If there is one constant about economics it is the manner in which the discipline views tastes. Generally, economists assume that consumers have stable and well-defined preferences. That is, there is little change in individual utility functions over time. Obviously, there are exceptions. In the late 1980s, medical research supported oat bran as an important dietary ingredient, and suddenly, individuals wanted oat bran. After oat bran was shown to not be particularly healthy the preference for it shifted back just as precipitously. But generally, while tastes may change through life, over relevant periods of study we expect such changes to be small enough to ignore.
The same assumption is not made about income and prices. In fact, 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. It is the assumption about stable preferences that allows economists to analyze price and income changes.
You should recall that 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 line connecting the utility maximizing points of consumption for all budget levels is called the income-consumption line. In the two good world at least one of the goods must be a normal good. If one of the goods is an inferior good, the income-consumption line will have a negative slope over the income range for which it is inferior. The shape of the income-consumption line depends on the individual's utility function. If it bends more towards one good as income increases it indicates preferences value that good more.
Related to the income-consumption line is the Engel curve. The Engel curve relates the individuals expenditure on each good individually to total income. Since we are assuming prices are constant, it is the same as relating the quantity consumed of each good to total income.
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As usual, convention has the graph of the Engel curve backward from causality. While we are looking at the effect of income changes on consumption, like demand and supply curves, quantity is on the horizontal axis, making it more difficult than it need be for students to understand. Figure 4.30 shows an Engel curve for good X which was derived from the income-consumption line given in figure 4.29a. The horizontal axis again measures X. But the vertical axis now measures income. From figure 4.29(a), we can see that if income increases from M1 to M2, consumption of X increases as well. For normal goods the Engel curve is upward sloping.
The shape of the Engel curve, like the shape of the income-consumption line, depends on the individual's utility function. Figure 4.30 showed a relatively steep Engel curve, which indicates that while the consumption of X increases with income, it does so slowly. Alternatively, if the Engel curve were relatively flat, it would indicate that consumption of the good increases more than proportionately with income.
Service is a good which shows an increase in consumption as income goes up. A survey reported in that article said only 46 percent of those with incomes below 20000 dollars felt they got good service. But 57 percent of those with incomes between 20000 and 50000 dollars felt good about the service they received. Sixty-one percent of those with incomes exceeding 50000 dollars felt they got excellent or good service. Apparently, presuming you get what you pay for, the Engel curve for service would look like that shown in figure 4.31. As income goes up, the consumption of service increases at an increasing rate.
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.
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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. The price consumption line connects the utility maximizing points of consumption for different prices of a good, holding income, tastes, and the prices of other goods constant. One is shown in figure 4.33. Under some general assumptions about good Y, mostly that is represents all other goods, the slope of the price-consumption line tells us about the individual's price elasticity of demand. If the price-consumption line for good X is parallel to the horizontal axis, this individual will have unitary demand elasticity for X. If it is positively sloped the individual demand is inelastic, and if it is negatively sloped it is elastic.
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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.