4. From Consumer Choice to Consumer Demand

The theory of consumer choice allows us to predict that if a consumer's preferences behave according to certain criteria, and if the consumer's budget is fixed, then she will choose one particular, unique bundle when faced with a market for the economy's resources. In a short while we will examine how well this bundle fits some of the criteria for an appropriate allocation that we considered in Chapter 1. Before this, we should take some time to explore how the theory of consumer choice provides a justification for the concept of consumer demand, that is, for the downward-sloping demand curves that you may remember from an introductory course. The results will be mixed; as we will see, our assumptions are strong enough to guarantee that the demand curve exists, but they are not strong enough to guarantee that it always slopes downward. Nevertheless, they do allow us to make some strong conclusions about the unusual case in which demand curves are not downward-sloping.

To begin to construct a demand curve, we will need to draw a somewhat convoluted intermediate graph called the price-consumption curve; and to better understand some of the properties, we will need to make use of a closely related graph called the income-consumption curve. We will detail of each of these in order.

4.1 The Price-Consumption Curve and the Demand Curve

The price-consumption curve is an intermediate graph between the graph of consumer choice and the demand curve. The question that a demand curve attempts to answer is, if we change the price of one good, holding constant the consumer's income, her preferences, and the price of all other goods, how does the quantity she demands of that one good change? The price-consumption curve asks the same question, but simply draws the result differently. Specifically, we start by drawing the consumer's chosen bundle with a particular budget and set of prices, just as we did in the previous section. Then, we alter the price of the good on the X-axis, and we watch what happens to the bundle that the consumer chooses.

This process is shown in Figure 4.1. The resources of the economy are bread and roses. We assume that the consumer has an income of $30, and that the price of roses is fixed at $1. We then examine what happens to her consumption of both bread and roses and her consumption of bread as the price of bread changes. Starting at the price of $3, she chooses bundle A, which consists of 12 roses and 6 loaves of bread. Then, as the price of bread drops to $2, she chooses bundle B, which consists of 14 roses and 8 loaves of bread. Finally, as the price drops to $1, she chooses bundle C, which consists of 10 roses and 20 loaves of bread. We can imagine changing the price of bread to many other amounts between $1 and $3, and plotting the amount of bread and roses that the consumer chooses at these various prices. If we connect these bundles into a line, we get the price-consumption curve, which is shown by the thick light-gray curve ABC in Figure 4.1.

Figure 4.1: The price-consumption curve for bread and roses.

We have shown here the typical case, that as the price of a commodity (in this case bread) drops, the consumer chooses to purchase more of it. This need not be the case - for example, we could have drawn the graph so that point B was above and to the left of A (we will draw such a graph shortly and see what happens). However the case of the quantity falling as the price increases is by far the typical one.

On the other hand, what happens to the quantity of roses chosen as the price of bread changes is uncertain. There are two different possibilities indicated by 4.1. In the region from A to B, the quantity of roses demanded goes up as the price of bread goes down; in this case, the price-consumption curve is upward-sloping. We call this region the complements region. On the other hand, on the segment of the curve from B to C, the price-consumption curve is downward-sloping; the consumer decreases her consumption of roses as she buys more bread. This is called the substitutes region. You may recall from an introductory course that complements are goods that are consumed together, such as hot dogs and buns. As the price of hot dogs falls, the quantity of hot dogs demanded typically increases. But so, concomitantly, does the quantity of hot dog buns demanded. On the other hand, substitutes are goods that are consumed in place of each other, such as fruit juice and soda. Thus for example, as the price of fruit juice increases, people typically consume less fruit juice. However, the quantity of soda they demand typically increases, as they consume soda in its place.

What is noteworthy here is that goods may be complements at some prices and substitutes at others. Theory does not tell us anything further about when they might change their relationship. One example is that older studies of the mobile phone industry found that cell phone subscriptions and land lines were complements; possibly, as cell phones dropped in price, people wanted to talk on the phone more, so they bought more land line services. However, more recent studies have found the two to be substitutes. This may be because the price of cell phone usage has dropped enough that a cell phone can now be used in place of a land line, which was not practical at the higher prices seen in the 1990s.^4.1

Figure 4.2: Constructing a demand curve from a price-consumption curve.

All of the information necessary to construct a demand curve is contained in the price-consumption curve; we simply have to extract it. This is shown in Figure 4.2. We draw a graph below the price-consumption curve with the same horizontal axis. Then, on the vertical axis, we draw the price associated with each of the budget lines in the price-consumption curve. For each bundle chosen, we draw a vertical line from that bundle straight down until the point on the new curve where the price it was chosen at is listed on the vertical axis. The curve connecting the ends of each of these lines is the demand curve. It thus shows, holding income, preferences, and the price of other goods constant, how the quantity demanded of the X-axis good changes as the price of that good changes.

We have done enough to show that the demand curve exists; as long as preferences satisfy all of our assumptions U1 to U5, the consumer will chose exactly one bundle at any given budget and set of prices. The demand curve is simply a line connecting these bundles as prices change. (It is perhaps worth noting that without all five assumptions, the demand curve may not exist, since there may be more than one bundle chosen by a consumer at a given set of prices.) We will not be able to guarantee that the demand curve is downward sloping, but to examine the question of upward-sloping demand curves, we need to say a bit about the effects of income changes on the quantity demanded.

4.2 The Income-Consumption Curve and the Engel Curve

Just as we might wish to graph the effects of price changes on consumer's chosen allocation, we might also wish to understand the effects of a change in her income. This can be done with a very similar curve to the price-consumption curve, called the income-consumption curve. Here, instead of altering the price of the good on the X-axis, we alter the consumer's budget, leaving preferences and prices the same. We then plot the chosen allocation of the good along the X-axis.

This is shown in Figure 4.3. We hold the price of bread fixed at $3 and the price of roses at $2. We then alter the consumer's income from $30 to $45 to $60 and see what she chooses. At $30, she chooses 5 loaves of bread and 7.5 roses. (Unfortunately, assuming that consumers can purchase fractions like half a rose is necessary for consumer choice theory to work because all lines need to be smooth.) When we raise her income to $45, she buys 9 loaves of bread and 9 roses. Finally, when we raise her income to $60, she buys 7 loaves of bread 19.5 roses. The income-consumption curve is the curve that traces out these various bundles of bread and roses as her income changes.

Figure 4.3: The income-consumption curve and the Engel curve.

Below the income-consumption curve, we can plot the Engel curve. Here, the quantity of the X-axis good chosen is plotted against the consumer's income. We can generate this curve from the income-consumption curve by drawing a line straight down from the chosen bundle; the Y-axis of the Engle curve lists budgets, and we draw the line down from the income-consumption curve until we reach the size of the budget that the particular bundle was chosen at.

Like the income-consumption curve, the Engel curve can generally be either upward or downward-sloping, and unlike the demand curve, neither type of slope is necessarily expected. Where it is upward sloping, as in the region from $30 to $45, the consumer buys more of the good as her income goes up. Such a good is called a normal good. On the other hand, where the curve is backward-bending, she buys less of the good as her income goes up. It is then called an inferior good.

Notice that, just as with complements and substitutes, goods can be normal at some incomes and inferior at others, and in fact commonly are. For example, at very low levels of income, peasants in poor countries typically buy more cereal grains as their income goes up; cereal grains are generally the cheapest of grains, and as they buy more they are getting more nourishment. On the other hand, at higher levels of income, where basic nutrition is satisfied, an income increase may cause these peasants to substitute away from cereal grains toward tastier foods. Estimated food-at-home expenditures in the United States for 2005 are shown against income in Figure 4.4. This is not exactly an Engel curve, since the expenditures on various food categories are in dollars and not in units of food; still, it helps illustrate how goods may be normal or inferior at different price levels. As can be seen, at the lowest of incomes, expenditures on meat and cereal are rising with income, possibly as households buy more of these foods when their income rises to get cheap calories. Around $15,000 per year, expenditures on these categories fall with income, possibly as consumers switch to tastier or healthier goods. Finally, at high enough levels, expenditure on all types of food at home are rising with income; this may reflect a switch to higher-quality foods more than an increase in the number of units of food purchased.

Figure 4.4: Expenditures on food at home in the United States in 2005 plotted against income. Source: U.S. Bureau of Labor Statistics, ``Consumer Expenditures in 2005.'' Report 998, (2007), Table 2. Incomes shown are median of income category.

4.3 The Income and Substitution Effects

There is a theoretical way to break down the effects of a price change into two steps. These two steps take place simultaneously, so it is impossible to observe them separately. Nevertheless, the exercise of considering them separately can help us understand a bit more about how price changes alter the consumer's well-being, and can also give us an indication of why a particular demand curve might have the shape it does.

The first effect of a change in price is that it has an effect on the consumer's wealth. Consider a change in the price of a major item in a typical consumer's budget, such as his rent or his auto insurance. If the price of renting an apartment goes down, the consumer will find that he is a bit wealthier because he has more money left over at the end of the month. The effect of a change in a consumer's income on his purchases is called the income effect, and the key factor generating the income effect is just that a change in prices can also indirectly leave a consumer wealthier or poorer.

We might then ask whether the consumer chooses to spend some of that new income on the good whose price changed, or on some other good. For example, after rents goes down, our consumer may choose to spend more on a nicer apartment, in which case we would say that the income effect is positive. Another way of saying that the income effect is positive is that the good is a normal good. In other words, a good with a positive income effect would have an upward-sloping Engel curve. On the other hand, he may wish for some reason to spend less money on a nicer apartment as his income goes up (suppose he wishes to travel more and doesn't stay at home as much). In this case the income effect is negative. Another way of saying that the income effect is negative is that the good is an inferior good.

The second effect of a price change is that a good whose price has dropped becomes relatively cheaper compared to other goods. Suppose, for example, that a consumer spends her entire income on apples and oranges. Initially, a dollar can buy an apple or an orange. If, after a price change, a dollar buys one apple or two oranges, then oranges suddenly look like a bargain. The effect of a change in the relative price of a good, holding his level of well-being constant, is called the substitution effect. The substitution effect is always positive; in other words, based on the consumer choice theory from Chapter 3, we know that given assumptions U1 to U5, a relative price change will always cause the consumer to buy relatively more of the good that has become relatively cheaper.

We can use the framework of indifference curves to separate out these two effects. A straight-forward policy example can be made from the tax subsidies that are given to people who save for retirement in various types of accounts, such as Invesment Retirement Accounts (IRAs) or 401-K pension plans. Consider the situation described by the indifference curves in Figure 4.5. The consumer divides her income between consumption and retirement saving. Initially she is given the budget and choice problem that leads to the solution at point A. If the government offers tax breaks to people who invest in retirement accounts, the price of acquiring a dollar of retirement income effectively falls. Thus, the -intercept of the budget line shifts out, and we are left with a new consumer choice problem whose solution is B.

Figure 4.5: The effect of a tax break on investment expenditures.

Clearly, both the income and substitution effects potentially play a role in this saving decision: The tax break both causes saving to be relatively more rewarding compared to consumption, and also gives the consumer some extra income because she is able to reach a higher indifference curve. To separate out these two effects, we draw a separate line (shown in light gray) whose slope is the same as the new budget line, but which meets the same indifference curve as the old budget line. In other words, the light gray line shows where the consumer would end up if she faces the same prices as she does after the tax break, but has her budget reduced so that she is only able to achieve the same level of satisfaction that she does before the tax break. We then plot a new point, C, where this light gray line meets the old indifference curve. This bundle is the one she would buy if she faced this new, light-grey budget line. Since the prices she faces change from A to C, but not her utility level, there is no income effect; the change of her preferred bundle from A to C is purely the result of the substitution effect. The effect causes her savings to jump from $4,000 to $9,000, so we would say that the size of the effect is $5,000. On the other hand, in moving from C to B, there is no change in relative prices, so there is no substitution effect. Going from C to B reflects purely the fact that the price change allows her to achieve a higher indifference curve. This is the income effect: The increase in her savings from $9,000 to $13,000 is a reflection of the fact that she has more money left over once she saves what she did before, and she chooses to use some of that additional income for increased savings. Specifically, the size of the income effect is $4,000. What this graph tells us is that the incentives offered by a tax break may be two-fold: On the one hand, they increase the incentive to save because they make saving seem cheaper relative to other things one could do with one's money. Whether or not this is appropriate depends on whether or not one thinks that the normal price of saving is wrong (perhaps it is too high because people irrationally undervalue the future, or perhaps saving money has positive effects on others, such as one's children, that individuals to not account for in making one's decisions). The second effect of the tax break is that it leaves people with extra money to spend as they please. Since saving is generally a normal good (that is, the wealthy tend to save more), it seems reasonable to assume that some of this extra income will be saved.

For another example, let's look at the income and substitution effects in a slightly abstract way. Consider the number of hours a person works per week. Assuming a typical individual needs eight hours per day (or 56 hours per week) of sleep, she has 112 waking hours in the week, and she can spend them either working or consuming leisure time (``leisure'' here being described broadly to include time spent eating, showering, etc.). On the other hand, suppose the wage is $10 per hour. Then if she spends all of her time working and none enjoying leisure, she can make 112x$10 = 1120. If she spends none of her time working, her income is obviously $0.

Figure 4.6: The substitution effect takes us from A to C, the income effect from C to B.

In this way, the decision about how many hours to work can be viewed as a consumer choice problem, where the two goods in question are leisure and money income. We will draw money income on the X axis and leisure on the Y-axis. The budget will always have a Y-intercept of 112 hours of leisure, but the money income available will depend on the wage. Specifically, we can think of an increase in the wage as a decrease in the price of money income (in units of how many hours of leisure it costs).

Figure 4.6 examines what happens when the wage jumps from $5 per hour to $15 per hour. The highest indifference curve going through the $5 per hour budget leads the worker/consumer to bundle A, which includes 65 hours of leisure time per week (i.e., 112-65 = 47 hours of work) and a weekly income of $235. An increase in the wage to $15 per hour now allows her to choose the bundle B, where she has 90 hours of leisure time per week (i.e., she works for 22 hours) and earns $330 in weekly income.

To separate out the income and substitution effects, we consider the hypothetical light grey budget line, from which the worker would have chosen the bundle C. Here, the worker is on the same indifference curve that she has reached with A- that is, she is equally well-off at A and C. However, the light grey budget line going through C has the same relative price of leisure and money income as the one going through B (it is as if we raised the wage but reduced the number of hours in a day so that the worker draws no benefit from the wage raise). Thus, the movement from A to C tells us: If we hold her level of well-being constant, and only change relative prices of earnings and leisure to what they are after the wage increase, how much would her earnings change? This tells us the substitution effect. On the other hand, moving from C to B tells us, is we were to keep relative prices constant but move the consumer to the same level of well-being she would have with a $15 wage (for example if we somehow made days longer without changing the wage), how much would her money income change? This will be the income effect. So, for example, if the Bundle C contains $600 in money income and 35 hours of leisure, then the income effect of the wage increase will be negative - specifically, $330 - $600 = $-270, meaning that money income is an inferior good. However, the substitution effect will be $600 - 235 = $365.

In practice, it is generally observed that leisure time is a normal good, so that people do increase their leisure time when they get more income. However, the effect of a wage change is different for different groups of people. For men, the positive income effect of leisure generally does mean that they decrease their work hours when their wage goes up, but not to the extent that it actually lowers their income (in other words, they are likely to choose a point B that is above and to the right of point A in Figure 4.6). For women, and other groups that spend fewer hours per week at work, the income effect of a wage change, though still positive, will be smaller, so that the substitution effect will dominate. Therefore, they will choose to have fewer hours of leisure after a wage increase, typically landing them at a point B that is below and to the right of point A.^4.2

4.3.1 The Slutsky Income and Substitution Effects

One difficulty with determining the income and substitution effects in the two previous examples is that the point C on the hypothetical budget lines in figures 4.5 and 4.5 is not observable because we have never seen the consumer purchase with these budget lines. One solution, rather than asking how much the consumer would purchase if she faced the new prices but just enough income to make her indifferent about the price change, is to ask how much she would purchase if she faced the new prices, but her income was lowered so that she could now exactly afford what she purchased before. This situation is illustrated in Figure 4.7. The points A, B, and C are exactly as in Figure 4.5, but we have added a point D that is on a new hypothetical budget, one that has the new prices but passes through the consumer's previous consumption bundle A. If we consider D as our substitution point instead of C, then the substitution effect, called the Slutsky substitution effect, tells us how much more the consumer saves at point D than at point A, while the Slutsky income effect tells us how much the move from D to B has changed the consumer's savings. (The standard income and substitution effects, which use point C as the substitution point, are known as the Hicksian income and substitution effects.) We know from Section  3.6 that if prices and income change such that a consumer can afford what she could afford before, then she is strictly better off than she was before. This is also true of the Slutsky substitution point D: it includes some of the income effect of the price change. Whether this causes the Slutsky substitution effect to overstate the substitution effect and understate the income effect, or understate the substitution effect and overstate the income effect, depends, resepectively, on whether the good is normal or inferior.

Figure 4.7: The Slutsky income and substitution effects.

Point D will not itself be observable for a single consumer, unless we just happen to have data on that consumer's purchases with the new prices and that budget constraint. We might, for example, get such data if we are able to subject consumers to a laboratory experiment where we observe their purchases in many different scenarios. In a carefully controlled laboratory experiment, though, we could even recover point C by subjecting the consumer to a lower and lower budget, and seeing how low the budget has to go before the consumer would rather forego the price drop and return to point A.

Nevertheless, we can observe the budget line that passes through point D. This leaves us with two advantages over point D. First, if we have data on a large number of consumers with different incomes, and we are willing to assume that all consumers have the same preferences, then we may very well observe one consumer with the budget line that passes through A before the price change and B afterward, and another consumer with the budget line that passes through D after the price change. This would allow us to draw conclusions about the income and substitution effects for the first consumer. Second, because the budget line passing through D is observable, including the income required to attain that budget line, we could make a statement like, ``The effect of the tax break on a consumer's well-being is the same as the effect of $5000 of additional income,'' if that is the difference in income between the budget line passing through D and the one passing through B. Of course, this will statement will slightly understate the income effect, but it provides a feasible approximation.

Figure 4.8: Two price changes with income and substitution effects separated.

4.3.2 The Compensated Demand Curve

Suppose that we could estimate a point such as C in Figure 4.5 for several different price changes. This is illustrated in Figure 4.8, where the price of heating oil drops from $2.00 to $150 to $1.50 per gallon. The outcomes A, B, and  B' show the amounts of heating oil that the consumer actually purchased. These are points along the consumer's price-consumption path. On the other hand, we could plot the amount of heating oil that the consumer would have purchased if the gain from the price change were exactly offset by a loss in income. Points A, C, and C' are points along a hypothetical price-consumption path that consists of such purchases. Just like the price-consumption path can be used to plot a demand curve, this hypothetical price-consumption path can be used to plot a hypothetical demand curve, which reflects the amount that the consumer would purchase at different prices, purely due to the substitution effect. This demand curve is shown in Figure 4.9. This demand curve is called the compensated demand curve (sometimes called the Hicksian demand curve), and it allows us to visualize how much of the change in the quantity demanded of a good is due to substitution, and how much is due to income effects, as a price drops. Note that because the substitution effect is positive - people with convex indifference curves always buy relatively more of a good as its price drops - the Hicksian demand curve will always be downward-sloping. In the next section, we see that this property will not necessarily hold for regular demand curves.

Figure 4.9: The compensated demand curve.

4.4 Giffen Goods

As mentioned above, nothing in our theory of preferences can rule out the possibility that the quantity of a product demanded by a consumer will increase as the price of a product increases. An example of a consumer purchasing more when the price rises is shown in Figure 4.10. Here, our consumer has a budget of $120 and the price of bread is $2 per loaf. Initially, the price of potatoes starts out at $1.50. He chooses bundle A with 24 loaves of bread and 48 potatoes. The price of potatoes then falls to $1. He now chooses bundle B, with 40 loaves of bread and 40 potatoes. Thus the quantity of potatoes chosen has actually fallen when the price dropped!

Figure 4.10: A Giffen good. As the price of potatoes falls, the quantity demanded decreases.

Such a good, where the quantity demanded decreases when the price decreases, so that the demand curve is sloping upward, is called a Giffen good. Our examination of the income and substitution effects can tell us something about Giffen goods. Since the substitution effect is always positive, it will always cause a person to buy more potatoes when the price of potatoes drops. Only the income effect could cause a person to buy less of a good when its price drops. In other words, Giffen goods are heavily inferior goods. Thus, we can draw bundle C, with 70 potatoes and 15 loaves of bread, so that the movement from C to B shows the pure substitution effect. Remember that the substitution effect is always positive, so that bundle C has more potatoes than bundle A. (Specifically, the substitution effect is 70-48=22.) For a good to be a Giffen good, the income effect needs to be negative and larger in magnitude than the substitution effect. In this case, the income effect is 40-70 = -30, which is larger in magnitude than the income effect.

A much-debated study by Gerald Dwyer and Cotton Lindsay found evidence that during the Irish potato famine, potatoes may have been a Giffen good.^4.3 Why did they look there? Well, there are lots of inferior goods, but the income effect of most price changes is usually small. We consume many goods in our daily life, and a price change in one of them is not likely to change our income drastically. So to find a Giffen good, we have to find one that is both strongly inferior and takes up a large percentage of a person's income. The story that Dwyer and Lindsay tell is that Irish peasants substituted wheat for potatoes as they became wealthier. At this extreme level of deprivation, they simply could not afford a nutritious meal of bread given their income. However, as the price of potatoes fell, they were able to balance their consumption of potatoes with more bread.

Giffen goods, if they even exist, are extremely rare. Nevertheless, they cannot be ruled out using the standard neoclassical theory of preferences given in Chapter 3. We could ensure that Giffen goods do not exist by imposing restrictions on preferences by requiring that no good is too inferior. We could also assume, as Marx and other classical economists did, that people have an ability to produce important goods on their own, and that prices align with the cost of home production. In this case, a person's response to a drop in price would be to produce less at home and buy more in the market, which would ensure downward-sloping demand. In any event, economists have chosen not to impose such restrictions because Giffen goods are not considered a serious problem; saying ``assume that the demand curve slopes downward'' does not raise as many eyebrows as saying ``assume that the consumer always buys the same set of goods given the same prices.'' Moreover, we can make predictions about when, if ever, we would see an upward-sloping demand curve, and why.

4.5 Market Demand: The Standard Case

The standard case for market demand supposes that people form their preferences independently of each other. This implies two slightly implausible assumptions. First, it implies that people do not consider other people's tastes in forming their own. This would be difficult to justify for a number of goods, ranging from clothes, where people tend to copycat each other, to foods, where people learn to cook from each other. However it may be more plausible for goods whose functioning is more universal and difficult to alter, such as water or salt. Second, it supposes that people's desires do not depend on how much other people actually consume. Thus, for example, we have to assume that people are neither altruistic nor mean-spirited. Again, there are certainly many cases where the effects of altruism are effectively zero.

Providing that these assumptions hold, we can generate market demand simply by adding up individual demand in a fairly mechanical way. Consider the following table of three people and their demand for roses at a given price. The market demand at that price will then simply be the sum of their individual demands, as shown in Table 4.2.

Figure 4.11shows how this is done on a graph: At any particular price, we take the quantity demanded by each individual at that price, shown by the distance of the curve from the axis. We then add each individual's quantity demanded and get the quantity demanded for the market as a whole at that price.

Figure 4.11: The market demand curve at any price is the horizontal sum of the individual demand curves of people in the market.

To take an algebraic example, suppose that the market for wart hogs consists of three individuals who do not know each other: Bob, Lucinda, and Zhang. The quantity of wart hogs that Bob demands can be described in terms of the price as Q_B = 10-5P; the quantity that Lucinda demands can be described by the equation Q_L = 6-3P; and the quantity that Zhang demands can be described by the equation Q_Z = 14-7P. To figure out the market demand, we just add the quantities demanded by each of the three individuals and any given price. In other words, QD = Q_B + Q_L + Q_Z. So, if we simply add these three together, we get Q_D = 10-5P + 6-3P + 14-7P = 30-15P. A line representing each of these equations is shown in Figure 4.11.

Figure 4.12: Individual and market demand for wart hogs.

4.6 The Advantage of a Market Outcome: Pareto Optimality

As we saw in Chapter 1, the assumptions that we have made about preferences are sufficiently strong to allow us to state conclusions about whether or not a particular allocation of goods is Pareto optimal. It turns out that, if all of our assumptions U1 to U5 are satisfied, and goods are exchanged in a market with a uniform price, and individuals make purchasing decisions independently of each other, then the resulting allocation will in fact be Pareto optimal. Moreover, the tools of indifference curves and consumer choice are powerful enough to demonstrate that this is so. This result is known as the First Welfare Theorem. There is a broader version of the theorem that encompasses production as well as exchange; however, a slow and careful examination of Figure 4.13 can help us see how the theorem works for the problem of exchange by itself.

Figure 4.13: Prices that can improve on the market outcome for a given individual.

What we refer to as a market equilibrium is a set of prices and allocations such that nobody wishes to change her allocation, that is, buy or sell, given the current prices. We have not shown that such an equilibrium exists in an economy (our assumptions are, in fact, mostly enough to guarantee one, but this is a discussion we are omitting for lack of space). However, we can say, that if it does exist, we can analyze it using a consumer choice problem. Specifically, every consumer's allocation will be a variation on the outcome in Figure 4.13, where the consumer has chosen her favorite combination of the economy's two goods, nuts and Bonkers. Some consumers may have different budgets, some may have different indifference curves from each other, but because every consumer faces the same prices, every consumer will have a budget line of the same slope (-p_X/p_Y) and choose an allocation on an indifference curve that is tangent to that budget line and veers away from it in a convex way, just like point A.

Now, looking at the above allocation, we need to consider whether it is Pareto optimal. If it is not, then there must be at least one consumer who will be made better off by a re-allocation of goods without making someone else worse off. Suppose we are looking at that consumer. What re-allocations would improve upon outcome A for that consumer, without putting someone else on a lower indifference curve? Clearly we can rule out any re-allocations above and to the right of Outcome A; in these allocations, the person would be getting more of both goods, meaning that some of both goods would have to be taken away from someone else. But if more is better for all consumers, then taking the goods away from that other consumer would make the other consumer worse off. Similarly, any allocations below the indifference curve sketched in Figure 4.13 can be ruled out because they would make the consumer we are looking at consumer worse off.

The only remaining question is the outcomes in the shaded area, which are above the consumer's current indifference curve but still involve her giving up some of one good and gaining some of the other good. Is there a way for some consumers to trade - that is, for some to give up nuts for Bonkers, and others to give up Bonkers for nuts - that would make at least some of them better off without making anyone worse off? Well, the thin lines show price ratios at which the consumer might be willing to give up one for the other and be better off. Call this consumer Person 1. If Person 1 is to give up nuts for Bonkers, then she would only be willing to exchange along a steeper price ratio - that is, she would only be willing to give up less nuts for the Bonkers than market prices currently dictate. Such a price ratio is illustrated by the line segment AB. But this means that Person 1's trading partner, whom we shall call Person 2, would have to give up Bonkers for nuts at the same steep price ratio. Keep in mind that Person 2's current allocation looks just like A, because Person 2 faces the same prices, and therefore has a budget line and an indifference curve with the same slope, as Person 1. This means that giving up Bonkers for nuts at the same price ratio would put Person 2 somewhere along the line segment AD, making her worse off.

We can make the same conclusion by looking at what happens in the other direction. If the consumer is to be made better off by giving up Bonkers for nuts, she is only willing to do so at a flatter exchange rate than market prices currently bear, represented by the line segment AC. However, this means that her trading partner would have to give up nuts for Bonkers at this same flatter price ratio, putting her trading partner somewhere along the line segment AE and making the trading partner worse off.

We have thus shown that, given a set of market prices, there is no way to improve upon any individual's allocation without making some other individual worse off. Thus, the allocation given by the market is Pareto optimal.^4.4

It is important to note that the First Welfare Theorem is a result about quantities, not about prices. That is, it says nothing about whether the prices that the market winds up with are in any way optimal. Rather, it says that, given those prices, consumers will choose the bundles that they consume in such a way as to not be wasteful.

In a sense, the definition of Pareto optimality is tailored to reflect the ways in which entrepreneurship can avoid ``wasted'' utility. Imagine if there were a way to re-allocate goods to make some group of people better off without making anyone worse off. An entrepreneur might be able to spot this possibility. If so, he could negotiate a contract between the parties who would have to exchange goods to achieve this re-allocation. In turn, he could take a small amount of goods from one of the parties that is being made better off and keep it as compensation for his efforts, while still leaving that party better off. Markets allow entrepreneurs to get rid of ``wasted'' utility, and an equilibrium could be thought of as an allocation at which there is no opportunity for an entrepreneur to re-allocate goods.

4.7 The Weaknesses of Consumer Theory

The strength of the theory of consumer choice, as spelled out above, is in both the simplicity of its assumptions and in the strength of its results. Our five assumptions largely center around the ``smoothness'' of a person's preferences: That they require him to rank allocations of goods from best to worst; that he prefers a balanced selection of goods; that his wants are unsatisfied; that one can smoothly substitute one good for another and leave himself equally well off. From these assumptions we get both the result that demand is well-defined - that is, that given prices and income, there is precisely one quantity of a good that he will want - and that a market environment produces a Pareto optimal allocation, which is in general the best one can say about any allocation using ordinal utility theory. We also get the theory of consumer choice, which allows us to predict how people will change their consumption of goods when faced with a change in prices, such as that caused by a tax or a grant. Moreover, the theory of preferences that we depend on can be tested to see whether people really abide by it and how.

Nevertheless, there are fundamental difficulties in using this set of assumptions to predict and evaluate consumer behavior, coming from two directions: First, there are subtle ways in which our assumptions might not be satisfied; second, even if they are satisfied, and an allocation of goods is Pareto optimal, there is still much to learn. After all, there are many Pareto optimal allocations, including, generally, complete inequality (i.e., one person gets everything). Which of these allocations will markets generally lead to, and will they have (or lack) any desirable properties? We will deal with four problems of the first type, which either cause a market allocation to not be Pareto optimal, or else give us a very unsatisfying form of Pareto optimality: Externalities, altruism, strategic behavior, and endogenous preferences. We will then turn to the second question and address the shortcomings of Pareto optimality as a benchmark for market performance and discuss what other benchmarks are available.

4.7.1 Externalities

There is a tacit assumption that people form preferences only concerning their own consumption, over which they have control. But in many situations, people have preferences over other people's consumption. For example, consumption of gasoline pollutes; this, in turn, affects the well-being of others besides the person who is actually using the gasoline. An effect of someone's economic activity on someone else, for which there is no compensation, is called an externality. There can be positive externalities as well as negative ones. For example, planting flowers in front of one's house may create pleasure for one's neighbors as well as oneself, while going to school and learning a subject may cause you to share that knowledge with friends and acquaintances without demanding compensation from them.

Externalities cause trouble for market outcomes because that they create situations in which people would prefer to change their own consumption only if everyone else would commit to changing their assumption accordingly. However, markets neither require nor (by themselves) allow for any coordination between consumers, so such a commitment cannot be achieved. For example, a consumer might have a marginal utility of m for consuming a gallon of gasoline. However, if she knew that her consuming an additional gallon of gasoline implied that everyone else would also consume one more gallon of gasoline, her marginal utility might for gasoline be lower than m. Her gasoline consumption, in turn, might have a polluting effect that, for the rest of the world combined, is large enough to be noticed; however, the effect of her own pollution on herself is trivial, so she does not take it into account. This situation is shown in Figure 4.14, where the consumer makes choices between public and private transportation. The dark indifference curve shows the person's preferences over the market choices she is given, while the lighter indifference curve shows how her utility would change if she represented every consumer together - that is, when she consumed more or less gasoline, she knew everyone else would do exactly the same. The light gray indifference curve is steeper, which reflects the fact that she would have a higher marginal rate of substitution if everyone else behaved just like her. In other words, an additional gallon of gasoline is worth fewer subway trips to her, because when she gives it up, knowing that everyone else will as well, she (literally) will breathe more easily. So consuming more has a smaller value to her if she knows everyone else will consume more as well.

Figure 4.14: An externality affects preferences over others' consumption.

In thinking about whether consumers choose the correct amount of gasoline in response to market prices, consider the choice problem of a benevolent dictator who could allocate purchasing decisions for everyone. The individual consumer, given her preferences and her inability to affect others' choices, will choose outcome A, where her indifference curve meets the budget line. However, the light gray indifference curve, which represents the consumer's preferences if the externality is taken into account, dips below the consumer's budget line. If everyone faces this externality, then the dictator could put everyone onto a higher indifference curve by forcing everyone to consume an allocation such as B with more subway trips and less gasoline.

There is also a market solution to this problem that would not require the government to make allocation decisions for people. One can think of an externality as a case of a missing market: People would like to pay others to change their behavior, but effectively this means creating a separate market for each individual's consumption, which is an enormous and costly coordination problem (for example, in a market of a million people, each person has to make one million payments). An approximate solution can be provided by taxing harmful activities and subsidizing beneficial ones. For example, if the government subsidizes the price of flower pots using revenues gained from the general population (say, via income taxes), then flower pots will be cheaper and, assuming they are not a Giffen good, people will plant more flowers and make their neighbors better off. Effectively, the government tax has created a market through which the rest of the population can pay flower-growers for their activity. There is not a simple, formulaic method for choosing the appropriate amount of the tax, but there may be means to figure out the amount the average person would pay for an additional unit of the externality - such as figuring out the cost to clean up the pollution created by a gallon of gasoline - and try to align the tax with this amount.

The size of the externality created by gasoline consumption is the subject of intense political debate; one study puts it at about $1.75 per gallon, including 30 cents per gallon for pollution, 60 cents per gallon for congestion effects, and 70 cents per gallon for injuries, plus an unknown amount for international conflicts created by petroleum issues.^4.5 In this case, a Pigouvian tax on gasoline of $1.75 per gallon would cause consumers to substitute gasoline for other items at the rate indicated by the light grey indifference curve, thereby allowing them to achieve a higher indifference curve. To illustrate this situation, consider Figure 4.15. Here, a consumer has a monthly budget of $1,500, which she can spend on gasolune or on other things. At an untaxed price of $3 per gallon, the consumer could buy upto 500 gallons of gasoline if she spent all of her budget on gasoline, as shown by the black budget line. The darker indifference curves I₁ and I₂ show her preferences over gasoline consumption without taking the externality into account; she would choose bundle A, with 330 gallons of gasoline and $510 spent on other items (admittedly this is a bit of an excessive gasoline budget, but it makes the drawing clearer). The lighter gray indifference curves C₁ and C₂ show what her preferences would be if she were compensated for the negative externality caused by her gasoline consumption. They intersect her budget line at point B. Now, suppose that the government taxes gasoline by $2 per gallon (a nice round number close to $1.75), so that it now costs $5/gallon, and then refunds whatever it equally to consumers to spend as they please. The consumer's budget line would then end up like the dotted black line. Here, the dotted budget line passes the dark grey line I₁ at point B, meaning that this is the bundle that the consumer will choose with her new budget. It is also the bundle that the benevolent dictator would have chosen given the old budget and the compensated indifference curves C₁ and C₂.

Figure 4.15: A Pigouvian tax of $2 on gasoline will correct the externality.

It should be mentioned that we can also use consumer theory to demonstrate why a tax of this nature is generally better for consumers than a blanket limit on gasoline consumption such as our benevolent dictator might create. Suppose that the economy actually consists of two individuals, Akbar and Jeff, who value gasoline differently - in other words, they have different marginal rates of substitution between gasoline and other goods. This is illustrated in Figure 4.16. Here, Akbar's uncompensated and compensated indifference curves are shown by I_A and C_A respectively; he would choose outcome A in an unregulated market and outcome B if he were penalized for the negative effects of his gasoline consumption. Jeff, on the other hand, has a lower marginal utility of gasoline at any particular level of consumption; given the same budget, he would choose outcome C in a free market and outcome D if he were penalized for the externalities he causes. If we were to limit per-capita gasoline consumption, say to some outcome between B and C, then neither Akbar nor Jeff would be happy: Akbar would be consuming less than he would even if he were compensated for the externalies he causes, and Jeff would be consuming more than he would if he were compensated for the externalities that he causes. In other words, a re-allocation from Jeff to Akbar would make both better off, meaning that the situation is not Pareto optimal. A tax on gasoline, on the other hand, would create a Pareto optimal situation by allowing them both to set their consumption where the slope of the (taxed) budget line is equal to the slope of their compensated indifference curves.

A strict limit on behavior that creates negative externalities may nevertheless sometimes be justified using a Rawlsian logic. Suppose that the behavior deprives some people of their rights - for example, it randomly kills some people (as cars certainly do) or leaves others without access to basic necessities of life such as clean air. The Rawlsian maximin allocation would argue that the well-being of the worst-off person should be considered more important than anyone else's well-being. Arguably, the worst-off person is the one who is dead due to the externality, so a strict limit that prevents this person from being killed - by prohibiting the behavior that causes the externality - would be defensible as a policy that maximizes the well-being of the worst-off person.

Whether one prefers the Rawlsian argument or the utilitarian argument is probably a matter of taste and degree. Few people would support an all-out ban on non-essential driving just because it might cause an extra person to die from air pollution; at the opposite end, most support bans on drunk driving rather than taxing people who drive drunk for the negative externalities they cause.

Figure 4.16: If different people have different marginal rates of substitution between gasoline and other products, a per-capita cap on gasoline consumption will not be Pareto optimal.

4.7.2 Altruism (and Malevolence)

In the case of externalities, the consumption decisions of others enter into a consumer's preferences and utility function. There may also be cases, however, where the well-being of others (or perhaps simply the perceived well-being of others) also affects one's utility. For example, people appear and claim to be concerned about the well-being of their family members and friends; and in general, most people express a distaste for the idea that others live a life of complete deprivation.

If people are altruistic, then a strict market allocation (that is, where individuals spend their own budgets autonomously) may not be Pareto optimal. Let us consider a hopelessly romantic case based on the O'Henry story The Gift of the Magi. Suppose that Jim's utility is and Della's utility is , where u_j and u_d are Jim's and Della's consumption, respectively, and a is some constant. This implies that both Jim's and Della's utilities increase with their own consumption, and with each other's utility, but at a decreasing rate. Readers who know calculus can verify that Jim's marginal utilities for his own consumption and Della's consumption are and , respectively, while Della's marginal utilities for Jim's and her consumption, respectively, are and . If we assume that consumption is in dollars so that the price of consumption is one, then the equal marginal principle tells us that Jim's utility is maximized when MU_j(c_j) = MU_j(c_d), or c_j = c_d/a²; similarly, Della's utility is maximized when c_d = c_j/a².

Since each person's marginal utility is decreasing in both his or her own consumption and in each other's consumption, this implies that Jim will want to give Della money to consume whenever c_j > c_d/a² and Della would want to give Jim money for consumption whenever c_d > c_j/a². This only creates a problem when a>1, i.e., the marginal utility that Della and Jim get from each other's consumption at any given level is higher than the marginal utility they get from their own. In this hopelessly romantic situation, the two grey areas in Figure 4.17 would overlap, and Jim and Della would insist on giving money to each other but refuse to take any on their own. Nevertheless, all such points are Pareto optimal in a slightly odd way, since transferring money to one of the two would lower that person's utility and raise the other person's.

Figure 4.17: If altruistic individuals' consumption is too unequal, they will want to donate money to each other.

We could think of the Rawlsian maximin allocation as an extreme version of altruism, in that it is equivalent to each individual having the utility function u_j = u_d = min(c_j,c_d). If consumption is the only activity in the economy, then the Rawlsian maximin allocation will always recommend complete equality of outcomes, and indeed if these were Jim and Della's utility functions, they would end up sharing their income evenly. Rawls of course recognized that this would leave individuals without any incentives to work, and therefore favored inequalities that benefit the disadvantaged by making the economy and society stronger.

If we are being very strict about what we define as a market outcome, that is, if a market outcome is one where individuals only consume from their own budgets, then altruism does prevent markets from providing Pareto optimal outcomes. However, this problem is easily remedied if we allow individuals to transfer funds to each other; people may simply donate money until their marginal utility per dollar of someone else's happiness is equal to the marginal utility per dollar of their own. There may also be problems when individuals do not personally know the persons to whom they wish to contribute; this is where governments and organized charities may play a role. Therefore, considerations of altruism do not pose any great policy challenges aside from making the somewhat obvious statement that government transfer programs may be necessary to create a Pareto optimal outcome if individuals are altruisitic.

Conversely, it is possible for malice to play a role in people's preferences; one might argue that some governments implement policies based on racial, religious-based, or anti-gay malice for political gain. Although there may be some value in developing a formal understanding of such a situation, there is little value in developing appropriate policy measures to help governments exercise malice.

4.7.3 Strategic Behavior

There are times when one makes purchasing decisions not based on the satisfaction a good provides, but rather because of some ulterior social motive. Consider, for example, the market for flowers. Certainly, there are plenty of cases where individuals buy flowers for their own enjoyment. But more commonly, people buy flowers for others. Why? In some cases, probably simple altruism: They get pleasure from seeing the other person smile. But seemingly altruistic motives can sometimes be more complicated. Flowers brought to a host can signal appreciation for hospitality; flowers brought to a lover can signify desire to continue a relationship. The recipient might not even enjoy the flowers, yet may still feel satisfaction for having received the signal that the flowers transmit. So clearly, a simple model of consumer behavior whereby consumers have preferences for flowers, and make purchases based on those preferences, leaves out a great deal of information.

You may recall from the first chapter that when attempting to model situations where individuals make strategic choices, and where the final outcome is dependent on interactions of those choices, we often turn to the tools of game theory. We introduced the prisoner's dilemma game, in which people in a group, each pursuing individual self-interest in an anti-social manner, led to a perverse outcome. There are potential prisoner's dilemmas in consumption when people make decisions strategically in response to each other.

One type of non-cooperative game, called a signalling game, looks at behavior that people engage in to indirectly (and usually imprecisely) signal information about themselves to others. A simple example is given by the table in Figure 4.3. Suppose that Pat and Robin are interviewing for the same job. Pat is better qualified than Robin, but the interviewer is not certain that Pat is interested in the job. Pat and Robin both contemplate whether or not to go out and buy expensive, dark suits to wear to the interview. The workplace is a very casual environment, and the interviewer has no particular personal taste for dark suits. However, if Robin wears a dark suit and Pat does not, the interviewer may decide that Robin is more serious about the job and hire Robin. Thus, both candidates have a strong incentive to wear a dark suit. So the situation may very well lead to the outcome where they both wear dark suits and Pat gets the job. However, Pat would also have been chosen as the best qualified candidate if neither had worn an expensive dark suit. Thus, in effect, the dark suits are a pure waste of resources, and do not result in a Pareto optimal outcome (since everyone would have been better off if the candidates had spent their money on something they like better than dark suits).

Many important consumption decisions may be described as strategic rather than self-interested or altruistic: Parents paying their children's college tuition so as to create an open-ended obligation on the part of the child; buying expensive cars or yachts primarily for the purpose of ``keeping up with the Joneses''; listening to music one doesn't actually like to impress one's friends. Not all of these activities are wasteful. For example, paying college tuition for one's children may actually increase efficiency, since parents may be able to effectively use information about their children that other sources of tuition money (e.g., banks) do not have (although this practice does create inequality since the poor have less money to offer their children). Even when there is a waste of resources, there may not be an effective solution to the inefficiency; people probably do buy an excessive amount of flowers, but even most socialists probably do not want a government official dictating when they can and cannot buy roses. Still, consumption of goods for strategic reasons can demonstrably lead to wasteful outcomes.

There is some experimental evidence that social norms help people avoid such economic outcomes. For example, a paper by Ernst Fehr and Simon Gächter shows that when people encounter an individual who is acting as a free-rider (that is, a person who other people pay for public goods that he consumes while not paying himself), they will punish that individual even if they incur a personal loss to do so and do not expect any future reward.^4.6 In other words, society can avoid the non-cooperative equilibrium of a prisoner's dilemma if its members are conditioned to enforce rules that punish anti-social behavior. Nevertheless, if people do not recognize that a person is acting anti-socially, or do not have the means to punish this person, then they may not be able to prevent an outcome that is not Pareto optimal.

4.7.4 Endogenous Preferences

We have seen in the previous section how one's consumption habits can be influenced by the activities of others (externalities), by the well-being of others (altruism), and by their expected effect on others (strategic behavior). It is also possible for one's preferences to be influenced by the preferences of others, or by one's own past behavior. For example, people's taste in music may be affected by what plays on the radio, or by what others listen to around them. Other preferences may be habit-forming: For example, someone may come to prefer the coffee at Starbucks or at Dunkin Donuts simply because it is what she is used to, and not because it is somehow objectively ``better'' coffee; had she grown accustomed to the coffee somewhere else, she might very well prefer the coffee at that place.

The problem that these types of endogenous preferences pose for consumer theory is that they essentially reverse the logical order by which decisions are made. Consumer theory starts with people's tastes as primary; based on tastes (and facing a certain set of prices and income), people make consumption decisions; in turn, based on each individual's consumption decisions, we derive overall market demand. With endogenous preferences, the logic now becomes circular: Market demand, in turn, influences people's preferences.

This produces two shortcomings, and we will discuss each in some detail.

The first shortcoming is that it is no longer clear that market demand is well-defined in the long run. We saw above that as long as our assumptions about consumer theory are satisfied, a consumer will only choose one bundle of goods at a given set of prices. This implies that we can draw out a well-defined price-consumption curve and demand curve. However, if one's tastes are now influenced by one's friends' consumption, this is no longer true. Individual choices can no longer be determined separately and then added up to form market demand.

Consider, for example, an economy where there are two people, Klaus and Dieter, and two types of drinks: Margaritas and melonballs. Both Klaus and Dieter would like to appear distinctive have their own favorite drink, rather than preferring the one that the other does. So, we can imagine the two developing their preferences after some jockeying; after this, their preferences form the usual indifference curves and the situation is back to one where our assumptions are satisfied. However, it is completely arbitrary whether Klaus will end up preferring margaritas and Dieter will end up preferring melonballs, or vice versa. Thus, it is impossible to say in advance how much of a given drink each person will demand at a given price.

There are two common cases of endogenous preferences that are relatively easy to analyze. One, called the bandwagon effect, exists when people copycat each other's consumption habits. For example, in the case of clothing fashion, people tend to buy what they see others wearing. A graph of this situation is shown in Figure 4.18; here, an individual, Ralph, has a certain demand curve for low-riding jeans. At a price of $30, he demands one pair. When the price drops to $20, he now demands two pairs; but everyone else demands more as well. The result is that Ralph sees everyone else wearing low-riding jeans, and now becomes more interested in buying them. His demand curve thus shifts out to a new one, where he demands 3 pairs of jeans when the price is $20. This means that the overall market demand can be described by the gray demand curve, which goes through a quantity of 1 at a price of 30 and a quantity of 3 at a price of 20. The market demand curve is therefore flatter than the demand curves that individuals would have if they did not take others' preferences into account. Obviously, then, if the bandwagon effect exists, we cannot just sum up individual demand curves to obtain market demand the way we did in the previous section.

Figure 4.18: The bandwagon effect.

The opposite of the bandwagon effect is known as the snob effect; this occurs when seeing others buy an item lowers a person's demand for it. This might occur when people wish to appear to have distinctive taste for goods, such as artwork or food, that are not shared by everyone else. The workings of the snob effect are exactly parallel to the workings of the bandwagon effect, and are shown in Figure 4.19. Here, as the price of a painting goes down from $150 to $100, Ralph is interested in buying more. Given his usual demand curve, he would purchase three. But then he sees other people with the same painting; his preferences change, and his demand curve for paintings shifts in. After everything is settled, he demands two paintings at a price of $100. Thus, the market demand curve, shown by the light gray line, is less responsive to price changes than individuals' demand curves would be absent a response to others' consumption.

Figure 4.19: The snob effect.

The effect of other people's preferences on our own need not be so simple as to make us wish to copycat them or not copycat them. We might, based on our friends' behavior, come to think of tea as a rainy-day drink or watching movies as something that one does on Thursdays. Certainly, the list of how others can influence us is endless. And, most of these effects are either small enough or random enough that the analyst can ignore them without any dire consequences. However, it bears reminding that when others do influence our preferences, market demand is not just the sum of individual demand, so we have to be cautious about extrapolating from data on individual choices to estimate market demand curves and vice versa.

A second difficulty with endogenous preferences is that we may no longer be able to guarantee that an outcome that consumers choose is utility-maximizing in a narrow sense: They may maximize their utility given their current preferences, but we do not necessarily know that their current preferences are the best ones they could have formed. This is well-illustrated by the case when a person's taste is influenced by her own past consumption. Suppose that early in her childhood, Alejandra's parents divorce. They then work full time and are no longer able to find the time to cook, so that they order out a lot. Alejandra begins to like the taste of fast food, so that by the time she is an adult, she prefers it to the taste of her parents' cooking. Her situation is shown in Figure 4.20; the dark line indicates her current indifference curves. She now values fast food more (that is, one would have to give her many home-cooked meals to replace a fast food meal and leave her equally well off), and so she buys a food menu that tends to be heavy on fast food, shown by allocation . On the other hand, the light gray line shows how her preferences might have ended up had she grown up eating home cooking. In this case, given the same budget and prices, she would have ended up cooking more meals at home as an adult, choosing allocation .

Figure 4.20: Preferences may be affected by past consumption.

In which case is she better off? Judging people's tastes is a dangerous business for social scientists to get into, and it is not a business for which economists have any particular qualifications. Yet to the extent that tastes represent mindlessly formed habits, we may legitimately ask which habits are good. We would say that ex post, that is, after her adult preferences have been formed, Alejandra prefers more fast food, and so her purchasing decision will be utility-maximizing and therefore, in the end, Pareto optimal. However, ex ante, that is, before her tastes have been formed, a taste for fast food may not be Pareto optimal at all; it may be an unhealthy habit that one wishes one did not have.

It is not clear when social scientists do and do not have the right to second-guess people's tastes. However, they arguably do in at least a few instances. If the government clearly knows more about the effects of taste formation than people whose tastes are being formed, then it has a legitimate reason to intervene in the formation of those tastes. For example, children's lunch programs might be designed so that children become accustomed to healthy food; advertising that showcases products that the government knows to be unhealthy but most people may not (for example, various medicines) might be restricted; schools might wish to develop a taste for reading in children; etc. Some governments take stronger positions and try to influence art or television programming; it is a matter of much debate whether such government activities are done in the interest of an impressionable population or whether they are patronizing. If television programming and advertising really do alter people's preferences (rather than just providing them with information), and the government does not regulate advertising, then it is left to the private sector to form these preferences in a profit-maximizing way, which may also not lead to the healthiest tastes.

4.7.5 Consumer Choice and Non-Utilitarian Distribution Criteria

We have spent the last two chapters evaluating the cases in which market outcomes are and are not Pareto optimal, and we have seen mechanisms for correcting these outcomes when they fall short. Nevertheless, Pareto optimality is a fairly weak efficiency criterion, and we have seen other, stronger criteria for the allocation of an economy's goods and services that may be more satisfying. One might naturally wonder if the framework of consumer choice can be altered examine how well markets abide by the more modern criteria of distributive justice introduced by late 20^th Century philosophers. For example, to what extent do they produce an allocation that maximizes the well-being of those least well off, as Rawls would have us do? To what extent do they provide an adequate minimum level of functioning, as Sen would require? How well do they equalize opportunities for achieving life plans, as Dworkin suggests an allocation should?

Not only is there not an answer to these questions, but the problem can run somewhat deep. Rawls, Sen, and Dworkin all used different frameworks to analyze the allocation problem. According to all of them, mechanisms for allocation should be grounded in a social contract. Dworkin and Rawls then offered different variations on an ``original position'' from which the social contract ought to be negotiated, while Sen, though not as specific about the negotiation process, suggested that it should take into account the ability of people to develop meaningful lives. The criteria for acceptable allocations of goods and services that each of these philosophers developed then flowed from the possibilities inherent in negotiating a social contract. Consumer theory, on the other hand, is developed on the basis of the preferences of individuals. To the extent that market transactions allow for social contracts, they are merely contracts of how much to buy at a certain price, and the only means by which we can evaluate these contracts are by the ways in which they arbitrate well between different people's preferences. This leaves us with little language to consider criteria for distribution that are not based on preferences.

Consider, for example, the role of convictions in the allocation of goods. Social contracts are ideally based in part on moral convictions, but it may or may not be possible to represent convictions by preferences. To illustrate, let us consider three different statements that a vegetarian might make. Some would be satisfied with the statement ``I do not like meat.'' Consumer theory can more or less satisfy this; such a vegetarian's preferences will fail to satisfy the more-is-better criterion, but as long as there are non-vegetarians in the market, this person's indifference curves and choices will not look any different from those of someone who places an extremely small value on meat and does not purchase any. Next, there is a slightly stronger statement, ``I do not like it when others eat meat.'' Essentially, this person faces a negative externality when others eat meat. To the extent that there are others like this person, a Pigouvian tax on meat that discourages meat consumption may balance this person's dislike for others' eating meat with other people's preference for eating it.

However, some vegetarians would make a third, stronger statement: ``It is wrong for people to eat meat.'' This is not a preference, but a conviction. Although one could think of convictions as tastes, they potentially contain a more urgent element. The person with the conviction can rationally debate her convictions with others in the market, as well as with the analyst. To the extent that she convinces others of her convictions, those people's outlook on the welfare of society will also be altered. But whether her convictions are right or wrong is a matter of logic, and not a matter of preference. Therefore, if it really is wrong to eat meat, our social contract should reflect this, while if we are simply worried about people's distate for meat, this distaste can be easily arbitrated by market mechanisms.

Convictions aside, to what extent do markets satisfy these other criteria for distribution? It is not always clear, but perhaps not too badly. Rawls, for example, advocated a distribution that maximized the minimum allocation of primary goods. He defined income as one of these goods, and did not get more specific about how that income should be spent. Rawls' criteria therefore might arguably be satisfied by and allocation that maximizes the income of the poorest person. However, in consumer theory, we take consumers' income as given. We will therefore have to wait until we examine production and markets, where we actually look at mechanisms that determine how income is distributed. If income is distributed in a way that matches Rawls' criterion, there may be little to require about how it is actually spent. On the other hand, to the extent that primary goods actually constitute individual goods (such as soap, coffee, etc.), a Rawlsian might demand a policy that ensures a minumum distribution of these goods. We looked at two candidates for such policies, namely food stamps to guarantee food consumption and laws against pollution when they leave someone without minimal environmental standards, that might be justified on Rawlsian grounds where utilitarian criteria might find them questionable.

The criterion of Sen, that an allocation of goods should leave everyone with the minimum capability to function and lead a meaningful life, cannot be evaluated within consumer theory for the simple reason that consumer theory does not leave us with the language to evaluate it. The Weak Axiom of Revealed Preference allows us to observe only the degree to which different goods satisfy people's tastes, not the degree to which they bring meaning to people's lives. Certainly, people are likely to prefer goods that they find meaningful, but there is no guarantee that preferred goods will bring one's life any meaning at all.

Dworkin's criterion is probably the easiest to satisfy with standard consumer theory. Recall that Dworkin argued for providing people with equal opportunities, and argued that individuals should be responsible for their tastes, but not for the circumstances they are born into. Dworkin therefore emphasized mechanisms that equalize opportunities for consumption, such as opportunities for earning income, but chose not to worry about how people use those opportunities. Therefore, as long as the distribution of income is fair, and people spend their incomes according to their tastes (which they do according to consumer theory), Dworkin's criterion leaves us little to complain about.

4.8 Conclusions

The theory of consumer choice and demand that we have reviewed in the last two chapters offers a complete and concise framework for predicting and evaluating the outcomes of consumer decisions. We know very precisely what assumptions about consumer behavior are required: We need assumptions U1 through U5 about consumer preferences, and we need the assumption that individuals' consumption decisions neither affect each other's tastes (even their own tastes) nor each other's well-being. Given all of these assumptions, we have the result that a market outcome is Pareto optimal, meaning that it will not leave any opportunities for wasted utility.

The weakness of the theory are twofold: First, not all of its assumptions will necessarily be satisfied in any consumption situation; and second, Pareto optimality is a somewhat vague criterion by which to judge an outcome. The first problem may be at times a strength rather than a weakness of the theory, to the extent that we know what types of policies can correct a market outcome when one of our assumptions fails to hold: A Pigouvian tax can correct an externality, a ban on cigarette advertising can prevent children from developing a taste for smoking, etc. The second weakness may be more damning. First of all, there will generally be many Pareto efficient solutions to an economic problem, and it would be nice to know whether an unregulated market or a particular government policy leads to one of the more appealing Pareto efficient outcomes or one of the less appealing ones. Second, more recent theories of allocation have emphasized the importance of issues of rights and due process when evaluating an allocation, and treating every economic conflict of interest as a conflict of preferences will not take such issues into account. Nevertheless, the theory of consumer choice provides strong results in the situation when one does not care too much about the above issues. For example, in analyzing the market for apples or oranges, one might not care a great deal about how people's preferences for these fruits were arrived at. However, the broader, more abstract, and more long-term the outcome being analyzed, the more cautious we have to be when applying the theory of consumer choice to a problem.

Key Concepts and Definitions

• The price-consumption curve is drawn by showing a series of consumer choice problems where the consumer's budget and the price of the good on the X axis are held constant, but the price of the good on the X axis varies. The price-consumption curve is just the line connecting the various allocations that the consumer chooses. Where the price-consumption path is upward-sloping, the goods are referred to as complements, and where it is downward-sloping, they are referred to as substitutes.
  
• The demand curve is drawn by taking each point on the X axis of the price consumption curve, and on the Y axis, drawing the price at which that quantity was chosen.
  
• The income-consumption curve is drawn by showing a series of consumer choice problems where the prices of goods stay constant, but the consumer's total budget is moved up and down. The income-consumption curve is just the line connecting the various allocations that the consumer chooses at different levels of income.
  
• The Engel curve is drawn by taking each point on the X axis of the income-consumption curve, using that point's X coordinate as the X coordinate of that point on the Engel curve, and for the Y coordinate, using the level of income at which that point was chosen. In regions where the Engel curve is upward-sloping, the good is a normal good, and in regions where it is downward-sloping or backward-bending, the good is an inferior good.
  
• The substitution effect of a change in prices measures the extent to which consumers change their quantity demanded as a good becomes relatively cheaper or more expensive. The substitution effect is always positive, meaning that consumers always buy more of a good as it becomes relatively cheaper when compared with other goods.
  
• The income effect derives from the fact that a price increase makes a consumer poorer, and a price drop makes the consumer wealther. When the price of a good falls, it leaves the consumer with some income left over after she buys what she bought before; she may either spend that income on the good whose price has dropped, or she may spend it on other goods. The income effect will be positive for normal goods, meaning it will cause a consumer to buy more of a normal good when its price drops, and it will be negative for inferior goods, meaning it will cause a consumer to buy less of an inferior good when its price drops.
  
• A Giffen good is a good for which the demand curve is upward sloping, i.e., the consumer buys less as the price falls. A Giffen good is a heavily inferior good - that is, the income effect for the good must be negative and larger in magnitude than the substitution effect.
  
• If people's preferences are formed independently of others' preferences and consumption choices, then the quantity of a good demanded by a whole market is just the sum of individuals' demand curves in that market. The market demand curve can be drawn by drawing the horizontal sum of the quantities demanded on each individual's demand curve at any given price.
  
• If assumptions U1 to U5 are satisfied, and If people's preferences are formed independently of others' preferences and consumption choices, then the quantities chosen by consumers at any set of prices in a market will be Pareto optimal. This result is known as the First Welfare Theorem.
  
• An externality is an effect of someone's economic activity on someone else, for which there is no compensation. A positive externality benefits the other person, while a negative externality harms him.
  
• If consumption of a good creates a positive externality, the consumer's marginal utility for the good is smaller than it would be if she were compensated for the externality. As a result, the amount chosen by a set of individuals in a market is Pareto optimal. A subsidized price for the good can equalize the amount chosen and restore the Pareto optimality of the allocation. Conversely, if consumption of a good creates a negative externality, then the consumer's marginal utility for the good is larger than it would be if she were charged for the externality that her consumption creates. Again, the amount chosen by consumers will not be Pareto optimal, but an appropriately sized tax on consumption of the good can restore the Pareto optimality of the outcome. If consumers have different preferences about consumption of the good, then a subsidy or tax will generally be Pareto superior to a strict per-capita limit on the amount consumed.
  
• If consumers are alruistic, then consumption decisions will not be Pareto optimal in many circumstances unless they are allowed to transfer income to each other. This may require organized intervention of a government or charitable organization if people do not know the individuals toward whom they feel altruism.
  
• If consumers purchase goods for strategic reasons, for example to send a signal to others, then wasteful consumption may ensue as people clamor to send the loudest signal. Not all consumption done for strategic reasons is wasteful, and even if it is, there is not necessarily a clear policy intervention that can effectively prevent wasteful consumption.
  
• If people's tastes are influenced by their past consumption, or others' consumption, then market demand may not be equal to the combined demand of individuals. Moreover, tastes may not always be formed in a healthy way, and if policy-makers know more about the effects of taste formation than the people whose tastes are being formed, it may be appropriate to intervene in the taste-formation process in a way that encourages healthier tastes.

Study Questions

1. Mikey spends all of his money on honey and oats. His demand for honey (in jars), as a function of its price, is QD = 20 - 5PH, regardless of his income or the price of oats, where QD is the number of jars of honey he demands. Suppose he has a budget of $50 and oats cost $2 per box. Draw his price-consumption curve, putting honey on the X-axis, as the price of oats goes from $1 to $3 in intervals of 50 cents. (Hint: Figure out his consumption of honey first; whatever he has left over he will spend on oats.) At what prices are honey and oats complements? At what prices are they substitutes?
2. Cigarettes are currently subject to heavy excise taxes. While the taxes are primarily justified as a means of discouraging teenagers to smoke, via an appeal to the prevailing wisdom that teenagers are irrational and don't know what's good for them, cigarette taxes apply equally to adults. Assume that adults are rational and aware of the consequences of purchasing cigarettes, and choose to purchase them in a way that best satisfies their preferences given their incomes, the price of cigarettes, and the prices of other goods. How might questions of externalities, altruism, strategic consumption, and endogenous preferences justify taxing cigarette purchases by adults as well?

Footnotes

...^4.1

See ``Fixed to Mobile Substitution'' by Case Associates, available at http://www.casecon.com/data/pdfs/casenote40.pdf.

....^4.2

For a detailed discussion of labor supply behavior, see a labor economics textbook, such as Ronald Ehrenberg and Robert Smith, Modern Labor Economics: Theory and Public Policy, 9th edition. Lebanon, IN, USA: Addison-Wesley (2005), Chapter 6.

...^4.3

Gerald Dwyer and Cotton Lindsay, ``Robert Giffen and the Irish Potato,'' American Economic Review, March 1984, 188-192.

...^4.4

Some astute readers may have noticed that this illustration assumes that the consumer is not in a corner solution, i.e., that the consumer chooses a positive amount of both goods. However, as mentioned earlier, there is nothing in the theory requiring her to do so. A corner solution is actually not a problem: For example, if she were in the upper-left corner, where she is consuming all Bonkers and no nuts, there are actually fewer price ratios at which she would be willing to give up Bonkers for nuts and be better off, compared to the consumer who has chosen some of each good. In other words, there are fewer possibilities for Pareto improvement at a corner solution than at a balanced solution.

...^4.5

See Ian Perry, ``Is Gasoline Undertaxed in the United States.'' Resources 148 (Summer 2002).

...^4.6

Ernst Fehr and Simon Gächter, ``Cooperation and Punishment in Public Goods Experiments.'' American Economic Review 90(4): 980-994 (2000).