The classics versus the labor theory of value - Part VI - The Marginal Revolution
A cost-price theory is not the same than a labor theory of value
The Marginal (Copernican) Revolution
Let me first summarize the main points of the previous posts in this series about the history of price theory:
The classics did not have a theory of value (of use)
For the classics, it was a given that value of use is subjective
They had a theory of price based on the cost of production
Let me summarize the main points of the marginalist theory:
A theory of value (of use) is added to the body of economic theory
Subjective value is explained instead of being taken as given
Price theory is flipped: Final prices explain the cost of production
Succinctly, the Copernican revolution is equivalent to the marginal revolution in economics. Price theory is turned upside-down. Price theory goes from
cost → price to
price → cost.
The point of the marginal revolution was not to contrast a subjective theory of value to a labor (or cost) based theory of value but to solve the logical inconsistency in the classic price theory. The problem in the classic theory was the implied circularity of explaining price with costs and costs with prices.
The marginalists escape from this situation by adding a new component to economic theory: A theory of subjective value. The marginalist theory of price can be outlined as follows:
Marginal value → price → cost
This approach has no circularity because marginal value does not require an economic explanation. The problem was apparent for the marginalist thinkers. In the Austrian literature, for instance, the issue of how prices determine the cost of production was known as the “imputation problem.”
It is incomprehensible to properly understand the implication and motivation behind the marginal revolution without a proper understanding of the classic price theory. For instance, it is clear now that it does not make much sense to compare the marginal theory of value with the classic theory of price because those theories are about different issues. Similarly, there is no comparison between the marginal theory of value and the classic theory of value (of use) because the latter did not have one in the first place. What makes sense is to compare the marginalist and classic theories of price. Repeating myself, the following table summarizes the differences between the classics and the marginalists.
(Menger) vs (Jevons and Walras)
It is common to group the three marginalists (Menger, Jevons, and Walras) as one set of individual thinkers who independently arrived at the same theory in the early 1870s. In broad terms, this is correct. The three presented a marginal theory of value, and the three presented a
marginal value → price → cost theory. The three of them agreed that the classic price theory was wrong. However, a closer inspection of their theories shows subtle but essential differences. Jevons and Walras are closer to each other than either of them is to Menger.
Let me start with Jevons and Walras. Consider first the following passage by Jevons (1871, p. 44):
A quart of water per day has the high utility of saving a person from dying in a most distressing manner. Several gallons a day may posses much utility for such purposes as cooking and washing; but after an adequate supply is secured for these uses, any additional quantity is a matter of comparative indifference. All that we can say, then, is, that water up to a certain quantity, is indispensable; that further quantities will have various degrees of utility; but that beyond a certain quantity the utility sinks gradually to zero; it may even become negative, that is to say, further supplies of the same substance may become inconvenient or harmful.
This passage presents the principle of marginal utility with water as an example. But soon after, Jevons (1871, pp. 45-46, bolds added) continues the following way:
Thus the total utility of food we eat consists in maintaining life, and may be considered as infinitely great; but if we were to subtract a tenth part from what we eat daily, our loss would be but slight. We should certainly not lose a tenth part of the whole utility of food to us. It might be doubtful whether we should suffer any harm at all.
Let us imagine the whole quantity of food which a person consumes on an average during twenty-four hours to be divided into ten equal parts. If his food be reduced by the last part, he will suffer but little; if a second tenth part be deficient, he will fell the want distinctly; the subtraction of the third tenth part will be decidedly injurious; with every subsequent subtraction of a tenth part his sufferings will be more and more serious, until at length he will be upon the verge of starvation. Now, if we call each of the tenth parts an increment, the meaning of these facts is, that each increment of food is less necessary, or possesses less utility, than the previous one.
What Jevons is doing in the second passage is confusing the principle of marginal utility with that of satiation. Marginal utility is about the same good satisfying different preferences, not about how many units (as arbitrarily defined) are needed to fulfill one preference (i.e., hunger or thirst).
Consider now Walras (1874, pp. 461-463, bolds added):
We may say in ordinary language: “The want which we have for things, or the utility which things have for us, diminishes gradually as consumption increases. The more a man eats, the less hungry he is; the more he drinks the less thirsty, at least in general and apart from certain deplorable exceptions. The more hats and shoes a man has, the less need he has of a new hat or a new pair of shoes; the more horses he has in his stables, the less effort he will make to procure another horse, provided we neglect impulsive acts which our theory may ignore except when accounting for special cases.” But in mathematical terms, we say: “The intensity of the last want satisfied is a decreasing function of the quantity of the commodity consumed”; and we represent these functions by curves […]
Like Jevons, Walras is also confounding the principles of marginal utility with that of satiation. The following example may help. An art collector needs ten paintings to have a complete collection. Marginal utility states that the second collection of 10 (equal) paintings has a lower utility than the first ten paintings. And that the value of each collection is determined by the value of the marginal (the last) collection. The economic good is the collection, not the individual paintings. The examples of food and water build a marginal theory based on paintings rather than collections. Similarly, if the good is a car, it makes no sense to talk about the marginal theory of the first, second, third, and fourth wheels. The proper framing involves the marginal utility of the first, second, third, and fourth car.
Jevons and Walras’s treatment is still present today. Consider the following passage by Acemoglu, Laibson, and List (2015, p. 65, bolds added):
The more you have of something - for instance, slices of pizza - the less gain there is from acquiring another unit of the same good.
This is an example of a concept called diminishing marginal benefit: as you consume more of a good, your willingness to pay for an additional unit declines. An easy way to remember this concept is to think about donuts. My first donut in the morning is worth a lot to me so I am willing to pay a lot for it. My fourth donut in the same sitting is worth much less to me, so I am willing to pay less for it. In general, the more donuts I eat, the less I am willing to pay for an extra donut.
Consider now Menger (1871, p. 124, bolds added):
The lives of men depend on satisfaction of their need for food in general. But it would be entirely erroneous to regard all the foods they consume as being necessary for the maintenance of their lives or even their health (that is, for their continuing wellbeing). Everyone knows how easy it is to skip one of the usual meals without endangering life or health. Indeed, experience shows that the quantities of food necessary to maintain life are only a small part of what well-to-do persons as a rule consume, and that men even take much more food and drink than is necessary for the full preservation of health. Men consume food for several reasons: above all, they take food to maintain life; beyond this, they take further quantities to preserve health, since a diet sufficient merely to maintain life is too sparing, as experience shows, to avoid organic disorders; finally, having already consumed quantities sufficient to maintain life and preserve health, men further partake of foods simply for the pleasure derived from their consumption.
Menger also uses a food example but he is more upfront about different needs or preferences. Jevons and Walras think in mathematical terms, and the cases of food and water satisfy the convenience of differentiability in a utility function. Menger thinks in “economic” terms, focusing on discrete goods because that is the norm. For him, continuity and differentiability are neither requirements nor desired features of economic theory. It could be argued that because continuous goods are only a rare subset of all goods, Menger’s approach is more rigorous than that of Jevons and Walras. Mathematical tractability should not be confused with theoretical rigor or precision in economic terms.
An example of their different approaches is what happens in equilibrium. For Jevons (1871, p. 95) and Walras (1873, p. 145), the marginal rates of substitution (MRT) must be equal in equilibrium. In mathematical terms (where
U is the utility function,
p is the market price, and
x,y are two goods):
Menger (1871, p. 187, bolds added) does not conclude that MRT must be equal because perfect divisibility is not a needed component of economic theory:
This limit is reached when one of the two bargainers has no further quantity of goods which is of less value to him than a quantity of another good at the disposal of the second bargainer who, at the same time, evaluates the two quantities of goods inversely.
While Menger develops a general application of the marginal theory of value, Jevons, and Walras develop a particular (or narrower) application due to the mathematical constraint of continuity and differentiability. In the case of Jevons and Walras, mathematical convenience seems to have gotten the upper hand over economic precision. The mathematical approach facilitated the confusion between marginal utility and satiation.
Alfred Marshall: A Step Back
Interestingly, price theory makes a back step with Marshall’s work. This is of significance because Marhsall’s work still influences contemporary textbooks.
The marginal theory builds demand and supply from the consumer’s marginal utility. For the consumer, the price is the maximum willingness-to-pay (WTP) given the expected marginal utility the good will yield. If the consumer has n goods, his WTP is how much money he will pay for one more (n + 1). For the seller, the price is the minimum willingness-to-receive (WTR). If the seller has n goods, how much money is the minimum he must be offered to give up one unit (n - 1). Both buyers and sellers are consumers making a marginal evaluation to decide whether or not to trade. The former is adding one unit to his stock, and the latter is reducing his inventory by one unit.
There is a reason economists talk about “demand and supply” and not “demand and production.” Suppliers and producers need not be the same economic actors. The owner of a Picasso does not sell based on the cost of production but on the (marginal) utility he gets from owning the painting.
Marshall derives the supply curve from the production cost, not the marginal utility. For Marshall, utility (demand) has a more substantial influence on prices in the short term, and cost of production (supply) substantially impacts prices in the long run. Marshall’s (1890, pp. 348-340, bolds added) thought is summarized in one of the most famous passages in economics:
We might reasonably dispute whether it is the upper or the under blade or a pair of scissors that cuts a piece of paper, as whether value is governed by utility or cost of production. It is the true that when one blade is held still, and the cutting is affected by moving the other, we may say with careless brevity that the cutting is done by the second; but the statement is not strictly accurate, and is to be excused only as long as it claims to be merely a popular and not a strict scientific account of what happens.
In the same way, when a thing already made has to be sold, the price which people will be willing to pay for it will be governed by their desire to have it, together with the amount they can afford to spend on it. Their desire to have it depends partly on the chance that, if they do not buy it, they will be able to get another thing like it at as low a price: this depends on the causes that govern the supply of it, and this again upon cost of production. But it may so happen that the stock be sold is practically fixed. This, for instance, is the case with a fish market, in which the value of fish for the day is governed almost exclusively by the stock on the slabs in relation to the demand: and if a person chooses to take the stock for granted, and say that the price is governed by demand, his brevity may perhaps be excused so long as does not claim strict accuracy. So again it may be pardonable, but it is not strictly accurate to say that the varying prices which the same rare book fetches, when sold and resold at Christie’s auction room, are governed exclusively by demand.
Taking a case at the opposite extreme, we find some commodities which conform pretty close to the law of constant return; that is to say, their average cost of production will be very nearly the same whether they are produced in small quantities or in large. In such a case the normal level about which the market price fluctuates will be this definite and fixed (money) cost of production. If the demand happens to be great, the market price will rise for a time above the level; but as a results production will increase and the market price will fall: and conversely, if the demand falls for a time below its ordinary level.
In such a case, if a person chooses to neglect market fluctuations, and to take it for granted that there will anyhow be enough demand for the commodity to ensure that some of it, more or less, will find purchasers at a price equal to this cost of production, then he may be excused or ignoring the influence of demand, and speaking of (normal) price as governed by cost of production – provided only he does not claim scientific accuracy for the wording of this doctrine, and explains the influence of demand in its right place.
Thus we may conclude that, as a general rule, the shorter the period which we are considering, the greater must be the share of our attention which is given to the influence of demand on value; and the longer the period, the more important will be the influence of cost of production on value. For the influence of changes in cost of production takes as a rule a longer time to work itself out than does the influence of changes in demand.
Marshall’s theory can be summarized as the classic + marginal theory.
Understanding the classic price theory points to a problem in Marshall’s theory: He rebuilt the circularity present in the classic price theory. In Marshall’s approach, the cost of production (supply) needs an explanation that does not depend on another analysis of demand and supply (cost of production). Menger, Walras, and Jevons argued that the classic price theory was wrong. Marshall, on the contrary, argued that it wasn’t wrong but incomplete.
As this series of posts shows, talking about labor-theory of value or cost-theory of price is not splitting semantics. The implications are profound and far-reaching. The case of Marshall is just one example of the risks of overlooking the history of economic thought. The interpretation of what the marginal revolution was about is another one.
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