Indifference Curve Analysis

1. What you’ll learn to do: find consumer equilibrium using indifference curves and a budget constraint

Although numbers can be used to illustrate consumer preferences, economists don't believe that we can objectively measure someone's utility. In this section, you'll learn an alternative way of identifying consumer equilibrium that only requires that you can rank preferences - that is, you can say whether you prefer Option A to Option B.

LEARNING OBJECTIVES

• Describe the purpose, use, and shape of indifference curves
• Explain how one indifference curve differs from another
• Explain how to find the consumer equilibrium using indifference curves and a budget constraint

Economists use the vocabulary of maximizing utility to describe consumer choice. So far in the text, we have described the level of utility that a person receives in numerical terms. This section presents an alternative approach to describing personal preferences, called indifference curve analysis, which avoids the need for using numbers to measure utility. By 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.

Source: Steven Greenlaw and Lumen Learning, https://courses.lumenlearning.com/wmopen-microeconomics/chapter/indifference-curves-analysis/
This work is licensed under a Creative Commons Attribution 4.0 License.

2. What Is an Indifference Curve?

People cannot really put a numerical value on their level of satisfaction. However, they can, and do, identify what choices would give 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 three indifference curves that represent 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. First we will explore the meaning of an individual indifference curve and then we will look at the relationship between different indifference curves.

2.1. The Shape of an Indifference Curve

The indifference curve Um has four points labeled on it: A, B, C, and D (see Figure 1). Since an indifference curve represents a set of choices that have the same 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 (point B) from 11 books and 40 doughnuts (point C) or from 12 books and 35 doughnuts (point D). She would also receive the same utility from any of the unlabeled intermediate points along this indifference curve.

Indifference curves have a roughly similar shape in two ways: 1) they are downward sloping from left to right; 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 slope of the indifference curve means that Lilly must trade off less of one good to get more of the other, while holding 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 three must be equal to the marginal utility that she would lose if her consumption of doughnuts was cut from 120 to 84 - so that her overall utility remains unchanged between points A and B. Indeed, the slope along an indifference curve as the marginal rate of substitution, which is the rate at which a person is willing to trade one good for another so 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 of a good, the marginal utility from each additional unit becomes lower. Compare two different choices between points that all provide Lilly an equal amount of utility along the indifference curve Um: the choice between A and B, and between C and D. In both choices, Lilly consumes one 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 only five (from 40 to 35). The reason for this difference is that points A and C are different 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 be relatively high while the marginal utility of additional doughnuts is relatively low - so on the margin, it will take a relatively large number of doughnuts to offset the utility from the marginal book. At point C, however, 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 take a relatively smaller number of doughnuts to offset the change of one marginal book. In short, the slope of the indifference curve changes because the marginal rate of substitution - that is, the quantity of one good that would be traded for the other good to keep utility constant - also changes, as a result of diminishing marginal utility of both goods.

2.2. Try It

Allison's preference for donuts or coffee is mapped by an indifference curve with coffee on the horizontal axis and donuts on the vertical axis. At her utility-maximizing consumption bundle the marginal rate of substitution is 5 donuts for a single coffee. Which point along the indifference curve shown below is her most likely utility-maximizing choice?

• Point C
• Point A
• Point B

Peggy returns from trick-or-treating with 50 pieces of chocolate and 50 pieces of caramel. Last year she returned with only 5 pieces of chocolate but over 300 pieces of caramel, yet she finds her stash of candy to be equally enjoyable this year as last. Which of the following statements must be true?

• Peggy always receives more utils eating chocolate than caramel.
• The only explanation for Peggy's indifference between this year and last is that her tastes have fundamentally changed. She no longer enjoys caramel as much as she did before.
• Peggy's indifference curve of chocolate and caramel is convex.

2.3. Check Answers

• Point C
  Incorrect At this point the indifference curve is shallow and the marginal rate of substitution is small. Allison would have to consume many cups of coffee in exchange for losing a single donut while remaining on the same indifference curve.
• Point A
  Correct! At this point the indifference curve is steep and Allison would have to consume a significant number of donuts in exchange for a single coffee to remain on the same indifference curve.
• Point B
  Incorrect. At this point the marginal rate of substitution, the absolute value of the slope of the indifference curve, approaches one and she would only have to consume a single extra donut in exchange for a single coffee.
  
  

• Peggy always receives more utils eating chocolate than caramel.
  Incorrect The shape of the indifference curve implies that the marginal rate of substitution changes depending on her relative consumption of chocolate and caramel. She may be indifferent between 5 chocolates 300 caramels and 300 chocolates 5 caramels.
• The only explanation for Peggy's indifference between this year and last is that her tastes have fundamentally changed. She no longer enjoys caramel as much as she did before.
  Incorrect. Her indifference curve may be identical to last year while she is simply at a different point along that curve where marginal substitution is closer to one.
  
• Peggy's indifference curve of chocolate and caramel is convex.
  Correct! As with all other indifference curves Peggy’s marginal rate of substitution between caramel and chocolate changes depending on the relative consumption of the two foods.

3. The Field of Indifference Curves

Each indifference curve represents the choices that provide a single level of utility. Every level of utility will have its own indifference curve. Thus, Lilly's preferences will include an infinite number of indifference curves lying nestled together on the diagram - even though only three of the indifference curves, representing three levels of utility, appear in Figure 1. In other words, an infinite number of indifference curves are not drawn on this diagram - but you should remember that they exist.

Higher indifference curves represent a greater level of utility than lower ones. In Figure 1, indifference curve Ul can be thought 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 (five to three) and doughnuts (100 to 84), so point F is clearly preferable to point B. Given the definition of an indifference curve - that all the points on the curve have the same level of utility - if point F on indifference curve Uh is preferred to point B on indifference curve Um, then it must be true that all points on indifference curve Uh have a higher level of utility than all points on Um. More generally, for any point on a lower indifference curve, like Ul, you can identify a point on a higher indifference curve like Um or Uh that has a higher consumption of both goods. Since one point on the higher indifference curve is preferred to one point on the lower curve, and since all the points on a given indifference curve have the same level of utility, it must be true that all points on higher indifference curves have greater utility than all points on lower indifference curves.

These arguments about the shapes of indifference curves and about higher or lower levels of utility do not require any numerical estimates of utility, either by the individual or by anyone else. They are only based on the assumptions that when people have less of one good they need more of another good to make up for it, if they are keeping the same level of utility, and that as people have more of a good, the marginal utility they receive from additional units of that good will diminish. Given these gentle assumptions, a field of indifference curves can be mapped out to describe the preferences of any individual.

3.1. Try It

Menna's consumption of movies and video games is measured on a graph with movies on the horizontal axis and video games on the vertical axis. The units are in hours and her budget constraint is defined by the number of hours she has budgeted for entertainment during her school vacation. Consider the four points below showing different ways she may choose to allocate her time.

Which point does not belong on the same indifference curve as point A?

• B
• C
• D

Below are a set of nested indifference curves reflecting consumer preferences between good A and good B. The red curve represents a greater level of utility for consumers than that attained at any point on the blue curve. Which of the graphs is not plausible for a field of indifference curves?

3.2. Check Answers

• B
  Correct! If point A is on the indifference curve then B cannot lie on the same curve. At point B Menna consumes more of both movies and video games than point A so it must lie on a higher indifference curve.
• C
  Incorrect. Point C would lie at the point along the indifference curve where the marginal rate of substitution is close to one.
• D
  Incorrect. Point D would lie at the point along the indifference curve where the marginal rate of substitution is high.

Incorrect While the slopes of the indifference curves are different it is not implausible that consumers relative preferences may change somewhat at different utility levels.

Incorrect. The two curves displayed are a typical example of nested indifference curves.

4. The 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 down, and the slope is steeper on the left and flatter on the right - the specific shape of indifference curves can be different for every person. Figure 1, for example, applies only to Lilly's preferences. Indifference curves for other people would probably travel through different points.

Utility-Maximizing with Indifference Curves

People seek the highest level of utility, which means that they wish to be on the highest possible indifference curve. However, people are limited by their budget constraints, which show what tradeoffs are actually possible.

Maximizing Utility at the Highest Indifference Curve

Return to the situation of Lilly's choice between paperback books and doughnuts. Say that books cost $6, doughnuts are 50 cents each, and that Lilly has $60 to spend. This information provides the basis for the budget line shown in Figure 1. Along with the budget line are shown the three indifference curves from Figure 1. What is Lilly's utility-maximizing choice? Several possibilities are identified in the diagram.

The choice of F with five books and 100 doughnuts is highly desirable, since it is on the highest indifference curve Uh of those shown in the diagram. However, it is not affordable given Lilly's budget constraint. The choice of H with three books and 70 doughnuts on indifference curve Ul is a wasteful choice, since it is inside Lilly's budget set, and as a utility-maximizer, Lilly will always prefer a choice 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 choice B of three books and 84 doughnuts, which is on the indifference curve Um. If Lilly were to start at choice G, 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 move 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 choice.

The highest achievable indifference curve touches the budget constraint at a single point of tangency. Since an infinite number of indifference curves exist, even if only a few of them are drawn on any given diagram, there will always exist one indifference curve that touches the budget line at a single point of tangency. All higher indifference curves, like Uh, will be completely above the budget line and, although the choices on that indifference curve would provide higher utility, they are not affordable given the budget set. All lower indifference curves, like Ul, will cross the budget line in two separate places. When one indifference curve crosses the budget line in two places, however, there will be another, higher, attainable indifference curve sitting above it that touches the budget line at only one point of tangency.

4.1. Try It

Jacob is taking a two week vacation where he will spend most of his time and budget at either amusement parks or day spas. He has set aside a budget of $1,200 dollars for his two favorite activities. During the first week he spent $200 at amusement parks and $400 at day spas for a total of $600. During the second week he spent $400 at amusement parks and $200 at day spas. If Jacob found both of his weeks equally enjoyable, was he maximizing his enjoyment subject to his budget constraint? Why or why not?

• No. Jacob would have achieved greater utility by consuming a more equal balance of amusement parks and day spas during both weeks.
• No. Utility maximization is only possible if the indifference curve does not intersect the budget constraint at any point.
• Yes. Because the indifference curve is convex it can cross budget constraint at multiple points

Muhammad is consuming the optimal quantity of movies and popcorn at Point A when the price of movies suddenly drops. Which of the following points represents a plausible new utility-maximizing equilibrium after the price drop?

• Point C
• Point D
• Point B

4.2. Check Answers

• No. Jacob would have achieved greater utility by consuming a more equal balance of amusement parks and day spas during both weeks.
  Correct! If two points on the same indifference curve touch the budget constraint then a point on a higher indifference curve, with a more equal consumption bundle, is possible.
• No. Utility maximization is only possible if the indifference curve does not intersect the budget constraint at any point.
  Incorrect. Utility maximization subject to a budget constraint occurs at the single indifference curve which is tangent to the budget constraint.
• Yes. Because the indifference curve is convex it can cross budget constraint at multiple points
  Incorrect. If an indifference curve crosses the budget constraint at multiple points then it by definition cannot be the highest utility indifference curve achievable with a given budget.

• Point C
  Correct! C would fall along a new indifference curve greater than the original indifference curve. The quantity consumed of both goods has increased after the price decrease.
• Point D
  Incorrect. Point D would represent a lower indifference curve than Point A. which is an implausible new equilibrium as real income has increased.
• Point B
  Incorrect. If the price of a good decreases the consumer should be able to move to a higher indifference curve.

5. Try It

These questions allow you to get as much practice as you need, as you can click the link at the top of the first question ("Try another version of these questions") to get a new set of questions. Practice until you feel comfortable doing the questions.

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