finalexam

History of Economic Thought

Notes for Week 08

We have already seen that Jeremy Bentham was one of the founders of utilitarianism and

a leader of the Philosophic Radicals of the late 18th/early 19th century. When we first introduced

him, earlier in the semester, we focused primarily on the political implications of his ideas,

namely the democratic implications of his utilitarian principle “The greatest happiness for the

greatest number.” Now what we need to do is explain a bit more his utilitarian theory of human

behavior. This is necessary because his conception of human behavior was eventually taken up,

but in a more exacting fashion, by a new group of economists starting in the 1870s.

The classical tradition of Adam Smith, Thomas Robert Malthus, David Ricardo, Karl

Marx, and John Stuart Mill was eclipsed by a new crop of economists who began to organize

their ideas in a fashion that had more in common with Bentham than with Smith, Ricardo, or

Marx. In the 1870s, three economists, Wesley Stanley Jevons, Carl Menger, and Leon Walras,

independently of each other and initially unaware of each other’s work, published their theories

of individual utility maximizing behavior. Each of them was convinced that a proper scientific

understanding of economics must start with the idea of the rational, utility maximizing

individual. This set into motion a way of thinking that eventually came to be called Neoclassical.

With the publication of the works of Jevons, Menger, and Walras, economics shifted its

concern away from questions of economic growth and distribution, to questions of resource

allocation and relative scarcity. Instead of asking how economies grow over time, or how

economic growth is impacted by the distribution of income, these economists were more

concerned with figuring out how resources are allocated in the production of a given level of

output. And instead of organizing their ideas in terms of classes of people (workers, landlords,

and capitalists), these economists organized their ideas around a hyper-rational utility

maximizing individual, which presumably captured the way all individuals behave regardless of

economic class.

We will study this new era in economic thought, often called the marginalist revolution,

or marginal revolution, by focusing on the work of Leon Walras as a representative example of

this mode of reasoning. But before doing so, we need to reconsider Jeremy Bentham, so as to put

the “marginalists” in their proper context.

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Jeremy Bentham

As we’ve already seen, Bentham was convinced that humans are nothing more than

extremely complicated felicific calculators, forever engaged in lighting speed calculations of the

pleasure and pain which a course of action might entail. Every choice or action was ultimately

the result of calculations made regarding the relative balance of pleasure and pain such a choice

or action might bring about. If the pleasure which a potential course of action is thought to bring

about exceeds its possible pain, then the activity will be undertaken, if not, then not.

Central to this way of thinking was the notion that we, as individuals, are incapable

judging the actions of others to see if they are behaving in ways that maximize their net pleasure.

The most we can do is understand our own calculations of pleasure and pain, but we have no

way of knowing how someone else evaluates pleasure or pain. And precisely because all choices

are made by the individual, independently of others, we have no way of evaluating the relative

value of other people’s choices. All we have knowledge of is our own preferences (our notion of

what gives us pleasure and pain), not the preferences of others. Therefore, we are not able to

evaluate the actions of others, since we are incapable of getting inside their heads and

understanding their preferences.

This way of thinking assumes that humans have nothing in common with one another,

that somehow our preferences are entirely subjective and self-made, not the result of a common

heritage, socialization, history, genetic pool, etc. This, of course, is problematic and, I would

argue, wrong. We are social creatures and the choices we make are heavily influenced by

socialization, culture and history, not to mention a common genetic structure. What’s more, the

act of choosing and measuring the worth of differing possibilities, inevitably carries with it

attempts to learn from the choices and preferences of others, as well as comparing one’s

preferences to those of others. Individual preferences are influenced by the environment of which

one is a part and molded by the socialization to which one is exposed. In short, preferences are

largely social constructs, and choices frequently reflect that social context. Yet, Bentham

imagined that preferences and choices were entirely private to the individual and, as such,

beyond the capacity of others to truly understand. In short, Bentham and his follower (including

contemporary neoclassical economists) viewed individual preferences as sovereign, untainted by

socialization.

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There are two ways of conceiving this proposition. First, we can think of it as a political

statement regarding the proper relationship between the state and the individual. In other words,

claiming that individual preferences are sovereign, existing before the state and standing

independently of the opinion of others, is another way of saying that the state’s power must

ultimately be justified by the opinions of sovereign individuals. In short, there is a limit beyond

which the state must not transgress, unless reasonable arguments can be made that stay true to

the principle of individual sovereignty. From this perspective, whether or not individual

preferences exist independently of the broader social context is less relevant than the claim that,

regardless of where preferences come from, the individual has a right to express them. This

version of the idea seems reasonable but is more of a political statement than a scientific one. It’s

not intended as a statement of how individual preferences are formed, or how individuals make

choices, it’s instead a political proposition claiming that the individual has preferences,

regardless of how formed, that must be honored by the state.

Second, as a theory of human behavior this proposition is palpably false. Individual

preferences are forever being constructed through interaction with others. Socialization,

education, social mores, all play a role in molding the preferences of individuals, creating a

community of people who share common beliefs and values, including the values that reflect

consumption, the accumulation of wealth, and reputable occupations. In short, the preferences

and opinions of individuals are formed through a complex dialectical interaction between society

and the individual.

Yet, while Bentham believed that one could not, as a strict principle of science, judge the

adequacy of another person’s decisions (since they are ultimately a private, sovereign, choice),

he nevertheless was convinced that education would make us all better “choosers”, encouraging

us to make choices that are more refined and uplifting, rather than debased and low-class. So,

while we cannot force another person to make the “correct” choice, we can rest assured that the

probability of making the right choice will increase with education. Thus, the best way to bring

about a society of enlightened “choosers” was through public education, allowing everyone to be

educated and become better calculators of pleasures and pain. Bentham was convinced that

educated people would inevitably make better choices than uneducated people. It’s important to

keep in mind, however, that the kind of education Bentham had in mind was that of the classic

liberal arts; that is, an education that focuses on philosophy, ethics, history, mathematics, the

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arts, etc. He did not mean the kind of practical education that one finds in trade schools or

business schools.

Clearly, there’s a tension in Bentham’s conception of individual preferences and choice.

On the one hand he insists that they are sovereign and stand independently of the preference and

choices of others. On the other hand, and despite claiming that we cannot, as scientists, pass

judgment on the preferences of others, he prefers a society of educated individuals over one of

untrained hedonists. In other words, preferences can be molded by the group, either informally

through socialization and acculturation, or formally through conscious instruction and education.

Bentham’s acceptance of the latter possibility contradicts the idea that individual preferences and

opinions stand independently of the group or society at large.

Closely related to this idea was Bentham’s belief that society is nothing more than a

fiction, a convenient term we use to describe a collection of individuals. Society, Bentham

believed, does not exist independently of the individuals that make it up. That is, the belief that

we can think of a society as a system that has a history, culture, and outlook that’s different from

that of another society is really another way of saying that the choices and actions undertaken by

the individuals in the first society is different from that of the choices and actions of the

individuals in the second society. The idea that the individual reflects the values and ideals of the

society of which she/he is a part, is non-sensical to Bentham. He instead argued that the values

and ideals of a society are nothing more than the aggregation of all the individual preferences

and choices.

This way of thinking about the relationship between the individual and society started

with Bentham and became central to economic thinking with the arrival of the marginal

revolution; and it is still a central component of contemporary neoclassical economics. The way

we usually encounter this belief is in our microeconomic courses, where the student is taught the

logic of utility maximization to explain the notion of the individual demand curve, and is then

told that market demand, or aggregate demand, is nothing more than the summation of all the

individual choices made by all the individuals in society. Society, in short, is just a summation of

individual behaviors and beliefs.

The theory of human behavior that emerges from the utilitarian perspective is essentially

a passive one; that is humans are portrayed as creatures that only respond to stimuli of pleasure

or pain. If, somehow, the configuration of all possible pleasure and painful stimuli could be held

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constant, then the human will quickly determine those actions that provide the greatest net

pleasure and continue reproducing those same actions until the external stimuli are changed. In

short, the human remains in equilibrium until circumstances change. That is, the individual

human is not thought of as needing, or desiring, action; the individual is not seen as an entity that

achieves ends that emerge from the imagination; instead, all action is the result of external

stimuli of pleasure or pain. The extreme version of this idea is found in the neoclassical theory of

the consumer, which imagines humans will continue consuming the same utility maximizing

goods as long as the prices and initial endowments remain unchanged (preference patterns are

always assumed stable by the neoclassicals).

This vision of human behavior was criticized by Marx and Veblen, as well as Nietzsche;

and while Smith never had an opportunity to respond to this theory, since it emerged as a popular

idea after his death, it’s obviously inconsistent with his notion of sympathy. Smith, Marx and

Veblen see humans as purposeful, teleological, agents who become in the process of doing; that

is, work and creativity is central to what it means to be human – we imagine, create, and do

things, independently of external stimuli. Perhaps the wittiest critique of this position was

offered by Friedrich Nietzsche (in the late 19th century) who said, “Humans do not strive for

happiness; only the Englishman does that.”

Before closing my remarks on Bentham, I need to draw attention to a policy proposal

that was discussed by Bentham and was later taken up by Neoclassical economists in the 20th

century, namely the welfare implications of income and wealth redistribution. Bentham accepted

the possibility that a redistribution of wealth and/or income from the wealthy to the poor could

increase the level of net happiness for society as a whole (for the greatest number of people). But

while he accepted this as a possibility, he also believed that such a policy would heighten the

insecurity (and consequently pain) of property owners, due to the loss of property which such a

proposal would entail. What’s more, the pain of those whose property is reduced could outweigh

the happiness of those whose property is enhanced. Therefore, despite acknowledging the

benefits that redistributing wealth from the rich to the poor could bring about, he did not

advocate this policy because he believed that the unhappiness of those whose wealth was

reduced would outweigh the happiness of those whose wealth was increased.

This policy proposal is interesting not simply because it underscores the possibly radical

implications of utilitarianism (that wealth and income redistribution might be consistent with

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“the greatest happiness for the greatest number” principle), but because it’s an early precursor of

a way of thinking called welfare economics, which took off in the 20th century with the work of

Arthur Pigou, a famous neoclassical economist. Like Bentham, Pigou also explored the

possibility of redistributing wealth and income as a way of increasing the happiness of society as

a whole, what he called the welfare of society. The field of welfare economics which Pigou set

into motion, sought to lay out the conditions under which redistribution might, or might not,

improve the welfare of society as a whole.

Finally, it should be noted that Bentham’s theory of choice was limited by the fact that he

framed the issue in terms of absolute amounts of pleasure and pain. That is, he thought of the

choice which an individual would make as being the result of a calculation of the amount of

pleasure that such a choice might bring about relative to the level of pain it might entail. It

wasn’t until the marginalists came along in the 1870s that it became obvious that rational choice

is not a function of the absolute amount of pleasure versus pain, but rather a function of the

marginal pleasure (benefit) versus the marginal pain (cost) which a choice might entail. This

distinction was monumental and helps explain why it wasn’t until the 1870s that Bentham’s

initial hunch about utility maximization evolved into an analytical framework that came to

dominate the discipline.

Leon Walras

Leon Walras was a passionate, idealistic, thinker driven by a desire to improve humanity.

He thought of himself as a socialist, but not as a Marxist or utopian socialist, but more in the

mold of Fabian Socialism or democratic socialism. He favored the nationalization of land and

believed that the rents collected by the government should be used to fund a variety of

progressive social programs. He was comfortable with the idea of nationalizing industries that

were natural monopolies and was in favor of the redistribution of income and wealth as a way of

rectifying the economic inequalities characteristic of capitalist societies. It’s important to not lose

sight of this because his major theoretical contribution, the theory of a general competitive

equilibrium (GCE), is inevitably invoked by economists who see capitalism as having an

inherent tendency to move toward a full and efficient utilization of resources; and, as such, does

not require government programs intent on promoting full employment, efficiency, income

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redistribution, or a wide range of public goods. Walras would not have agreed with this. In short,

it’s a mistake to classify Walras as a free-market ideologue.

He spent a lifetime trying to figure out the nature of exchange and the properties he

thought were inherent to a competitive market system. He wanted to resolve, once and for all,

whether or not a system of free competitive markets is capable of coordinating the actions of all

the individuals in the system (as Smith had suggested, though never proved) in such a fashion

that resources are fully employed. In the process of developing the mathematical argument

needed to explain this idea Walras also uncovered the conditions under which such a state of

affairs might not work and, as a result, would require government action. In other words, he saw

his GCE theory as providing a guide for public policy, in the sense that it clearly demarcated

conditions under which competitive free markets could work, and conditions under which they

wouldn’t.

Walras started by working out the mathematics of individual exchange. He wanted to

explore how the rate of exchange is determined by individuals (traders) who are intent on

offering one good in exchange for varying amounts of another good. The focus is on exchange

and not production (as was the case with the Classicals). As such the items being exchanged

don’t have to be the result of on-going production, they can be anything; and for that reason, the

neoclassicals start using the term “good” instead of the term “commodity” to describe the things

being exchanged in the market. Remember that the term “commodity” is intended to apply to any

good that is produced with the intention of earning a profit upon its sale. In contrast a good is

anything that has utility or use value, regardless of whether it’s a commodity. Thus, a pretty rock

found in the wilderness is a good, but a MacDonald’s hamburger is a commodity. Of course, all

commodities are goods, but not all goods are commodities. The former are produced for profit,

while the latter are not.

So, to come back to Walras’s original explanation of individual exchange, the items to be

traded by the two participants to an exchange (the buyer and the seller) are goods which may or

may not be commodities. At this point, the issue of whether or not they’re commodities is

irrelevant to the logic of exchange. All that matters is that both participants to the exchange own

something which they’re willing to exchange, in varying amounts, for the right of owning the

other good. Later on, after having developed the logic of individual exchange he places

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production for profit, and thus commodities, within the context of a GCE. We’ll see that later in

the next note.

Since the items being exchanged are goods and not necessarily commodities, the issue of

production cost is irrelevant to the logic of individual exchange. Each trader, when

contemplating how much of any one good to offer in exchange for another good, is not

considering issues of cost; all that she or he is concerned with is the subjective pleasure,

satisfaction, contentment, or utility, that the ownership of such a good might provide. So,

exchange is now placed in the realm of utility, with each trader trying to estimate the utility that

might be gained from owning the desired good, versus the utility that will be lost from offering

in exchange the good currently owned. In other words, the motivation to enter into exchange,

according to Walras, is the desire to enhance or maximize utility.

This should immediately alert the contemporary reader to an interpretation of utility

maximization that has been lost in contemporary textbooks. Now-a-days it’s common to find

textbook interpretations of utility maximization that focus on consumption, literally consumption

– as in consuming hamburgers and French fries and soft drinks. The examples are invariably

food items as a way of underscoring the sense of satiation we inevitably experience when

consumption goes beyond a certain point. But Walras didn’t see utility in this fashion. Utility

wasn’t a function of how much one could consume, it was instead a function of ownership. In

other words, it was the ownership of something that generated utility, regardless of whether one

literally consumed the good. Thus, he saw humans as deriving utility from the ownership of land,

buildings, clothing, a pretty rock, etc., as well as food. But, in an effort to maximize utility the

individual will enter the marketplace in the hope of offering varying amounts of whatever goods

she/he might currently own, and is willing to part with, in exchange for other goods which the

trader is convinced will increase her/his total utility. In other words, we enter into exchange in

an effort to increase our utility. So, with Walras, utility maximizing behavior is intimately tied to

market behavior – we buy and sell things because we want to improve our utility.

Figure 1 displays the behavior that Walras, and all the early neoclassicals, assumed was

common to humans. The top graph shows how utility behaves as the ownership of B increases.

Note that utility increases at a diminishing rate. The bottom graph shows how marginal utility

behaves as the ownership of B increases. Note that it continually diminishes as the ownership of

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B increases. The marginal utility curve measures the extra amount of utility that’s derived from

owning just a little bit more.

Figure 1

While utility and marginal utility have these properties, regardless of the good in

question, the intensity of utility and marginal utility will vary from one good to another and from

one individual to another. For some individuals the marginal utility of any good might be higher

or lower than it is for other individuals. And for any one individual, the marginal utility of

different goods will in general vary. Thus, while marginal utility diminishes with the ownership

of any one good, the intensity of the desire for one extra unit of a good can vary from individual

to individual and from good to good.

What’s more, Walras, and all the neoclassicals, saw utility as a purely private estimation

untainted by the opinions of others. That is, our individual estimations of utility are sovereign in

the sense that they emerge from subjective preferences that somehow exist independently of the

group, society, or culture of which we’re a part. A major reason for this requirement is that, if

utility were indeed dependent on our interaction with others, on our socialization, on our

exposure to culture (and the advertising and business media that molds that culture), then

neoclassicals would not be able to claim that market outcomes are the result of sovereign

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individual choice. Central to the neoclassical message is the idea that it’s the consumer that’s

driving the system and it’s his/her preferences that dictate what will be produced and how it will

be produced. But if, individual preferences are largely molded by socialization and culture, and if

culture in a capitalist society is molded by the ideology and profit motive of the business class,

then it’s not necessarily true that utility is an expression of individual preference, it might instead

be an expression of the ideology and profit motive (marketing) of business. In this case, market

outcomes are not the result of consumer choice; they might instead be the result of sovereign

business interests. We consume not in response to our private and highly rational estimations of

desire but rather in response to the profit motive of business.

None of these issues enter into Walras’s conception of utility, he proceeds throughout his

Elements of Pure Economics on the assumption that the utility the individual experiences from

owning various amounts of anything are a purely subjective estimation and no effort is made to

figure out the role, if any, of socialization, culture, or group behavior.

It’s important to note that Alfred Marshall was a bit more pragmatic in his discussion of

utility maximizing behavior. He was aware of the fact that socialization and culture have an

influence on the individual’s estimation of utility, but he did not see this as an indictment against

this way of thinking. While our preferences may indeed be molded by culture, and business

culture in particular, this does not mean that we are incapable of arriving at an estimation of

desires (utility) independently of our cultural surroundings. We do make choices that differ from

the group and while they may reflect the broad influence of culture and socialization, there’s

enough individuation to warrant the claim that, ultimately, a consumer’s choice is a reflection of

what he/she wants, even if there is a cultural influence. While market outcomes may not be a

reflection of consumer sovereignty in its pure form, since it will be adulterated by culture, it’s

nevertheless true that consumers exercise veto power in the sense that if there’s something they

don’t like they won’t buy it, regardless of all the hype surrounding the good.

Now, to come back to Walras’ interpretation of utility maximizing behavior; we can

imagine an individual owning good A (say apples) but wanting B (say bread) and analyze how

the individual’s total utility would change if he decided to purchase some B in exchange for

some A. The extra B purchased would generate a certain amount of marginal utility, adding to

the individual’s total level of utility; but the A that would have to be given up in exchange,

would bring about a reduction in marginal utility, reducing the individual’s total level of utility.

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If the marginal utility that’s gained from purchasing B exceeds the marginal utility that’s lost

from giving up A, then the individual’s total utility will have been increased by that exchange.

Indeed, the individual will be motivated to continue buying B and offering A as long as the

marginal utility to be gained from one more unit of B exceeds the marginal utility lost from

giving up A. This process will continue until the marginal utility gained from buying B just

matches the marginal utility lost from giving up A. At that point, the individual’s total utility will

have been maximized and will have ended up with a higher total level of utility than when the

exchange first started.

Figure 2 provides a graphic version of this idea. It should be noted that while Leon

Walras thought in these terms (using commodities A and B), this specific diagrammatic

technique is due to William Stanley Jevons. The top graph shows the marginal utility of B curve

and three curves showing the marginal utility lost by giving up units of A, at three possible rates

of exchange (prices) of B in terms of A. Note that the marginal utility lost is equal to the price of

B in terms of A multiplied by the marginal utility of A (that is pb,aMUa). Quantities of B are

measured on the horizontal axis with increasing amount of B going from left to right. The

marginal utility of B is measured on the left vertical axis. The marginal utility of B curve (MUb)

is shown downward sloping, decreasing as the ownership of B increases from left to right. The

more of B that’s owned, the lower the marginal utility gained from one more unit of B.

Now focus on the curve labeled pb1∙MUa. It represents the marginal utility of A

multiplied times the price of B (which, in turn, is equal to the amount of A that must be given up

for one more unit of B). If the price of B in terms of A is 1 (i.e., pb1 = 1), then the pb1∙MUa curve

is nothing other than the marginal utility of A curve (MUa). The marginal utility of A is

measured on the right vertical axis and quantities of A are measured on the horizontal axis going

from right to left. Note that the marginal utility of A (in this case pb1∙MUa , where p = 1)

diminishes as the ownership of A is increased from right to left.

If the individual owns A but no B, then he is up against the left vertical axis. As the

individual begins to offer units of A in return for B, he loses amounts of A as well as

increasingly greater amounts of marginal utility of A, moving up the pb1∙MUa curve. But, at the

same time, he gains units of B and marginal utility of B but at a diminishing rate, moving down

the MUb curve. The cost of purchasing one extra unit of B is the marginal utility of A that’s lost

from giving up A. Since the price of B in terms of A represents the amount of A that must be

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given up for one more unit of B, and the marginal utility of A represents the extra utility that’s

lost from giving up one more unit of A, then the product of pb and MUa, i.e., pb∙MUa, represents

the marginal utility that’s lost from purchasing one more unit of B.

Figure 2

So long as the marginal utility gained from one more unit of B exceeds the marginal

utility lost from giving up units of A, then the exchange is adding to the individual’s total utility

and she/he will be motivated to continue offering A in exchange for B. But each extra exchange

means that the marginal utility of B gained keeps getting smaller while the marginal utility of A

lost keeps getting greater; that is, total utility is growing at increasingly smaller rates, but

growing, nevertheless. Eventually, the individual will move to the point where the marginal

utility of B gained just matches the marginal utility of A lost. At that point there is no further

incentive to exchange, and the individual will have maximized utility. This occurs at the point

where the marginal utility of B curve intersects the marginal utility of A curve.

That is, the individual will maximize utility by exchanging good A for good B up to the

point at which the marginal utility gained from one more unit of B (MUb) just matches the

marginal utility lost from giving up units of A in exchange (pb,aMUa),

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MUb = pb,aMUa.

It should be noted that this condition is nothing more than the more familiar utility

maximizing condition the contemporary reader is more accustomed to seeing. Thus, if we

rearrange the above expression, we can restate this condition as

𝑀𝑈𝑏 𝑀𝑈𝑎

= 𝑝𝑏,𝑎

or, in monetary terms,

𝑀𝑈𝑏 𝑀𝑈𝑎

= 𝑝𝑏,$ 𝑝𝑎,$

which is the way in which this idea is most frequently expressed in contemporary textbooks.)

The above analysis was carried out on the assumption that the price of B was 1. But the

same outcome would occur if the price were different than 1. If, for example, the price of B is

increased, then the extra utility that’s lost from purchasing one more unit of B will increase,

because the extra amount of A that has to be given up increases, causing the extra utility of A

lost to also increase. This is represented in the above graph by showing two other pb*MUa curves

that are higher than the pb1*MUa curve. Each increase in the price of B causes the pb*MUa curve

to shift up. Note that each price increases, and consequently higher pb*MUa curve has the effect

of leading to a different utility maximizing choice. Indeed, the utility maximizing choice of B

purchased will decrease as the price of B increases from 1 to 2 to 3, other things equal. The

bottom graph in figure 2 shows the demand curve that’s derived from this kind of exercise. It

shows the utility maximizing amounts of B that the individual would purchase at different prices,

given his marginal utility of A and B schedules.

It’s important to note that, from the neoclassical perspective, the demand curve represents

the set of utility maximizing amounts of any good B which the individual would purchase at

various possible prices of B in terms of A. This does not mean, however, that all the choices

individuals make are always utility maximizing choices. Walras, perhaps more so than other

neoclassicals – and particularly with regard to contemporary neoclassicals, viewed utility

maximizing behavior as a learning process. As the price of a good increases, as in the above

example, we will eventually begin to purchase less of the item, but that doesn’t mean that the

amounts we begin to purchase at the higher prices will in fact be utility maximizing choices, we

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might make mistakes and purchase too little or not enough; in other words, we might be off our

demand curve. But all this means is that we are in a state of disequilibrium and, so long as

everything else remains the same, we will adjust our behavior and eventually move toward the

correct point on the demand curve, purchasing that amount which indeed maximizes our utility.

Any point off the demand curve must represent a situation where the marginal utility of B in

relation to the marginal utility of A is unequal, motivating the individual to either increase or

decrease the purchase of B in terms of A, until the marginal utility of B gained is just equal to the

marginal utility of A lost (which happens on the demand curve).

Walras saw the demand curve as the basis from which offer curves can be derived. Once

we know the utility maximizing amounts of anything that an individual might want to purchase,

we also know, by default, the amounts of other things that would be offered in exchange. Thus,

the demand curve for B in terms of A also provides us with information on the amounts of A that

would be offered at various possible prices of A.

Figure 3 provides a visual representation of this idea. The graph on the left displays the

demand for B in terms of A, while the graph on the right displays the offer (supply) of A in terms

of B. We’re assuming that the demand curve represents the set of utility maximizing choices the

individual would make at various possible prices of B in terms of A. And since the offer of A in

terms of B is derived from the demand curve, it too represents a set of utility maximizing

choices, though in this case it’s the utility maximizing amounts of A that would be offered at

various possible prices of A in terms of B.

The offer of A in terms of B is derived in the following fashion. We start by noting that

the price of B in terms of A is the rate at which quantities of A, Qa, are offered in exchange for

quantities of B, Qb. That is,

𝑝𝑏,𝑎 = 𝑄𝑎

𝑄𝑏⁄ .

The total amount of A that would be offered to purchase some amount of B must be equal

to the price of B (in terms of A) times the amount of B purchased. That is,

𝑄𝑎 = 𝑝𝑏,𝑎 ∙ 𝑄𝑏.

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This is shown on the left graph by the rectangle formed by pb,a,1Qb,1. The area covered by that

rectangle must be equal to the amount of A offered when the price of B in terms of A is pb,a,1.

That is, the area of that rectangle is equal to Qa,1 shown on the horizontal axis of the graph on the

right.

Figure 3

But note that the amount of A being offered on the right graph is dependent on the price

of A in terms of B. It would seem that we need to know the price of A in terms of B, before

figuring out how much A to offer. This is easily resolved by noting that the price of A in terms of

B is nothing other than the inverse of the price of B in terms of A. That is,

𝑝𝑎,𝑏 = 𝑄𝑏

𝑄𝑎 ⁄ = 1 𝑝𝑏,𝑎⁄ ,

so that the price of A in terms of B is inversely related to the price of B in terms of A. If the price

of B in terms of A is pb,a,1 then the price of A in terms of B must be pa,b,1 = 1/pb,a,1.

Given this, we can plot the quantities of A that would be offered, on the right graph, at

various possible prices of A in terms of B, since those quantities are equal, on the left graph, to

the areas formed by the product of the price of B in terms of A and the quantity of B purchased.

As the price of B in terms of A gradually falls on the left graph, the price of A in terms of B

gradually rises on the right graph, and the rectangles formed on the left graph map on to the

quantities of A offered on the right graph, at various possible prices of A in terms of B.

pb.a pa.b

Qb Qa

pb.a,1

pa.b,1

Qb,1 Qa,1

Demand Curve Offer Curve

16

Walras believed that every individual in society could estimate the utility maximizing

quantities of anything they wished to purchase at various possible prices, and this would generate

the utility maximizing quantities of all the other things they would offer in return. In short, each

individual would have a fairly well-developed idea of the demand and offer of everything. As a

result, there would be a demand and offer curve for every good that might be exchanged in

society. Adding up all the individual demand and offer curves for some specific good, say good

B in terms of good A, would provide us with the market demand and offer of that good.

Figure 4 shows the market demand and offer of good B in terms of good A. Obviously,

the rate of exchange that clears the market would be pb,a,e, and the market clearing quantity

would be Qb,e.

Figure 4

Note that this represents the market demand and offer of good B in terms of A. Another

set of curves would emerge if we were to instead think of the market demand and offer of good

B in terms of C, or B in terms of D, and so on. In other words, Walras imagined that we can

develop such curves for all the possible ways in which any one good could be exchanged for all

the other goods.

Db,a

Ob,a

Qb

pb,a

pb,a,e

Qb,e