How to Read a Fan Curve Given 2 Points
Learning Objectives
- Depict the purpose, use, and shape of indifference curves
- Explain how one indifference curve differs from another
- Explain how to notice the consumer equilibrium using indifference curves and a budget constraint
Economists use the vocabulary of maximizing utility to draw consumer choice. Then far in the text, we have described the level of utility that a person receives in numerical terms. This section presents an culling arroyo to describing personal preferences, called indifference curve analysis, which avoids the need for using numbers to measure utility. Past setting aside the assumption of putting a numerical valuation on utility—an assumption that many students and economists find uncomfortably unrealistic—the indifference curve framework helps to clarify the logic of the underlying model.
What Is an Indifference Curve?
People cannot really put a numerical value on their level of satisfaction. However, they can, and practise, place what choices would requite them more, or less, or the same amount of satisfaction. An indifference curve shows all combinations of goods that provide an equal level of utility or satisfaction.
For example, Figure 1 presents 3 indifference curves that stand for Lilly's preferences for the tradeoffs that she faces in her two main relaxation activities: eating doughnuts and reading paperback books. Each indifference curve (Ul, Um, and Uh) represents one level of utility. Offset we volition explore the meaning of an individual indifference curve and and then we will look at the relationship between unlike indifference curves.
Effigy 1. Lilly's Indifference Curves. Lilly would receive equal utility from all combinations of books and doughnuts on a given indifference bend. Whatever points on the highest indifference curve Uh, like F, provide greater utility than any points like A, B, C, and D on the center indifference curve Um. Similarly, any points on the middle indifference curve Um provide greater utility than any points on the lowest indifference bend Ul.
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Lookout the clip from this video carefully to see examples of indifference curves and what makes them useful. Each point on the indifference curves represents the same level of satisfaction.
Shape of an Indifference Curve
The indifference bend Um has four points labeled on it: A, B, C, and D (meet Figure 1). Since an indifference curve represents a ready of choices that have the aforementioned level of utility, Lilly must receive an equal amount of utility, judged according to her personal preferences, from two books and 120 doughnuts (point A), from three books and 84 doughnuts (bespeak B) from 11 books and 40 doughnuts (signal C) or from 12 books and 35 doughnuts (bespeak D). She would also receive the aforementioned utility from any of the unlabeled intermediate points forth this indifference curve.
Indifference curves take a roughly similar shape in two ways: 1) they are downward sloping from left to correct; 2) they are convex with respect to the origin. In other words, they are steeper on the left and flatter on the right. The downward gradient of the indifference bend means that Lilly must merchandise off less of one practiced to get more of the other, while belongings utility constant. For example, points A and B sit on the same indifference curve Um, which means that they provide Lilly with the same level of utility. Thus, the marginal utility that Lilly would gain from, say, increasing her consumption of books from two to 3 must be equal to the marginal utility that she would lose if her consumption of doughnuts was cutting from 120 to 84—and then that her overall utility remains unchanged between points A and B. Indeed, the slope forth an indifference curve as the marginal rate of substitution, which is the charge per unit at which a person is willing to trade one good for some other and then that utility will remain the same.
Indifference curves like Um are steeper on the left and flatter on the right. The reason behind this shape involves diminishing marginal utility—the notion that as a person consumes more than of a good, the marginal utility from each boosted unit becomes lower. Compare two different choices between points that all provide Lilly an equal amount of utility forth the indifference bend Um: the choice betwixt A and B, and between C and D. In both choices, Lilly consumes 1 more book, but between A and B her consumption of doughnuts falls by 36 (from 120 to 84) and between C and D it falls by simply v (from 40 to 35). The reason for this divergence is that points A and C are unlike starting points, and thus have different implications for marginal utility. At point A, Lilly has few books and many doughnuts. Thus, her marginal utility from an extra book will exist relatively high while the marginal utility of additional doughnuts is relatively low—so on the margin, it volition accept a relatively large number of doughnuts to offset the utility from the marginal book. At betoken C, all the same, Lilly has many books and few doughnuts. From this starting point, her marginal utility gained from extra books will be relatively low, while the marginal utility lost from additional doughnuts would be relatively high—so on the margin, it will have a relatively smaller number of doughnuts to outset the alter of one marginal volume. In short, the slope of the indifference curve changes because the marginal rate of exchange—that is, the quantity of one skilful that would be traded for the other skilful to keep utility constant—besides changes, equally a result of diminishing marginal utility of both appurtenances.
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Field of Indifference Curves
Each indifference curve represents the choices that provide a single level of utility. Every level of utility will take its own indifference curve. Thus, Lilly'southward preferences will include an infinite number of indifference curves lying nestled together on the diagram—even though only iii of the indifference curves, representing 3 levels of utility, appear in Effigy ane. In other words, an infinite number of indifference curves are not fatigued on this diagram—but you should remember that they exist.
College indifference curves represent a greater level of utility than lower ones. In Figure 1, indifference curve Ul tin be idea of as a "low" level of utility, while Um is a "medium" level of utility and Uh is a "high" level of utility. All of the choices on indifference curve Uh are preferred to all of the choices on indifference curve Um, which in turn are preferred to all of the choices on Ul.
To understand why higher indifference curves are preferred to lower ones, compare point B on indifference curve Um to point F on indifference curve Uh. Point F has greater consumption of both books (v to three) and doughnuts (100 to 84), so betoken F is conspicuously preferable to point B. Given the definition of an indifference bend—that all the points on the bend have the same level of utility—if indicate F on indifference bend Uh is preferred to betoken B on indifference curve Um, then information technology must be truthful that all points on indifference curve Uh have a higher level of utility than all points on Um. More generally, for any bespeak on a lower indifference curve, like Ul, you can identify a indicate on a higher indifference curve similar Um or Uh that has a college consumption of both appurtenances. Since one point on the college indifference bend is preferred to one point on the lower bend, and since all the points on a given indifference curve take the same level of utility, information technology must be truthful that all points on college indifference curves have greater utility than all points on lower indifference curves.
These arguments near the shapes of indifference curves and about higher or lower levels of utility do non require any numerical estimates of utility, either by the individual or by anyone else. They are but based on the assumptions that when people have less of one good they need more of another good to make up for information technology, if they are keeping the same level of utility, and that equally people have more than of a skillful, the marginal utility they receive from boosted units of that skilful will diminish. Given these gentle assumptions, a field of indifference curves tin can exist mapped out to depict the preferences of any individual.
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Individuality of Indifference Curves
Each person determines his or her own preferences and utility. Thus, while indifference curves have the same general shape—they slope downward, and the gradient is steeper on the left and flatter on the right—the specific shape of indifference curves tin can be different for every person. Effigy 1, for example, applies merely to Lilly'south preferences. Indifference curves for other people would probably travel through different points.
Render to the situation of Lilly'south choice between paperback books and doughnuts. Say that books cost $6, doughnuts are l cents each, and that Lilly has $60 to spend. This information provides the basis for the budget line shown in Figure ane. Along with the budget line are shown the iii indifference curves from Figure 1. What is Lilly's utility-maximizing choice? Several possibilities are identified in the diagram.
Figure 2. Indifference Curves and a Upkeep Constraint. Lilly's preferences are shown past the indifference curves. Lilly's budget constraint, given the prices of books and doughnuts and her income, is shown past the straight line. Lilly's optimal choice volition be point B, where the budget line is tangent to the indifference bend Um. Lilly would accept more utility at a bespeak like F on the college indifference curve Uh, but the budget line does not bear upon the higher indifference bend Uh at whatever point, and so she cannot afford this choice. A option similar 1000 is affordable to Lilly, but it lies on indifference curve Ul and thus provides less utility than choice B, which is on indifference curve Um.
The selection of F with v books and 100 doughnuts is highly desirable, since it is on the highest indifference bend Uh of those shown in the diagram. However, information technology is not affordable given Lilly'due south budget constraint. The choice of H with three books and 70 doughnuts on indifference curve Ul is a wasteful pick, since it is inside Lilly'southward budget set, and equally a utility-maximizer, Lilly will always prefer a option on the budget constraint itself. Choices B and G are both on the opportunity set. However, choice G of six books and 48 doughnuts is on lower indifference curve Ul than option B of 3 books and 84 doughnuts, which is on the indifference curve Um. If Lilly were to beginning at choice K, and then thought about whether the marginal utility she was deriving from doughnuts and books, she would decide that some additional doughnuts and fewer books would make her happier—which would cause her to motility toward her preferred choice B. Given the combination of Lilly's personal preferences, as identified by her indifference curves, and Lilly's opportunity set, which is determined by prices and income, B will be her utility-maximizing pick.
The highest achievable indifference curve touches the upkeep constraint at a single point of tangency. Since an infinite number of indifference curves exist, fifty-fifty if only a few of them are drawn on any given diagram, there will e'er exist one indifference curve that touches the upkeep line at a single point of tangency. All higher indifference curves, like Uh, will be completely in a higher place the budget line and, although the choices on that indifference curve would provide higher utility, they are non affordable given the budget set up. All lower indifference curves, like Ul, will cantankerous the budget line in ii separate places. When ane indifference curve crosses the budget line in two places, all the same, in that location will be some other, higher, attainable indifference curve sitting higher up it that touches the budget line at but one point of tangency.
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Watch It
Watch this video to utilize what you lot've learned about using indifference curves to find consumer equilibrium.
Try It
These questions allow you lot to get as much exercise as you need, as you tin click the link at the top of the first question ("Try another version of these questions") to become a new set of questions. Exercise until you feel comfortable doing the questions.
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Source: https://courses.lumenlearning.com/wm-microeconomics/chapter/indifference-curves-analysis/
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