As consumers, people are constantly forced into making choices. They face a variety of goods and services which can be purchased, but a limited amount of money with which those purchases can be made. The theory of consumer behavior explains how people can best utilize their resources to achieve the highest level of satisfaction possible.
 
 

What people consume is not necessarily what they prefer. Resource constraints - limits on time and money - force individuals to choose between alternative goods. Preferences are simply the way an individual ranks alternative goods or groups of goods. Some people like oranges, and some like apples. Economists tend to relate those preferences to utility, the satisfaction an individual will derive from consumption. Economists have found several desirable traits by which to characterize preferences. Most help in depicting preferences mathematically, but one is of particular interest here, a concept known as "more is better". "More is better" just means that, all else equal, a person prefers more consumption to less.

Utility

Economists can not directly measure utility or say how much one package of consumption is preferred to another because preferences are ordinal not cardinal. It is possible to say that one market basket is preferred to another, but not by how much. Faced with two possible baskets of goods, A and B, an ordinal ranking tells us that A is preferred to B. A cardinal ranking would be much stronger. It would tell us, for example, that basket A gives twice as much utility as basket B. Since we don't have a measure of utility, the best we can do is the ordinal measure.

Marginal Utility

The marginal utility of a good X, denoted MUX, is the change in total utility that comes from a small change in the amount of X consumed, holding all else constant. So if DX means a small change in the amount of X consumed, MUX=DU/DX, where DU is the change in utility. (With calculus, this is just MUX=¶U/¶X). One of the fundamental concepts of economics is the idea that (eventually) the marginal utility of all goods decreases as the amount of the good consumed increases. In other words, as an individual consumes more and more of a good, the marginal utility of the last unit consumed goes down. When marginal utility is falling as consumption increases it is called Diminishing Marginal Utility (DMS). If an individual consumes more of a good, the marginal utility falls, but if consumption of a good is cut back the marginal utility derived from the last unit consumed increases.

DMS seems to ignore "more is better", but not really. Utility refers to satisfaction from total consumption; marginal utility only to the additional satisfaction from one more unit of a particular good. "More is better" applies to utility only, not marginal utility. In short, everybody always wants more of something. But they might not want more of a specific thing.
 
 

Consumers do not have unlimited budgets. In general, a choice must be made on how to allocate money to purchasing different amounts of each good. The problem of consumer equilibrium is what that allocation should be. For the purpose of illustration, however, we will usually look at a two good world, with the only constraint being money. It helps simplify the analysis.

Assume an individual has an amount M of money available for purchases, and faces prices Px for good X and Py the good Y. Then the individual has a budget constraint given by the equation M=PxX+PyY. The total amount spent of good X, its price times the quantity consumed, plus the total amount spent on good Y, can not exceed the money available for purchases. The budget constraint gives the first rule for consumer equilibrium: Spend all your budget. If some of the budget is saved, it can be interpreted as a reserve for future consumption anyway, so the rule still holds, just across time.

The second rule is a bit more complicated. It tells how to allocate the budget across competing uses. Mathematically, the rule is to allocate the budget so MUX/Px=MUY/Py.. That is, allocate your available resources so the marginal utility per unit price of each good is equal. This means is the marginal utility for the last dollar spent on each good should be the same.

It is easiest to understand this rule by looking at possible adjustments if the rule is violated. Suppose, at some consumption package, the marginal utility of X equals 10 and the marginal utility of Y equals 20. And suppose both X and Y cost one dollar per unit. If one dollar that had been spent on X is transferred to Y, total utility would increase by about 10 units. One dollar less spent on X would reduce total utility by the marginal utility of X, given as 10. But as that dollar is spent on another unit of Y, the consumer gains the marginal utility of Y, or 20 units of additional utility. The net change is an increase of 10 units of utility.
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Graphs offer another way of understanding consumer equilibrium. What follows isn't new, just another way of looking at the problem.

The Indifference Curve

An indifference curve is a two dimensional graph representing the different combinations of goods that give the same level of utility to an individual. An indifference curve shows alternative combinations of X and Y that give the same value for U.

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Figure 4.2 shows a typical indifference curve. All points on the curve give the same specific value of utility, so the consumer is said to be indifferent between all points on the curve. By definition the consumer is equally satisfied with all points on a single indifference curve. Thus, U'=f(X1,Y1) and U'=f(X2,Y2) also. Every point on the curve shown gives the same level of utility, U'.
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A curve further from the origin than U', say U" as shown in figure 4.3, indicates a higher level of utility. That is, U" will be a larger value that U', indicating that the consumer would prefer any combination of goods on the curve U" to any combination of goods on the curve U'. (Remember these are ordinal values. Thus, we do not know how much more preferred U" is to U'.)
 
 

The slope of the curve shows the ease at which goods can substituted with the level of utility held constant, as shown in figure 4.5. Since both point 1 and point 2 are on the indifference curve labeled U', the consumer values both combinations of X and Y equally. She will be indifferent about giving up some Y to get more X, or some X to get more Y as long as she stays on the same curve. The slope tells us how much. If she were to move from consuming point 1 to consuming point 2, she would relinquish Y1-Y2=DY of Y but gain X1-X2=DX of X.  So DY/DX is simply the slope of the indifference curve, and it indicates how willing the person will substitute X for Y -- how much Y the person will willingly give up to get one more unit of X (and not change the level of utility), or alternatively, how much Y would substitute for a unit of X. It equals MUX/MUY so the MRTS=¶Y/¶X holding U constant. When the indifference curve is convex the person's willingness to substitute X for Y is decreasing as we move downward to the right on the curve.
 
 

In figure 4.6, a move from point 1 to point 2 shows an that a change of DX will replace DY1. A move from point 2 to point 3 shows 1 unit of X substitutes for DY2. The points were positioned so the change in X is equal for movement between each point. Since DY1 is clearly larger than DY2, the ability to substitute X for Y has diminished. This means that the amount of Y that will compensate for a unit of X gets smaller as the consumer has more X and less Y.

This conclusion comes from the concept of diminishing marginal utility. As we move from point 1 to point 2 and then to point 3, the individual is consuming more and more X but less and less Y. Because the individual consumes less of it, Y has a higher marginal utility. But since the consumer has a lot of X, additional X has little marginal utility. It becomes increasingly difficult to substitute X for Y; each additional unit of X can replace a smaller amount of Y.

The Budget Constraint

Budget constraints are the factor that limit the utility level that an individual can achieve. The budget constraint is a linear function of the form M=PxX+PyY, where M is the amount of money to be spent, Px is the price of good X, and Py is the price of good Y. M is the constraining factor, and we assume that the individual must pay the asking price, that is, both prices are assumed fixed.

Rearrange the budget constraint to the form Y=(M/Py)-(Px/Py)X. Notice, this states Y as a function of X, with a Y-axis intercept of M/Py and a slope of -Px/Py. The X-axis intercept is M/Px. Some budget constraints are shown in figure 4.16. Just as with the indifference curve, the farther the budget constraint is from the origin, the larger the budget. Thus, M" is larger than M'.

An important fact about budget constraints is that relative prices and incomes matter, not absolute levels. Thus, if all prices and income doubled, the budget constraint would not move. But if the relative value of income or prices change, there are shifts in the budget constraint. An increase in income, that is if M increases, gives a parallel shift in the budget constraint, just as was shown in figure 4.16. Changes in relative prices, however, will pivot the line since the slope is the negative of the ratio of the prices.

Suppose the price of X increases from Px' to Px". Since there is no change in M or Py, the Y-axis intercept does not move. But the slope is now steeper, and the value of the X-axis intercept, M/Px, falls. In figure 4.17, the curve would pivot in as shown.

Graphical Analysis of Utility Maximization

The utility maximizing point of consumption is found at the tangent between the budget constraint and an indifference curve. In figure 4.20, indifference curve U3 indicates a higher level of utility than does indifference curve U2. But no point on U3 lies within the consumer's choice set. They are all unattainable. If any point on a lower indifference curve like U1 that is also on or below the budget constraint is chosen, for example the consumption point 1, utility is not being maximized. It could be increased by substituting Y for X along the budget constraint until consumption is at point 2.

The characteristics of consumption at the point of tangent are the same as discussed above. First, by virtue that the point lies on the budget constraint, we know that all of the available resources are being spent. Second, the tangent between the budget constraint and the indifference curve indicates that MUX/Px=MUY/Py. Two curves always have the same slope at a tangent point. The slope of the indifference curve is the negative marginal rate of substitution, which we showed earlier equals -MUX/MUY. The slope of the budget constraint is -Px/Py. Setting these two values equal, and rearranging, produces the second rule for utility maximization.

This simple model can be used to analyze the policy effects and differences in individual consumption. One example is occupational safety. Few people would argue with the conjecture that, in general, workers prefer safer jobs to more dangerous ones, all else being equal. But the "all else being equal" is an important and constraining caveat. Safety is not a free good. Firms set salaries, benefits and job characteristics according to the value of the job in producing profit for the firm. Much as a firm can tradeoff salary and benefits (see the discussion about this in the section on budget constraints), the firm can also tradeoff costs of salary and other job characteristics, like safety. Since safety is costly, a firm may have to lower the salary offered a worker to increase the safety of the job.

This idea is illustrated in figure 4.22. On the horizontal axis we have measured the wages (compensation) offered the worker. Job safety is measured on the vertical axis. If a firm has a budget of M dollars for the job, a safety level of M/Ps is the most that can be achieved within that budget, where Ps is the price per unit of safety. Of course, if the entire budget is spent on making the job safe, as would be indicated by the point M/Ps on the vertical axis, there is nothing left for wages. Alternatively, all of M could be paid in wages, with no concern about job safety (point M on the horizontal axis).

Workers have preferences about the tradeoff of safety and wages, which fit into a utility function framework. The level of satisfaction derived from a job is positively related to both wages and safety. A worker who is very concerned with safety would have an indifference curve skewed in that direction, like curve Us, and would seek a job with Ss level of safety and wages of ws. A different worker, one who does not care as much about safety, and is much more interested in wages, might have an indifference curve like Uw. This worker maximizes his utility by finding a job with higher pay, even if the risks are greater. Within the budget constraints firms have for jobs, constraints which determine things like wages and job characteristics, workers maximize their utility by finding a job with the combination of compensation and characteristics which most closely maximizes their utility. This concept is called self selection. It indicates that individuals will often choose different characteristics in jobs to maximize their utility. They maximize utility at different points on the budget constraint because they have different utility functions, which just represents the idea that people have different tastes and preferences.
 
 

Utility maximization requires that the last dollar spent on each good yield the same marginal utility. Additionally, it requires that the budget constraint be binding. Consumers continually adjust on the margin to changing prices in the market, as well as to changes in their own income.

Income Changes and Utility Maximization

It is easy to observe changes in relative incomes and prices. Much of economics deals with how these changes effect the individual's utility maximizing consumption. Economists assume preferences don't change quickly so they can analyze price and income changes.

Income changes cause a parallel shift in the budget constraint. An increase in income will move the line outward, a decrease will move it inward. By finding the utility maximizing point of consumption on the new budget constraint, it is possible to classify goods a normal or inferior.

Figure 4.29(a) illustrates the impact of an income change when both goods are normal goods. Relative prices have not changed, so the slopes of the budget constraints are equal. But the relative budget is larger for the line further out, that is M2>M1. Utility maximization at each budget level shows the consumption of both X and Y increases if the amount spent is higher. Alternatively, one good can be an inferior good, as illustrated in figure 4.29(b). In this case, the consumption of X increases as M increases to M2, but the consumption of Y falls. Y is an inferior good. The i-c line just shows what happens to consumption as income changes.

The Effects of Price Changes
 
 

Changes in relative prices will pivot the budget constraint. How this will effect individual consumption again depends on the person's preferences. Panel a of figure 4.32 shows one possible situation. The price of good X falls from PX1 to PX2, shifting the horizontal intercept of the budget constraint from M/PX1 to M/PX2. Utility maximizing consumption moves from point 1 to point 2, and as shown the consumption of both goods increase.

A second possibility is that the consumption of X will increase but the consumption of Y will decrease (see panel b of figure 4.32). This graph shows the same shift in the budget constraint, but a different set of indifference curves. Other possible outcomes, not illustrated, is that the consumption of X will decrease while that of Y increases, or the consumption of one of the goods stays the same, while the other increases. About the only outcome that cannot happen is that the a decrease in the price of one of the goods causes the consumption of both of the goods to decrease. That would violate the "more is better" rule, since the new budget constraint dominates the old one at all points but the vertical intercept.

Income and Substitution Effects of Price Changes

An increase in the price of a good decreases the feasible set of consumption possibilities for all goods, not just for the good with a higher price. A price decrease, as shown in figure 4.34, expands the possible consumption set. The shaded area indicates new consumption packages that can be achieved if the price of X decreases to PX2 even if income and the price of Y do not change. An individual can increase her consumption of X, or Y, or both goods, and achieve a higher level of utility. It is almost like she received an income increase, because she can afford more utility.

In a way, this consumer is wealthier. Recall that the location and slope of the budget constraint depends on relative, not absolute, prices and income. If the price of X goes down, two relative values have changed; M/PX has increased, thus making X more affordable relative to income (the same income can buy more X), and PX/PY has decreased, so X is less expensive relative to Y than it was before the price decrease. These are two different changes with different implications on behavior. A consumer could interpret the larger set of feasible consumption possibilities as a wealth increase, essentially a bigger budget. She will feel like she has more to spend. And the change in prices makes X more attractive relative to Y, so she may substitute X for Y in her consumption decision.

Although the consumer sees only the net effect - that the price of X has decreased - it is instructive to isolate the distinct impacts on her behavior. Economists call the two separate effects the Income effect - the change in the consumption of X because the set of feasible consumption bundles has changed - and the Substitution effect - the change in the consumption of X because the price of it relative to the price of Y has changed. The total change in the consumption of X (and Y) is the sum of the income and substitution effects.

Figure 4.35 isolates the income and substitution effects from a decrease in the price of X. The consumer originally faces a budget constraint M=PxX+PyY, and her optimal consumption is at point 1. If the price of X decreases to Px* her budget constraint pivots out to reflect her new budget constraint M=Px*X+PyY, and now her optimal consumption would be at point 3. To understand how much of the change in her consumption is due to the income effect, and how much is due to the substitution effect, we decompose the total effect to two parts.

The income effect is attributed to her ability to buy more utility at the lower price of X. Thus, to eliminate the income effect all we need to do is eliminate her ability to achieve a higher utility level. That is, we keep her at the original utility level, U, by taking away some of her budget. This is the line tangent to the indifference curve labeled U, but with a slope consistent with the new price ratio Px*/Py. The budget constraint giving this line is M*=Px*X+PyY. By looking at the vertical axis, we can see that M* is less than M. The tangent is at point 2. It shows her optimal consumption at the new prices, with no ability to purchase higher utility. Any change in consumption can be attributed entirely to the change in relative prices, that is, this change in consumption is the substitution effect. In this case, the substitution effect on X of a decrease in the price of X is X2-X1. The substitution effect for a good is always opposite its change in price. If price of X goes down, the substitution effect says the quantity demanded of X will increase. It is often termed the compensated response of the quantity demanded for X to a change in its price. Notice that the substitution effect also moves the consumption of Y in the same direction as the change in the price of X.

Budget constraints M*=Px*X+PyY and M=Px*X+PyY are parallel, indicating that the only change is in the size of the budget. Since M is larger than M*, it shows an income response which is attributable to the change in the price of X. In fact, the income effect measures how much additional utility can be afforded, and is indicated by the move from point 2 to point 3. As drawn, both X and Y are normal goods, but as we saw above, consumption of a good due to income changes can be positive, negative or neutral. Thus, while we were able to say the substitution effect from a price decrease for X is always toward increase in the consumption of X, the income effect is uncertain. If X is an inferior good, X3 would lie to the left of X2. In fact, it is possible for the income effect to move opposite the substitution effect, and be larger, so that X3 would be to the left of X1. This is called a Giffen good, and would have an upward sloping demand curve. It is an inferior good with a price effect on the feasible consumption set so strong that an increase in its price causes the consumption of it to increase as well. Such a good must be very inferior and have a very weak substitution effect. Although there are many inferior goods, Giffen goods are very rare. For the rest of this book we shall ignore them.