Chapter 8: A Simple Model of Utility and Demand

Chapter 8: A Simple Model of Utility and Demand

8 Utility Theory (a way of thinking about preferences) and Demand
Theory (a way of thinking about the demand function). The goal is testable insights. Notes and teaching tips: 6, 12, 26, 27, 28, 29, 35, and 56. To view a full-screen figure during a class, click the red “expand” button. To return to the previous slide, click the red “shrink” button. To advance to the next slide, click anywhere on the full screen figure. 8

After studying this chapter you will be able to
Understand and describe preferences using the concept of utility Explore the marginal utility theory of consumer choice Understand how marginal utility theory helps to predict the effects of changes in prices and incomes on demand and to explore the paradox of value Explore some new ways of explaining consumer choices, and the insights they produce. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Copyright © 2013 Pearson Canada Inc., Toronto, Ontario
You want Ke$ha’s album of songs, Animal. Do you buy the CD album from Amazon for $11.88 or do you download it from the iTunes store for $7.99? Beyond simple preferences, what determines our choices as buyers of recorded music? How much better off are we because we can download an album for less than $10 and some songs for less than $1? Normally, diamonds are expensive and water is cheap, and we need water for life and can do without diamonds. Doesn’t that seem odd? Why is it the case? Why do we place a higher value on useless diamonds than on essential-to-life water? Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Consumption Choices The choices you make as a consumer, a buyer of goods and services, is influenced by many factors, which economists group as Consumption possibilities Consumption Preferences Consumption Possibilities Consumption possibilities: All the things that you can afford to buy given your budget constraint and commodity prices. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Consumption Choices (keeping it simple)
Let’s give Lisa only two consumption possibilities. She can buy only two goods: movies and pop. A Consumer’s Budget Line Consumption possibilities are limited by income, the price of a movie, and the price of pop. Income = Ppop (Qpop) + Pmovie (Qmovie) When Lisa spends all of her income, she reaches the limits of her consumption possibilities. Lisa’s budget line shows the limits of her consumption possibilities. The budget line is like a restaurant menu. This example has been well received: Emphasize that the consumer’s budget line is like a menu showing what affordable combinations of food and drink are available to the consumer. Ask them to compare the relative prices between two goods: food and drink and depict the affordable combinations a diner can purchase with a set income. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Consumption Possibilities Lisa has $40 to spend, the price of a movie is $8 and the price of pop is $4 a case. The table lists seven possible ways in which she can spend her $40. The graphs plots these combinations of movies and pop. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Consumption Possibilities
Lisa can afford combinations at the points A to F. When goods are indivisible (1 movie, 1 pop) they must be bought in whole units at the points marked. When goods are divisible (kg of rice, meters of cloth) they can be bought in any quantity. The line through points A to F is Lisa’s budget line. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Consumption Choice Preferences We use the term preferences –her likes and dislikes-- as the driver of the choices that Lisa makes Using the language of the Bentham utilitarian philosophy we call her benefit (or satisfaction) from consuming a good or service the utility from consumption. Total Utility Total utility: the total benefit one gets from consumption. The model assumes utility maximization as an objective of consumption, within the budget constraint. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Maximizing Utility From Table 8.1: Lisa’s total utility schedule. Total utility from a good increases as the quantity of the good increases. (i.e., marginal utility is positive) As Lisa sees more movies in a month, her total utility from movies increases, but at a decreasing rate. Where do the utility numbers come from? Year after year, you will get the same question from the curious student: “where do the utility numbers come from?” This edition tries to help with one answer to this question by telling the story of Lisa’s likes for movies and pop. We tell Lisa that we’re going to call the utility she gets from 1 movie a month 50 units of utility. Then we ask her to tell us, using the same scale, how much she would like 2, 3, and so on movies, and 1, 2, 3, and so on cases of pop. A second answer that you can’t give now, but you can promise when you get to the end of the chapter, is that we can infer the MU values from the prices (up to an arbitrary constant of multiplication). Because in consumer equilibrium, MUM/PM = MUS/PS = , we know that MUM = PM and MUS = PS. (Use this second explanation carefully, and don’t use the math as densely as we’re using it here. Spell it out at greater length in words and with intuition.) Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Maximizing Utility Marginal Utility Marginal utility from a good is the change in total utility that results from a unit-increase in the quantity of the good consumed. Assumption: As the quantity consumed of a good increases, the marginal utility from it decreases. We call this decrease in marginal utility as the quantity of the good consumed increases the principle of diminishing marginal utility. (intuitively appealing assumption) Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Maximizing Utility Table 8.1 shows Lisa’s schedules of marginal utility. The marginal utility from an additional unit of a good gets smaller as the quantity of the good consumed increases. For example, as the number of movies seen in a month increases, marginal utility from additional movies decreases. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Maximizing Utility Figure 8.2(a) maps Lisa’s total utility and marginal utility from pop consumption. Total utility from pop (vertical distance from base) increases as more pop is consumed. The diminishing bars along the total utility curve show the increased total utility (the marginal utility) from each additional case of pop. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Maximizing Utility Figure 8.2(b) re-maps the diminishing marginal utility from Figure 8.2(a). As Lisa increases the quantity of pop she drinks, her marginal utility from pop diminishes. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Utility-Maximizing Choice
A key assumption here is that the consumer (individual, household) chooses the consumption possibility (bundle of goods and services) that maximizes total utility. This is basically a calculus, or linear programing, problem but here we just use a spreadsheet approach The direct way to find the utility-maximizing choice is to make a table in a spreadsheet and do the calculations. Find the just-affordable combinations Find the total utility for each just-affordable combination The utility-maximizing combination is the consumer’s utility maximizing consumption choice Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Find Just-Affordable Combinations (A through F on the budget constraint). Lisa has $40 a month to spend on movies and pop. The price of a movie is $8 and the price of pop is $4 a case. Each row of Table 8.2 shows a combination of movies and pop that exhausts Lisa’s $40. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Consumer equilibrium is the situation in which Lisa has allocated all of her available income in the way that maximizes her total utility, given the prices of movies and pop. Lisa’s consumer equilibrium is 2 movies and 6 cases of pop a month. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

More intuitively the consumer arrives at consumption equilibrium by looking at choices made at the margin. Choosing at the Margin: Having made a choice, would spending a dollar more (or a dollar less) on a good bring more total utililty? Marginal utility is the increase in total utility that results from consuming one more unit of the good. Given the price of a good, one can think of the marginal utility per dollar, the marginal utility from a good that results from spending one more dollar on a good or service. This is a convenient way of comparing additional utility as between consumption goods. Marginal decision making is the core of the economic way of thinking. Get your students to appreciate that, aside from the concept of opportunity cost, marginal reasoning is the most important tool for understanding the economic perspective. Remind them that we have been using marginal reasoning for many chapters now: In Chapter 2 we derived the marginal cost of production from the PPF. In Chapter 5 we discovered that competitive equilibrium is efficient because marginal benefit on the demand curve equals marginal cost on the supply curve. In this chapter, we discover that equalizing the marginal utility per dollar across all goods and services maximizes a consumer’s utility. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

The marginal utility per dollar equals the marginal utility from a good divided by its price. Let MUM be the marginal utility from a movie, and PM the price of a movie. The marginal utility per dollar spent on movies is MUM/PM . MUP be the marginal utility of a pop, and PP the price of pop. The marginal utility per dollar from pop is MUP/PP. By comparing MUM/PM and MUP/PP , we can determine whether Lisa has allocated her budget in the way that maximizes her total utility, gives her most utility for the dollar. People don’t calculate and compare marginal utilities and prices. One of the challenges in teaching the marginal utility theory is getting the students to appreciate the fundamental role of a model of choice. The goal is to predict choices, not to describe the thought processes that make them. The physics model of the pool player’s choices (This Instructor’s Manual, Chapter 1) is relevant here. Gary Becker told the story a bit differently and more pointedly for present purposes. Here’s what he said (Parkin, Economics, first edition, 1990, p. 154): Cliff Lee [or substitute a currently hot pitcher] won the 2008 Cy Young award for the American League. He effectively knows all the laws of motion, of hand-eye coordination, about the speed of the bat and ball, and so on. He’s in fact solving a complicated physics problem when he steps up to pitch, but obviously he doesn’t have to know physics to do that. Likewise, when people solve economic problems rationally they’re really not thinking, “Well, I have this budget and I read this textbook and I look at my marginal utilities and the prices and determine what maximizes my utility.” People don’t do that, but it doesn’t mean they’re not being rational. Just because a Cy Young Award winner isn’t Albert Einstein doesn’t mean he can’t make rational decisions about pitching. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Utility-Maximizing Rule A consumer’s total utility is maximized by following the rule: Spend all available income Equalize the marginal utility per dollar for all goods NOTE: Beyond this simple two commodity setup the model actually allows for any number of commodities and “investment” decisions (e.g. education today, more income tomorrow) Marginal decision making is the core of the economic way of thinking. Get your students to appreciate that, aside from the concept of opportunity cost, marginal reasoning is the most important tool for understanding the economic perspective. Remind them that we have been using marginal reasoning for many chapters now: In Chapter 2 we derived the marginal cost of production from the PPF. In Chapter 5 we discovered that competitive equilibrium is efficient because marginal benefit on the demand curve equals marginal cost on the supply curve. In this chapter, we discover that equalizing the marginal utility per dollar across all goods and services maximizes a consumer’s utility. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Lisa’s Marginal Calculation Figure 8.3 shows how the utility-maximizing rule works. Each row of the table (on the next slide) shows a just-affordable combination. Start by choosing a row—a point on the budget line. Why don’t consumers simply choose the goods with the highest marginal utility? Students will find it relatively easy to simply memorize the rule that maximizing utility requires that the marginal utility per dollar is equal across all goods, but, intuitively, students still often expect marginal utility to be the only determinant of utility maximization. To provide some additional intuition, ask them to think about two goods they’re trying to choose between, like a new shirt and a new CD. Say a new shirt would have a marginal utility of 20, while a new CD would have a marginal utility of 15. The price of a new shirt is $30, while the price of a new CD is $15. Should you purchase the new shirt because it has a higher marginal utility? Not necessarily. You might prefer the shirt, but it costs twice as much as the new CD. Only if you like the shirt at least twice as much as the new CD would you be willing to pay twice as much for the shirt. Even though the CD has the lower marginal utility, it has a higher marginal utility per dollar (1 as opposed to 2/3). Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

In row D, MUP/PP > MUM/PM. Lisa spends too much on movies and too little on pop. If Lisa spends less on movies and more on pop, … MUM increases and MUP decreases. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Predictions of Marginal Utility Theory
A Fall in the Price of a Movie When the price of a good falls the quantity demanded of that good increases—the demand curve slopes downward. For example, if the price of a movie falls, we know that MUM/PM rises, so before the consumer changes the quantities bought, MUM/PM > MUP/PP. To restore consumer equilibrium (maximum total utility), the consumer increases the movies seen to drive down the MUM and restore MUM/PM = MUP/PP. The concept of utility is abstract and not comparable across people—and that can be a difficult idea to grasp. Students will initially be skeptical of measuring satisfaction with the concept of utility—not because the idea that consumer satisfaction increases with consumption is difficult to comprehend, but because there is no absolute standard by which different people’s satisfaction can be compared. Many students think that if one person’s utility can’t be converted into standardized units that are comparable across people, like converting spatial distance into miles or kilometers, then the concept simply isn’t worth understanding. (In mathematical terms, utility ordering is ordinal, not cardinal, making it impossible to directly compare separate utility functions.) Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

A change in the price of one good changes the demand for another good. You’ve seen that if the price of a movie falls, MUM/PM rises, so before the consumer changes the quantities consumed, MUM/PM > MUP/PP. (spend less to get a movie) To restore consumer equilibrium (maximum total utility), the consumer decreases the quantity of pop consumed to drive up the MUP and restore MUM/PM = MUP/PP. (more movies and less pop) Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Predictions Figure 8.4 illustrates these predictions. A fall in the price of a movie increases the quantity of movies demanded—a movement along the demand curve for movies, … and decreases the demand for pop—a shift of the demand curve for pop. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

A Rise in the Price of pop Now suppose the price of pop rises. We know that MUP/PP falls, so before the consumer changes the quantities bought, MUP/PP < MUM/PM. To restore consumer equilibrium (maximum total utility), the consumer decreases the quantity of pop consumed to drive up the MUP and increases the quantity of movies seen to drive down MUM. These changes restore MUM/PM = MUP/PP. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Figure 8.5 illustrates these predictions. A rise in the price of pop decreases the quantity of pop demanded—a movement along the demand curve for pop. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

A Rise in Income When income increases, the demand for a normal good increases. Given the prices of movies and pop, when Lisa’s income increases from $40 to $56 a month, she buys more movies and more pop. Movies and pop are normal goods. Table 8.5 shows these predictions. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

The Paradox of Value The paradox of value “Why is water, which is essential to life, far cheaper than diamonds, which are not essential?” is resolved by distinguishing between total utility and marginal utility. We use so much water that the marginal utility from water consumed is small, but the total utility is large. We buy few diamonds, so the marginal utility from diamonds is large, but the total utility is small. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Paradox Resolved The paradox is resolved by distinguishing between total utility and marginal utility. For water, the price is low, total utility is large, and marginal utility is small. For diamonds, the price is high, total utility is small, and marginal utility is high. But marginal utility per dollar is the same for water and diamonds. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Predictions … Value and Consumer Surplus The supply of water is perfectly elastic, so the quantity of water consumed is large and the consumer surplus from water is large. In contrast, the supply of diamonds in perfectly inelastic, so the price is high and the consumer surplus from diamonds is small. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Temperature and Utility: A (bad) Analogy Utility is similar to temperature. Both are abstract concepts, and both have units of measurement that are arbitrary. [This is false! We have ways of measuring temperature and the relationship between units of energy and raising one cubic centimetre of water one degree Celsius.] Nevertheless, concept of utility helps us make predictions about consumption choices. It give us a formal model for understanding why people buy more of a good when its price falls and why people buy more of most goods when their incomes increases. If utility is arbitrary, what use is it? The concept of utility is abstract, but the implications of utility analysis are concrete. Help the students be less concerned about the abstract nature of measuring utility by emphasizing that it is enough to be able to carefully analyze one consumer’s consumption decisions and extrapolate what this behavior could imply for market behavior in general. Appeal to those concepts that students already understand from earlier chapters by linking the abstract concept of utility with concrete implications of consumer behavior. For example, utility-maximization rules explain the law of demand and shifts in demand, as seen in chapter 3. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

New Ways of Explaining Consumer Choices
Behavioral Economics: Explores the ways in which humans compute and implement rational decisions that influence economic behavior—both the decisions that people make and the consequences of those decisions for the way markets work. There are three models (impediments) to rational choice: Bounded rationality Bounded willpower Bounded self-interest Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Bounded Rationality Bounded rationality is rationality that is bounded by the computing power of the human brain. Bounded rationality: Rational (utility maximizing) behavior is constrained by knowledge and mental skills. Faced with uncertainty, consumers cannot make pure (rational) utility maximizing choices. So they incorporate as well on other decision-making methods such as rules of thumb, listening to the views of others, or intuition (gut instinct). Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Bounded Willpower Bounded will-power: We all have less-than-perfect willpower, and other constraints, that prevent us from making a decision that we know to be right, or making one we know to be wrong, either of which we will later regret. Bounded Self-Interest Bounded self-interest: Limiting one’s self-interest in the interests of a larger group (family, community, nation). (Bad textbook examples) Main applications are in finance where uncertainty is the key factor and savings where future is the key factor. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

One behaviour observed by behavioural economists is more general and might affect your choices. The Endowment Effect The endowment effect is the tendency for people to value something more highly simply because they own it. IGNORE: The book’s explanation is not good. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Neuroeconomics: (highly speculative area where conclusions are overly drawn from scant evidence.) Neuroeconomics is the study of the activity of the human brain when a person makes an economic decision. Different decisions appear to activate different areas of the brain. Some decisions are made In the pre-frontal cortex where memories are stored and data analyzed and might be deemed rational. In the hippocampus where memories of anxiety and fear are stored and might be deemed irrational. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Controversy Should economics focus on explaining the decisions we observe or should it focus on what goes on inside people’s heads? This is the controversy. For most economists, the goal of economics is to explain the decisions that we observe people make, and not to explain what goes on inside people’s heads. Copyright © 2013 Pearson Canada Inc., Toronto, Ontario

Chapter 8: A Simple Model of Utility and Demand

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