Giffen’s Paradox and the Law of Demand

0:00Part of the motivation for the paper is that, you know, in many years of discussing Austrian economics with students, particularly graduate students, at our Rothbard Graduate Seminar, when discussing the differences between the Misesian, Rothbardian approach and the mainstream neoclassical Volrasian approach that most of us are taught in graduate school, one of the questions that consistently comes up relates to the so-called Giffen Good and the decomposition of Price Change Effects into Distinct Income and Substitution Effects. According to Mises, the laws of economics are apodictically true, the law of demand is stated not as a tentative empirical proposition subject to validation, falsification and so on but as something that is derived from first principles that's praxeologically true.

0:53How can it be, students often ask, how can you claim that demand curves are downward and Forward Sloping as a Praxeological Truth, when we know there are some rare exceptions, such as the infamous Giffen Good, discussed in Marshall's Principles. I couldn't find a picture of Sir Robert Giffen. Google Images didn't come up with anything. I don't know if you guys, any of you have, if you know if his portrait or photograph exists? If so, I'd love to have a copy of it. That's a picture from an old story about the Irish potato famine from which the Giffen story is derived, although apparently the account given by Robert Giffen that is related to Marshall's principles is somewhat fanciful, according to scholars who have investigated.

1:39For example, Giffen was a very small child during the time of the potato famine and reported some details as if they were first-hand, with things that a small child wouldn't have possibly known, but that's a subject for another day. So, you know, part of the background and context here is that, is the idea that the Mangerian tradition, the Austrian tradition, the work coming out of Menger, is actually quite a bit more diverse and heterogeneous than we often recognize. That among many contemporary Austrians, Mises, Rothbard are considered sort of standard mainstream figures in Austrian economics. Mises' views on methodology, on price theory and so on are often taken as sort of the quintessential 20th century Austrian views.

2:32And in fact, there's a lot more heterogeneity in the Austrian School from the very beginning, from almost the very beginning, at least from the second generation, that one of the great things in Guido Hulsman's biography of Mises is providing some content about the sort of milieu in which the Austrian School developed in Vienna and what the early Austrian School was like and that many of the second, well, many of the third and so-called fourth generation and Austrians were schooled in a very different approach from that of Mises, which Mises learned from Boehm-Bawerk. So we begin with the classic de-homogenization by William Jaffe between Menger and the two other marginal revolutionaries, Jevons and Valras. So we recognize Menger offering a very distinct approach to marginal utility theory, to value and price theory, than did his other marginalist revolutionary contemporaries.

3:28What people often don't recognize is that Menger's unique approach did not become the only approach within the Austrian School. In fact, one could identify two distinct traditions within the core value and price theory of the Austrian School. What Joe and I call the causal realist tradition, which starts from Menger and includes, most importantly, Boehm-Bawerk, The so-called Anglo-American Austrians, Wickstede, Federer, Davenport, to some extent J.B. Clark, and then Mises and Murray Rothbard. Whereas within the Austrian School, another sort of parallel approach, which we might call the neo-Valrasian tradition, was very important and influential in the Austrian School. Wieser himself had a very idiosyncratic position that was based on Menger's insights, in a very different direction than de Boehm-Bawerk. Schumpeter, of course, was extremely influential to the Austrians of Hayek's generation, though Schumpeter's own inclination was much more towards Wieser and even more so towards Walras. Maybe Hayek himself to some extent is in this neo-Walrasian tradition, sort of an interesting statement in an unpublished fragment that

4:42Hayek drafted in the late 80s for the New Pahlgrave Dictionary, which was published In 1992, in volume 4 of Hayek's Collected Works, but didn't make it into the New Pall Grave, he had this very unusual statement, he says, in talking about value and price theory, he says, equally important is what may well be regarded as the final formulation of the marginal utility analysis by J.R. Hicks. Of course, he's referring here to the sort of standard neoclassical indifference curve presentation of value theory. He says, Jair Hickson, the concept of the marginal rate of substitution, based on the indifference curve technique introduced by Irving Fischer and F.Y. Edgeworth, this conception of varying rates of substitution or equivalence, wholly independent of any conception of measurable utility, may well be regarded as the ultimate statement of more than half a century's discussion in the tradition of the Austrian School. That's a very odd statement if you assume that the indifference curve analysis are somehow distinct or different from Menger's view of value and utility theory.

5:49What do we mean by causal realist analysis? What are its basic features or aspects? Well, it proceeds along the following steps. A core idea is this notion of general interdependence among markets, among variables, if you like. Dr. Blau called it concept of total equilibrium. Think of it as like a kind of general equilibrium concept in a very extreme sense. So we start with some initial data, consumer valuations, people's ordinal preference rankings over different goods, and stocks of various goods. In a pure exchange economy, we would start with stocks of goods to be exchanged. In an economy with production, we would start with goods of factors of production that can be used by entrepreneurs in the production process.

6:38And so the result is an initial, if you like, equilibrium of an equilibrium structure of prices and quantities. Then we employ what Robbins called the method of variations or what Mises called state of rest analysis and what is more or less what most of us know as so-called comparative statics, right? Where we want to understand what is the effect of changing In one of these initial data, what effect does that have on outcomes? So we hold everything else constant, we vary this one particular datum, and we trace its effects in the market. So again, holding other things equal, we look at the variation in one variable, keeping everything else constant.

7:26How does this work for value theory? Well, let's walk through Menger's approach to the law of demand. Because it really is quite different from the approach that you get in the contemporary textbooks. So again, Menger starts with a preference ordering. The consumer has a ranking of different possible courses of action, different goods or bundles of goods that can be consumed. But there's also the key concept of supply. And Menger's notion of supply is that in the mind of the individual, There is a stock, a certain number of units of a good that are perceived to be homogeneous. So there's a concept of a stock of a good. There must be multiple units of a good which can be employed to alternative ends.

8:12So gallons of water or sacks of wheat or roast beef sandwiches. So this is still subjective, but in the mind of the consumer, those individual units are identical, equally serviceable. So they make up the components of the total supply of that good. And the law of demand, as most of us know it, in the Mangerian fashion, right? Is that additional units of this homogeneous good, additional units of this stock or supply, are, you know, allocated to successively lower and lower value uses. The concept of diminishing marginal utility. Now, note here that when Menger, in the Mengerian approach, when we talk about diminishing marginal utility, what we really mean is diminishing utility for marginal units of the good.

9:03Okay, so there is no quantity of marginal utility, right? We're saying that marginal units, additional units of the good, are allocated to uses that are less valuable to the consumer than the uses to which the previous units were allocated. So it's a completely ordinal notion. There are no quantities of utility. But it's important to remember that the adjective marginal applies to the units, not to the utilities. In fact, the term marginal utility is a little bit misleading in this context because many people think of it in sort of calculus terms, right? That means the change in total utility. But in Menger's concept, there is no total utility. There is only marginal utility.

9:48So you could even say the utility of the marginal unit or the total utility of the marginal unit, if you like. So with each additional unit, the utility, The total utility of that unit is smaller than the utility of the previous unit by virtue of the fact that it was allocated to a use that was lower on the consumer's valuation scale. Now also notice that the concept of marginal utility in Menger's framework only applies when you have multiple units of a homogeneous good. So if I only have one potato and one roast beef sandwich and one gallon of water and and one sack of wheat, it doesn't make any sense to talk about the marginal utility of any of those units because they're all heterogeneous.

10:35So we have to have multiple units of a homogeneous stock for the concept of marginal utility even to apply. And so Menger gets the downward sloping demand curve. We get the downward sloping demand curve on the assumption with the idea that the consumer's willingness to pay for successive units of a homogeneous good goes down as the number of units is increased, okay? Let's talk for a moment about the sort of Hicks Allen version of utility theory that is in the contemporary textbooks, right? So the starting point in the neoclassical valuation approach is not units of a homogeneous good, but bundles, heterogeneous bundles of goods, okay? So in Debreu's theory of value, there's N units of goods in existence, and consumers are assumed to have preferences over all possible combinations or N-tuples of those goods that are existence, right?

11:32So, you know, bundle, if there's three goods in existence, apples, pieces of candy and iPods, right, you can imagine three bundles. Bundle A is one, one and one. Bundle B is two, one and one. Bundle C is one, two and zero, and so on. So we think of all possible combinations of these three goods that can exist, and then we ask the consumer to rank each bundle, each one of those three item combos. So each bundle is heterogeneous, no two bundles are alike. And we could map them out in a space, let's say we forget about iPods for a minute, suppose there's only apples and candy, and we can label each bundle on a diagram like this, we can place it in two-dimensional space like this and then we ask the consumer for every pair of bundles, do you prefer bundle A to bundle B, bundle B to bundle A or neither A to B and then we draw, we construct the consumer's indifference map based on the responses to those questions and you have the sort of standard assumptions about the preference ordering that you have to have transitivity

12:40and so on. But again, remember, this is a preference ordering over bundles of goods. It's not an ordinal preference ranking over heterogeneous, it's not individual units of goods. So the consumer doesn't have a utility for apples or a utility for candy, right? The consumer only has preferences over different combinations of apples and candy. And then, you know, the combinations for which the consumer answers, I neither prefer one to the other, we say, ah, those must lie on the same indifference curve, and we draw indifference curves in the standard way. Now, how do you get demand curves out of this? Well, you do this, you start with an initial equilibrium in which there's a ratio of prices.

13:28Prices are represented by the ratio between the price of the good on one axis, the price of the good on the other axis. And we say, well, let's imagine all hypothetical exchange ratios that could exist. Give the consumer an amount of money to spend, income, they call it, really more like wealth, it's a stock and not a flow. And we say, given that amount of money and given a ratio of relative prices, what's the highest indifference curve on which the consumer can pick a bundle? And then we say, well, what happens if that price ratio were to change? So, in this example here, I just cut and paste this out of a textbook, right? So, I guess they have the initial equilibrium is at this point here.

14:13So, you have, so given income and the relative prices represented by this line, this point right here is the highest point that the consumer, highest indifference curve the consumer can get on. Say, well, what happens if the price of the good on the horizontal axis increases? So if the price of product B increases relative to the price of product A, the budget constraint pivots along this point here. We say, ah, the consumer can no longer afford the original consumption bundle. Now the best the consumer can do is this point right here. But notice, in the standard fashion, you say, ah, well, what if we were to vary, oh, sorry, I said this wrong. Here's the initial, I guess, sorry, it's a decrease in the price of B.

14:58So, starting here with the steeper line, the price of B decreases, the budget constraint becomes flatter, it pivots around this top point, and we say, well what if we were to vary the price ratio but keep the consumer on the original indifference curve, then where would he be? Well, if we simply changed the slope of the price line that kept the consumer on his pink indifference curve, then he would consume at a point like this. So they say, well, here's the substitution effect. Then allow income to increase, and you get out here to this final point here. So this is sort of standard decomposition of the effects of a price change into two separate pieces, a substitution piece and an income piece.

15:45Right, so if you do that, then it's conceivable under the sort of particular assumptions that you could actually have an income effect That's so large, it more than overcomes the substitution effect. So you have a good that's strongly inferior, like potatoes it is said, it's a large portion of the consumer's budget and so on. So you can have the substitution effect going from this point to this one, but then an income effect that actually pushes the consumer to a level of the good on the horizontal axis that's lower than it was before. Right, so the so-called Giffen good case is where the price of the good on the horizontal axis has gone up, sorry, the price has, did I get this wrong?

16:37Yeah, so the price is going down, that's right, the price has gone down, but he's actually consuming less of the good than he was initially. Okay, so the price has gone down and the quantity demanded has decreased, which sounds like an upward sloping demand curve. So in the standard Volrasian, Hixian, Dubruvian analysis, what we get, starting with these bundles and the rankings of bundles, is a kind of a conditional law of demand, where depending on the relative magnitudes of the income and substitution effects, the sign of the income effect and so on, if the price of a good goes down, the consumer could end up consuming more of that good, the same amount of the good, or less of the good, depending on the peculiarities of the case. Okay, so it's a very different notion of a sort of apodictically true universal downward sloping demand curve.

17:26So the demand curve could slope up in this sort of scenario. Now what's wrong with this? A few different ways to look at it. Right, one thing that's, there's a, first there's a kind of circularity here. And this comes up in sort of neoclassical production theory as well. Namely that, you know, what we're trying to explain ultimately is prices. So we say that prices in the market are the outcome of the interactions between supply and demand. Well, where does demand come from? Well, the market demand curve comes from a horizontal summation of individual demand curves. Where do individual demand curves come from? Well, we start with the preference ordering, the indifference curves and so on. We walk through the analysis that we've just given, but notice that the analysis on the previous slide said, I'd said, assume the price ratio is this, and what happens if the price of good B goes down while the consumer increases his quantity or decreases?

18:21Okay, but what made the price go down? Right, so we're starting by assuming prices that change arbitrarily outside the model, use that to derive the demand curve that is then used to explain what the prices are. So there's a circularity as opposed to a sort of causal analysis that moves from an initial cause to a subsequent effect, which is the way that Menger prefers to approach it. Just a note on indifference and a note on the potatoes and meat before I turn it over to Joe. So, again, notice that the neoclassical consumer, right, is ranking heterogeneous bundles, so Menger's concept of marginal utility simply doesn't apply at all in the neoclassical volration case.

19:10There's no marginal utility because there are only heterogeneous bundles. There are no homogeneous goods. That's not to say, well, in other words, the concept of substitution and income effects doesn't make any sense within the Mungarian tradition. Now, there is a notion of substitution at the margin in causal realist analysis, a few different notions. They're not exactly the same as the so-called substitution effect in the volration approach. Now, when a consumer gives up a unit of good A in exchange for a unit of good B, that tells us that the actor prefers the marginal unit of B to the marginal unit of A that he gave up. If you want to call that a substitution effect and say, well, the marginal utility of B is greater than the marginal utility of A, and it's sort of almost close to having marginal utilities that are equated at the margin, But you could say that. It's a little bit misleading, right?

20:06It's better to say the utility of a marginal unit of A, in the case of this exchange, exceeded the utility of the marginal unit of B, right? So it's not that one marginal utility was bigger or smaller than another, okay? Consumer has unequal valuations of the utilities of marginal units of goods. Now, in a market setting, right, when the price clears the market, right, It's the case that each buyer values the marginal unit of this homogeneous good that he purchased more than the price that he paid, right? And each seller values the price received more than the marginal unit of the good, the last unit that he sold. So there's, you know, there's a kind of equalization across the market, if you like.

20:55That's a loose sense of substitution at the margin or equality at the margin that makes sense within the causal realist approach. It's very different from the indifference curve version, okay? Now, finally, you know, people say, well, but isn't it the case that you have these weird situations like the potato famine, okay? Where, you know, consumers, they were eating potatoes, then the price of potatoes, whoops, price of potatoes went up so much that they had to spend so much money on potatoes, They didn't have any money left over to buy meat, so they ended up buying even more potatoes than they were before. So the price of potatoes went up, but that made them so poor that they had to substitute it to even more potatoes. So isn't that an upward sloping demand curve for potatoes?

21:41So, well, no, it's actually very easy to handle a case like this within the Mangerian tradition and still maintain the view that still maintain the law of diminishing marginal utility in Manger's formulation and the downward sloping demand curve, right? I mean, it could very well be that, you know, suppose the market price of potatoes is $1, and the price of meat is $6 per pound, and the consumer has $10, and so at those prices, he buys four potatoes and one pound of meat. Then the price of potatoes goes up to $2, so to buy four potatoes and one pound of meat would cost him $14, but he doesn't have $14. So he says, well, I'm just going to skip the meat, I'm going to spend all my money on potatoes, I've got five potatoes. So the price of potatoes went up and now he's consuming five potatoes instead of four. Isn't that an upward sloping demand curve? No, because what the consumer is purchasing in this example is meat and potato combinations.

22:39Okay, so if at prices of $1 per potato and $6 per pound of meat, the consumer buys four potatoes and one pound of meat, that tells that he has a preference ordering something like this. His highest, what he values the most is the four potato and one pound of meat combo, just below that is five potatoes, just below that is two potatoes and one pound of meat, and below that is $10. at the prices such that this bundle costs $10, this is his highest valued end, he gives up the $10, he gets bundle A. At a price of $2 a potato, he can't even afford bundle A, all he can afford is bundle B or bundle C. And if forced to choose between five potatoes or two potatoes and one pound of meat at those prices, he prefers five potatoes.

23:30Notice that A, B, and C do not represent units of a stock of a good, but rather heterogeneous bundles. If you were to perform the experiment, suppose you had heterogeneous meat and potatoes combos, suppose there's Swanson's steak and potatoes, frozen dinner, and each one is exactly the same. Even for Marshall's peasant, it would be the case that if he has five of those, Well, he would eat the first one and he would, you know, give the second one to his wife and he would give the third one to his dog and he would give the fourth one, you know, save the fourth one for later and the fifth one he would use as fishing bait or whatever. Okay, so he would still allocate each one of those Swanson's frozen dinners to a successively lower valued use.

24:16In other words, the law of diminishing marginal utility still holds for meat and potatoes bundles as long as we keep the characteristics of the bundles the same. Okay, up to this point our paper was basically based on barter exchange, even though Peter did introduce money at the end as an example. Now, I wouldn't have used candy and iPods, I would have used magnums of champagne and Broadway tickets, but that's just the difference between us. But once you do introduce money, and the causal realist always introduces money because we live in a monetary economy and when you purchase anything, you are in effect ranking units of money against units of goods.

25:07So, in that sort of an economy, whenever you purchase, let's say you go and purchase DVDs on sale from Best Buy, what you do is you buy as many DVDs, or you buy DVDs, excuse me, up to the point where the last DVD would have a lower marginal utility ranking than, let's say, the last $10. So if you buy three DVDs, that implies that the marginal utility of those DVDs exceed the marginal utility of $10. Now the point is, once you start talking about the marginal utility of money, you have to have an idea of how much that money can purchase. Or how much that money, how important is that money to you, that price, that $10?

25:53and that can only be based on some expectation that that money is going to have a given purchasing power in the market, immediately or at some point in the immediate future. So now we see that you have a monetary economy and that the marginal utility of money is very important. So when we advance to the monetary economy, we have to assume a third datum constant, and that is the demand for and the supply of money. That has to be assumed constant, which means that that fixes the purchasing power. Now that purchasing power, as I said, can be an expected purchasing power.

26:39What will money buy at the point that I'm going into the market? Now it's necessary to assume purchasing power fixed because without fixed purchasing power there would be no way to construct or formulate for the actor a coherent value scale upon which they're going to act. So the concept of a Giffen good now implicitly violates the setter's power of its assumption in the method of variations because it allows the demand for money, a basic datum, to change at the same time that the change in the supply of a particular good is being analyzed.

27:30So we're looking at the overall supply of some good, let's say potatoes, we're allowing it to increase, and then we're tracing out how the marginal utility will fall on people's value scales. If you allow at the same time the purchasing power of money to change, then it may be the case that money may fall at the same time in marginal utility rankings as the good is. In which case, you may very well wind up with a situation where you're actually buying more potatoes at a higher price or fewer potatoes at a lower price. So, there's an implicit violation there. Very quickly, because we're running out of time here, any economic exchange redistributes income and wealth which causes changes in people's value scale.

28:21So, for example, if we're analyzing an increase in the supply of money, we know, Mises has shown us that money is non-neutral, So that means when there's an increase in supply of money, it doesn't just raise prices, but at each step, it changes the distribution of wealth, because money is injected at a certain point, and then is spent in a certain sequence. So the whole distribution of wealth changes, which means that some people who may demand money more, have wealth redistributed in their favor, and others may be disadvantaged by that change. Now what that could mean is that even though the supply of money has gone up, if the people who receive a lot of the new money have an increased demand for money or a higher demand for money than the people who did not receive it, you could get the case where prices do not fall. Do we say therefore that the demand for money is maybe horizontal? Of course not.

29:09We say all other things given, we abstract from distribution effects, redistributions of Wealth and Income, we say that if you increase the supply of money, prices will rise. That's just a Ceres Paribus effect. And in fact, that's why we have an illusion of an upward-sloping supply curve under the Giffen Good. Because what we're allowing to happen, or what the people who believe in a Giffen Good are allowing to happen, is that as the price of potatoes goes up, they're implicitly allowing the purchasing power of money of the the heavy consumers of potatoes to be reduced. Their wealth is being reduced. So their whole value scale is being revolutionized. It's a different value scale. So the way to explain this ultimately is to point out that at the same time that the price of potatoes is falling, that the supply is increased, the price of potatoes is falling, for those people who buy a lot of potatoes, they're also experiencing at the same time an and an increase in the demand for potatoes because it's an inferior good, that is, as their income and their wealth falls, they will purchase more of that good.

30:16But overall, I'll end with this. The market demand curve has to slope downward. And the reason why it has to slope downward is because with the method of variations, you go back to the initial data, you allow one datum to change the supply, And for that supply to clear the market, when it increases, there has to be a decline in prices. So the overall market demand curve slopes downward. For segments of the population, it also slopes downward. However, there's an illusion there because we're allowing wealth and income to be redistributed, which violates the premise that all other things are held constant. Okay. Thank you.