Appendix B: Indifference Curves

Economists use a vocabulary that maximizing energy to explain people’s preferences. In consumer Choices, the level that utility the a person receives is explained in numerical terms. This appendix presents an different approach come describing personal preferences, dubbed indifference curves, which avoids any kind of need for using numbers to measure utility. By setup aside the presumption of placing a number valuation on utility—an presumption that many students and economists uncover uncomfortably unrealistic—the indifference curve frame helps come clarify the logic of the basic model.

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What Is one Indifference Curve?

People cannot really put a numerical worth on their level of satisfaction. However, castle can, and also do, identify what options would offer them more, or less, or the exact same amount that satisfaction. One indifference curve reflects combinations of goods that carry out an same level of energy or satisfaction. Because that example, figure 1 presents 3 indifference curve that stand for Lilly’s choices for the tradeoffs that she encounters in she two main relaxation activities: eating doughnuts and reading paperback books. Each indifference curve (Ul, Um, and also Uh) represents one level that utility. An initial we will discover the an interpretation of one certain indifference curve and also then we will look at the indifference curves together a group.

Figure 1. Lilly’s Indifference Curves. Lilly would receive equal energy from all points on a provided indifference curve. Any type of points top top the highest possible indifference curve Uh, favor F, provide greater energy than any kind of points favor A, B, C, and also D ~ above the center indifference curve Um. Similarly, any type of points ~ above the center indifference curve Um carry out greater utility than any points on the lowest indifference curve Ul.

The form of one Indifference Curve

The indifference curve Um has 4 points labeled on it: A, B, C, and D. Due to the fact that an indifference curve represents a set of options that have actually the exact same level of utility, Lilly must receive an equal amount that utility, judged follow to her an individual preferences, from two books and also 120 doughnuts (point A), from 3 books and 84 doughnuts (point B) indigenous 11 books and 40 doughnuts (point C) or from 12 books and also 35 doughnuts (point D). She would likewise receive the exact same utility from any kind of of the unlabeled intermediate points along this indifference curve.

Indifference curves have a roughly comparable shape in 2 ways: 1) they are downward sloping from left come right; 2) they are convex v respect come the origin. In other words, they space steeper top top the left and also flatter on the right. The downward slope the the indifference curve means that Lilly need to trade off much less of one great to get an ext of the other, when holding energy constant. Because that example, clues A and B sit on the very same indifference curve Um, which method that they carry out Lilly through the same level the utility. Thus, the marginal utility that Lilly would obtain from, say, increasing her consumption of publications from two to three have to be equal to the marginal energy that she would shed if her intake of doughnuts was reduced from 120 to 84—so that her all at once utility stays unchanged in between points A and also B. Indeed, the slope along an indifference curve is described as the marginal price of substitution, which is the rate at i m sorry a person is willing to trade one an excellent for another so that energy will continue to be the same.

Indifference curves favor Um space steeper top top the left and flatter ~ above the right. The reason behind this shape involves diminishing marginal utility—the id that together a human being consumes an ext of a good, the marginal utility from each extr unit i do not care lower. Compare two various choices between points that all provide Lilly an same amount of utility along the indifference curve Um: the an option between A and also B, and between C and also D. In both choices, Lilly spend one an ext book, but in between A and B her usage of doughnuts drops by 36 (from 120 to 84) and also between C and also D it drops by only five (from 40 come 35). The reason for this difference is the points A and also C are different starting points, and also thus have different implications because that marginal utility. At suggest A, Lilly has couple of books and many doughnuts. Thus, she marginal energy from an extra publication will be relatively high while the marginal energy of added doughnuts is reasonably low—so top top the margin, it will take a relatively big number that doughnuts to counter the utility from the marginal book. At suggest C, however, Lilly has actually many books and few doughnuts. Indigenous this beginning point, she marginal utility obtained from extra books will be reasonably low, when the marginal utility lost from added doughnuts would certainly be relatively high—so top top the margin, it will certainly take a fairly smaller number of doughnuts to balance out the readjust of one marginal book. In short, the slope of the indifference curve changes due to the fact that the marginal rate of substitution—that is, the quantity of one an excellent that would certainly be traded for the other great to save utility constant—also changes, together a an outcome of diminishing marginal utility that both goods.

The field of Indifference Curves

Each indifference curve to represent the selections that carry out a solitary level that utility. Every level of energy will have its own indifference curve. Thus, Lilly’s choices will encompass an infinite variety of indifference curve lying nestled together on the diagram—even though just three the the indifference curves, representing 3 levels the utility, show up on number 1. In other words, one infinite variety of indifference curves space not attracted on this diagram—but you have to remember that they exist.

Higher indifference curves represent a higher level of utility than lower ones. In figure 1, indifference curve Ul deserve to be thought of as a “low” level the utility, while Um is a “medium” level that utility and Uh is a “high” level the utility. Every one of the options on indifference curve Uh are preferred to all of the options on indifference curve Um, which consequently are desired to every one of the options on Ul.

To understand why greater indifference curves are preferred to reduced ones, compare suggest B top top indifference curve Um to point F ~ above indifference curve Uh. Allude F has greater usage of both publications (five come three) and also doughnuts (100 to 84), so suggest F is clearly preferable to allude B. Given the an interpretation of one indifference curve—that every the points on the curve have the exact same level that utility—if allude F ~ above indifference curve Uh is wanted to allude B on indifference curve Um, climate it have to be true that all points on indifference curve Uh have actually a greater level of utility than all points ~ above Um. Much more generally, for any point on a reduced indifference curve, like Ul, you have the right to identify a allude on a higher indifference curve favor Um or Uh that has actually a higher consumption that both goods. Due to the fact that one allude on the greater indifference curve is desired to one suggest on the lower curve, and since all the clues on a provided indifference curve have the very same level of utility, it need to be true the all point out on greater indifference curves have greater utility 보다 all points on reduced indifference curves.

These arguments about the forms of indifference curves and also about higher or reduced levels of utility execute not require any numerical approximates of utility, either by the separation, personal, instance or by anyone else. They space only based on the presumptions that when world have much less of one an excellent they need more of another great to comprise for it, if they are keeping the exact same level of utility, and that as world have much more of a good, the marginal energy they get from extr units the that good will diminish. Provided these gentle assumptions, a ar of indifference curves have the right to be mapped the end to explain the preferences of any type of individual.

The personality of Indifference Curves

Each human being determines their own preferences and also utility. Thus, if indifference curves have actually the same basic shape—they steep down, and also the slope is steeper ~ above the left and flatter on the right—the specific shape that indifference curves can be various for every person. Figure 1, for example, uses only to Lilly’s preferences. Indifference curves because that other civilization would most likely travel through different points.

Utility-Maximizing v Indifference Curves

People seek the greatest level that utility, which way that they great to it is in on the highest feasible indifference curve. However, people are restricted by their budget constraints, which present what tradeoffs are actually possible.

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Maximizing utility at the greatest Indifference Curve

Return come the situation of Lilly’s choice between paperback books and doughnuts. Speak that publications cost \$6, doughnuts room 50 cent each, and that Lilly has \$60 to spend. This information gives the basis for the spending plan line displayed in figure 2. Along with the budget line are shown the three indifference curve from figure 1. What is Lilly’s utility-maximizing choice? several possibilities are identified in the diagram.