drawn to the conflict that substitution can cause between established organizations and beneficiaries of the discovery of new opportunities. Substitution is a means by which people free themselves from the grasp of the economic “powers that be”. We learn that a seemingly dry economic concept is in fact helpful in understanding social upheaval and human progress. Which is why substitution is the first and most important concept to master in economics.
References
Chipman, John S. and Sébastien Lenfant. 2002. “Slutsky’s 1915 Article: How it Came to be Found and Interpreted.” History of Political Economy, volume 34:553-597.
Cournot, Augustin. 1897. Researches into the mathematical theory of the wealth. Originally published in French in 1838. Published in English in 1897 by the MacMillan Company.
TIME 3
BEFORE ECONOMISTS HAD BEGUN TO think clearly about supply and demand they were busy writing about time. The topic arose forcefully in the 19th century. The industrial revolution was bringing attention to the critical importance of long-term investments in large-scale projects. There could be a ten, or even twenty year lag between the money invested in a tunnel passing beneath the Thames and the toll revenues to be collected from it. Before the industrial revolution the existence of lags between outlays and outputs was difficult to notice. Long-term investments by private industry were few. Farmers might “invest” in livestock or planting a crop, but these seasonal, repetitive activities held little interest for economists. As factories and railroads were built, scholars started asking who in society should get the wealth from these novel investments.
Marxists argued that workers were the source of all wealth but were getting a bad deal from capitalists. Others believed that patience bred profits. To Eugen Böhm von Bawerk, a “political economist” and proto-economist of the budding Austrian school of economics, the time that money or “capital” spent in gestation contributed to the value of final output. It deserved remuneration. Today we barely understand what these squabbles were about but we should not denigrate them. They raised a flag above an important issue: how did time fit into economics?
Neither Marx nor Böhm von Bawerk were able to convincingly fit time into economic analysis because they lacked the intellectual tools. Economists of the 19th century had barely even begun to understand and model how consumers should divide their spending between goods in the here and now. A logically consistent model of consumption over time, a so-called dynamic model, would only start to make a very tentative and simple appearance in the 20
th century. The model that gradually emerged was little more than a ramped-up version of the static model of consumption. Instead of choosing only between different goods, consumers also had to choose between consuming more of a certain good now and less of it later.
The names of Milton Friedman and Franco Modigliani are associated with this early attempt to integrate time into economics. They are responsible for discovering the circumstances under which the ups and down in the stream of income a person anticipates to receive during his or her life time are uncoupled in a very particular sense from the ups and downs in consumption that person should plan in order to maximize wellbeing. They argued that in bad economic times a pleasure, or “utility”, maximizing consumer would seek to borrow against future income to keep consumption near some desired lifetime average. In good times the consumer would save surplus income in the bank to go back down to that average.
Their analysis was based on the restrictive assumption that even though you might save and earn interest in the future, in a “present value sense” such savings did not really change the sum of incomes you received over your lifetime. This allowed them to view the consumer as being motivated by a single datum called “permanent income”. By wrapping lifetime income into the only number the consumer needed to use in deciding how much to consume in any given year, Friedman and Modigliani banished time from the intertemporal analysis of wellbeing in the sense that the timing of income no longer played a role in the timing of consumption.
A more complicated integration of time into economics only started to develop in the latter part of the 20th century when economists realized that time periods might be interconnected in a much more convoluted manner than they had realized. In particular they considered what might happen if the choice to consume less today and invest in some productive technology actually increased lifetime income in a present discounted value sense. By introducing what might seem an innocuous wrinkle into the Friedman-Modigliani analysis these researchers stumbled into a frighteningly complex field of dynamic optimization known as the “calculus of variations”, and “optimal control theory”. If consuming less and saving more in any period really did increase your lifetime income, then the timing of consumption and the timing of income would have to be bound together. Recognizing this possibility gave birth to the field of real-business cycle macroeconomics. It also shaped our understanding of the constraints that the expectations of individuals may place on well-meaning social planners wishing to optimally guide the economy over time.
Time’s simple face
THESE MAY SEEM like obscure propositions so to understand the role of time in economics we need to first look at its simple interpretation as just another sort of good or service. Then we can move to the analysis of time as a distinct aspect of economics rather than just as a reinterpretation of goods in the static model of consumer behavior. A mastery of time may be the greatest challenge to someone seeking a mastery of economics, but one that can be surmounted by understanding that time in economics has but two faces.
To economists trained in the middle of the 20th century, time connoted “the permanent income hypothesis of consumption”, a term coined by Milton Friedman in the 1950s. A near copy of the Friedman model is “the life-cycle earnings theory” formulated by Franco Modigliani and developed at the same time as Friedman’s theory.
Neither title properly conveys the essence of the theory behind how people choose to space their consumption out over the years. Friedman and Modigliani both considered the economy from the perspective of consumers who had to decide when to spend the income they anticipated they would earn over their lifetimes. When Friedman and Modigliani came out with their theories many economists found the ideas hard to grasp. Then economists began to see that what Friedman and Modigliani had done was to add little more than a twist to the traditional model of how consumers chose between goods.
The twist was to treat the same good, such as a bag of potato chips, as being a slightly different good when consumed next year, and a very different good when eaten in ten years. The difference arose not out of any physical change in the good but from the assumption that people prefer to consume things now rather than to delay their pleasure by consuming them in the future. The only way to entice them to put off consumption would be to offer them some interest payment on the money they put aside today. The interest earned would allow them to buy slightly more of the same good in the future. By “slightly more” they meant that the added interest on savings did not contribute a penny to the present discounted value of lifetime income. So, the only new insight economists needed to fully understand the trade-offs involved between consumption now and in the future was that of present value and the associated concept of discounting. Let us see what these concepts mean.
Present value
THE PERMANENT INCOME hypothesis is based on the idea of an unvarying lifetime “budget constraint” that remains in balance (which accords with Errol Flynn’s view that any man who dies with more than $5,000 in his bank account has miscalculated). The sum of the value of spending over a lifetime must equal the sum of income earned over that lifetime, what is referred to here as “lifetime income”. Borrowing and lending allow us to make lifetime plans rather than only living in the moment. It is lifetime income, and not income in any given year, that should guide a person’s decisions on how much to spend in that year. The conclusion may at first glance seem jejune, but in fact it is of central importance to understanding the effect of government efforts to “stimulate” the economy.
To understand hypotheses about lifetime consumption, we first need to see how we can sum the value of income over a lifetime into one number that the consumer takes into account when planning how much to spend this year. The concept that allows us to sum incomes over time is that of present value and the related principle of income discounting. To those who have taken a business math class, discounting is a concept no sooner painfully learned than eagerly forgotten. To economists it is important to the point of obsession and forms the basis of all analyses of how people choose between doing something now and doing it later. Despite these qualifications, discounting is really not so difficult to understand, and in fact should be a part of every educated person’s bag of mental tricks.
To see this, suppose you can give up two years of salary and $100,000 of tuition to earn a Harvard MBA. If the MBA raises your salary by $100,000 a year over then next 30 years, by how much will your wealth increase? You might answer that it will increase by $3 million, but that is wrong. Even business magazines make the same error. The answer fails because it adds quantities that cannot be compared. No one who has $1,000 US and €1,000 would say that his or her wealth was $2,000 unless the two currencies were at par. Similarly, $100,000 today cannot be simply added to the $100,000 you anticipate to get in twenty or thirty years. How would you choose if someone offered you $100,000 today, or the same amount decades from now? If you are like most people, you would say, “Now!”
People value money now more than later because they want to satisfy their cravings for immediate consumption. Money in your hand now is also an opportunity to invest and get a return over the years. To add up the value of all those future $100,000 salary increases due to the MBA we need to be able to convert future dollars to present dollars.
The formula for this conversion can be put in words. How much money would you have to put in the bank today for it to grow to $1 by next year? That is the key phrase in all discussions of discounting. If the interest rate is five percent then with a few strokes on a calculator you find that 95.2 cents in the bank today will grow to $1 next year. In a sense, you can think of this as being able to exchange 95.2 cents today for $1 next year. Put differently, you can “buy” a future dollar for 95.2 present cents. To stretch a point, a future dollar has a present value of 95.2 cents. This is how bonds are traded. No one ever talks about the interest rate in bond markets because what gets traded are future dollars for present dollars. So a bond promising
a payment of $1,000 in ten years may sell for $700 today. One may infer that the present value of $1 in ten years is 70 cents now. So that string of $100,000 revenue increases over 30 years that comes from a Harvard MBA is not $3 million. It is the sum of what you would have to save in the bank today to earn $100,000 in thirty years, along with the sum of what you would have to save in the bank today to earn $100,000 in twenty-nine years, and so on all the way back to the present. Not surprisingly, this sum is called the “present value” of the income increase over thirty years. It is also called lifetime income in economic models.
Perhaps the most difficult thing to accept initially about present value is that when a person saves more money now to increase his or her income in the future this has no influence on the present value of his or her lifetime income stream. The proof is simple. If you save a dollar at five percent interest, you get $1.05 next year. From today’s perspective the present discounted value of that $1.05 is just $1. This is not just a curiosity arising from accounting mathematics. It is of crucial relevance to the Friedman-Modigliani analysis. It means that savings do not increase the discounted sum of lifetime income. At best savings can help you space consumption between periods. Savings cannot help you to increase consumption in a present value sense across your lifespan.