Ajaz ECO 204 2018-2019 Consumers-1 PDF

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

Department of Economics (STG), ECO 204, Sayed Ajaz Hussain __________________________________________________________________________________________

CONSUMER THEORY PART ONE: THE BASICS1 This version: 9/30/2018 1. Introduction We begin ECO 204 with “consumer theory”, one of most interesting topics in economics. Here is a very small sample of consumer theory applications: Derive customer demand curve from preferences, budget, and market prices Explain “Ordinary vs. “Giffen” goods, “Normal” vs. Inferior” goods, and “Veblen” goods Mean-Variance Portfolios (RSM 330) Inter-temporal Consumption and Savings (RSM 332) Advertising, Quantifying Market Segments Product Attributes and Pricing Pricing addictive goods Aid: “cash vs. in kind? School voucher programs Quantifying consumer welfare in pecuniary terms Is Uber is a complement/substitute to public transit? Quantifying Uber’s consumer surplus2 Public policy (for example, whether it’s better to raise revenue-neutral funds through excise or income taxes) Public health (for example, regulating and pricing marijuana and explaining why teenagers are having more oral sex); Pricing (Apple iPhone X and Chanel 2.55 vs. Hermes Birkin bags).

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Thanks: Matthew Oh and Asad Priyo. Feedback welcome: please e-mail [email protected].

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ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

Our goal is to develop a model of consumer behavior. 2. The Universe of Choices and the Consumption Set We begin by recognizing that economic agents (Homo Economicus) make ‘choices/decisions’ from an (infinitely long) list of items that we’ll call the “Universe of Choices”. The “Universe of Choices” includes, for example: “Where should I have dinner tonight?”, “Should I stop reading this boring chapter and do something else?”, “How many nights a month do I go clubbing at Stereo in Montreal?”, “How many martinis should I chug at happy hour tonight?” and so on: Universe of Choices = 𝑈 = {… , # Martinis at dinner? , … , #of nights clubbing at Stereo? , Sleep in 204? , . . }

Modeling consumer choice over the “universe of choice” is an impossibly complex task. Instead, we do something simpler: we will model the amounts of “commodities” (goods and services sold in markets) that a consumer will buy. We assume that consumers are price takers, i.e., have no “bargaining power” and label “goods and services” as “goods”. Next, in order to model the amounts of goods that a consumer will buy, we have to specify the quantities of good that are physically available for consumption (the “consumption set”). Suppose for example that we are modeling the consumption of one good, say pairs of Edward Green shoes sold at Leatherfoot. Suppose, Leatherfoot has 10 pairs of Edward Green shoes in your size. Then the consumption set of Edward Green shoes available for purchase at Leatherfoot is 𝐶 = {0,1,2,3,4,5,6,7,8,9,10}:

Now suppose you’re modeling the consumption of two goods -- here are some possible consumption sets: Hours of Leisure/Day

𝐶

24

Else

𝐶

𝐶

Else # of entrees tonight at Joso’s

𝐶=

2

1

𝐶

Food

Min Food

𝐶

0 # of entrees tonight at Sushi Kaji

Top row, left to right: The first consumption set is for a situation where goods 1 and 2 can be consumed in any non-negative amount 𝐶 = {( , ) ≥ 0}; the second consumption set is for a situation where the consumers can relax for any number hours between 0 to 24 hours a day and where “everything else” can be consumed in any non-negative amount: 2 ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

𝐶 = {( , ): All⏟else 𝑞1

⏟ ≥ 0, 0 ≤ Hours of Leisure per day ≤ 24}

𝑞2 The third consumption set is for a situation where the consumer can consume any amount of food greater than a minimum threshold while all else can be consumed in any non-negative amount:

⏟ 𝐶 = {( , ): Food

𝑞1

≥ 𝑀𝐼𝑁 > 0 , All⏟ else ≥ 0} 𝑞2

Bottom row, left to right: The first consumption set is for a situation where good 1 can be consumed in any amount but good 2 must be consumed in integer amounts: 𝐶 = {( , ): ≥ 0, = {0,1,2, . . }}; the second consumption set is for a situation for the number of entrees that can be ordered at any particular time at either Sushi Kaji or Joso’s (beware Joso’s NSFW and kitschy site) and represents the fact that you cannot be in both places at once: 𝐶 = {( , ): ( ≥ 0, = 0) ∪ ( = 0, ≥ 0)}

The third consumption set is for a situation where both goods must be consumed in integer amounts only: 𝐶 = {( , ): = {0,1,2, . . }, = {0,1,2, . . }}

Clearly, real life consumption sets can be complicated. For tractability, the “standard” consumption set in ECO 204 is to assume that the consumer can purchase any amount of non-negative good(s). For example, a consumer can choose any point “bundle” in the consumption set consisting of, for example, 𝑁 = 1 goods: As another example, a consumer can choose any point “bundle” in the consumption set consisting of, for example, 𝑁 = 2 goods:

Points on the “boundary” of the consumption set are known as “boundary bundles” whereas points inside the consumption set are known as “interior” bundles. In general, we assume that a consumer can choose any “bundle” in the consumption set consisting of 𝑁 > 1 (where 𝑁 is an integer) goods: 𝐶 = {( , , … ,

𝑁)

≥ 0}

That said, 99% of the time we’ll work with consumption sets of two goods.

3 ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

3. Consumer Preferences The consumption set tells us which bundles are physically available for consumption but it does not tell us which bundles are affordable nor does it say anything about the consumer’s preferences. To model consumer choice we need a way to represent preferences and indicate the set of affordable bundles. Here, we see how to represent preferences. A long time ago, (dead) economists believed that individuals could measure and quantify the “utility” of consuming goods. According to this “ancient economic” view, when someone said they had 100 ‘utils’ of “utility” from consuming good A and 50 ‘utils’ of “utility” from consuming good B, it meant that good A was “twice as good as”, or “had double the pleasure of”, good B. Modern economics takes a different perspective on “utility” – it is based on the idea that consumers can rank bundles in their consumption set. To do this, we need to define two preference operators: “better than” and “indifferent to”. Suppose that 𝑋 and 𝑌 are two bundles in the consumption set. Then the “better than ≻” and “indifferent to ~” operators are defined as: Definition: ≻ Relation

Consumer prefers bundle 𝑥 over bundle 𝑦 ⇔ 𝑥 ≻ 𝑦 Definition: ~ Relation

Consumer is indifferent between bundles 𝑥 and 𝑦 ⇔ 𝑥 ~ 𝑦

For example: at 4 am, DJ Ajax prefers spinning Da After over Webaba or that: Da After ≻ Webaba. Cindy is indifferent between Bottega Veneta and Louis Vuitton bags or that Bottega Veneta ~ Louis Vuitton.

Next, we assume that consumers have “Rational Preferences” which means they have “Complete Preferences” and “Transitive Preferences”:

The following example illustrates the difference between rational and irrational preferences. Suppose we ask three different individuals to rank the following three DJs in their consumption set of “cool study beats”:

Seth Troxler (Essential Mix)

Tiesto (sucks)

Art Department (Essential Mix) 4

ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

Suppose their responses are:

The Ryerson student does not have complete preferences because they are unable to rank bundles. As such the Ryerson student has irrational preferences.

The Ryerson Honors student has complete preferences (they are able to rank bundles) but their rankings are illogical. As such the Ryerson Honors student has irrational preferences.

Bob has complete preferences (he can rank all bundles) and his rankings are logical. As such Bob has rational preferences. In real-life, people often exhibit irrational preferences. For example, it is conceivable that someone would have the following rankings: Q: How do you feel about Red vs. Blue? A: Red ≻ Blue

Q: How do you feel about Blue vs. Orange? A: Blue ≻ Orange

Q: How do you feel about Red vs. Orange? A: Orange ≻ Red

This consumer has complete preferences (she can rank any pair of these three colors) but she does not have transitive preferences because if she says that Red ≻ Blue and Blue ≻ Orange then if her preferences were logical she should’ve said Red ≻ Orange. However, she actually said Orange ≻ Red from which we conclude that she doesn’t have transitive preferences. In ECO 204, we assume that consumers have rational preferences. 5 ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

__________________________________________________________________________________________ Here’s a review of a book written by Daniel Kahneman who won the Nobel Prize in economics for his work on “irrational” consumers. Book Review: Thinking, Fast and Slow by Daniel Kahneman A Nobel laureate’s new book cautions us not to trust our gut By Roger Lowenstein For the last decade or so a band of scholars has been trying to cast off the long-accepted “rational agent” theory of economic behavior—the one that says that people, in their economic lives, behave like calculating robots, making rational decisions when they buy a stock, take out a mortgage, or go to the track. These scholars have offered a trove of evidence that people, far from being the rational agents of textbook lore, are often inconsistent, emotional, and biased. Perhaps tellingly, the pioneers of this field were not economists. Daniel Kahneman and Amos Tversky were Israeli psychologists who noticed that real people often do not make decisions as economists say they do. Tversky died in 1996; six years later, Kahneman won the Nobel Prize for economics. Thinking, Fast and Slow, Kahneman’s new and most accessible book, contains much that is familiar to those who have followed this debate within the world of economics, but it also has a lot to say about how we think, react, and reach—rather, jump to— conclusions in all spheres. What most interests Kahneman are the predictable ways that errors of judgment occur. Synthesizing decades of his research, as well as that of colleagues, Kahneman lays out an architecture of human decisionmaking—a map of the mind that resembles a finely tuned machine with, alas, some notable trapdoors and faulty wiring. Behavioralists, Kahneman included, have been cataloging people’s systematic mistakes and nonlogical patterns for years. A few of the examples he cites: 1. Framing. Test subjects are more likely to opt for surgery if told that the “survival” rate is 90 percent, rather than that the mortality rate is 10 percent. 2. The sunk-cost fallacy. People seek to avoid feelings of regret; thus, they invest more money and time in a project with dubious results rather than give it up and admit they were wrong. 3. Loss aversion. In experiments, most subjects would prefer to receive a sure $46 than have a 50 percent chance of making $100. A rational agent would take the bet. Remarkably, and for similar reasons, golfers putt better when missing would leave them a stroke behind. As compelling as these examples are—repeatedly, we recognize our own biases—Kahneman’s greater achievement is to build a framework for how, or why, the mind reasons as it does. You may feel a spasm of doubt, as I did, when first introduced to his central contrivance—using two fictional “characters,” which he refers to as System 1 and System 2. Suspend your doubts for just a moment. System 2 is your conscious, thinking mind. We conceive of this active consciousness as the principal actor, the “decider” in our lives. System 2 thinks slowly; it considers, evaluates, reasons. Its work requires mental effort—multiplying 24 by 17 or turning left at a busy intersection. We attribute most of our opinions and decisions to this thinking, reasonable fellow. For Kahneman, however, the main protagonist is System 1. This is the agent of our automatic and effortless mental responses. System 1 can add single-digit numbers and fill in the phrase “bread and —.” It is equipped with a nuanced picture of the world, the product of retained memory and learned patterns of association (“Florida/old people”) that enable it to spew out a stream of reactions, judgments, opinions. System 1 can detect a note of anger in a voice on the telephone; it forms snap judgments about those we meet, Presidential candidates, investments that we might be considering. The flaw in this remarkable machine is that System 1 works with as little or as much information as it has. If it can’t answer the question, “Is Ford (F) stock a good investment?” it supplies an answer based on related but not really relevant data, such as whether you like Ford’s cars. 6 ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

System 1 simplifies, confirms—it looks for, and believes it sees, narrative coherence in an often random world. It does not perform complicated feats of logic or statistical evaluations. You hear about a terrorist incident and want to avoid all buses and trains; only if you slow down, employ the tools of System 2, do you realize that the risks of terrorism affecting you are very slight. Willpower requires effort; it is a feature of System 2. In an experiment, 4-year-olds who were able to delay eating an Oreo scored higher, a decade later, on IQ tests. Kahneman suggests that the ability to switch to System 2 is a sign of an “active mind” and a predictor of success. Contrivance though it is, this framework is remarkably effective in describing how we think; we believe we are creatures of our thinking selves, but many of our opinions merely ratify our automatic responses. In contrast to Malcolm Gladwell, Kahneman is telling us not to blink. Kahneman is perhaps least persuasive in his treatment of the business world. Noting that even top performers in business— also sports—tend eventually to revert to the mean, he attributes success largely to luck. This confuses events that may not be predictable with those that are determined by chance. A high-achieving retail store, to cite one of his examples, is not lucky—it is well-situated. And if its sales later decline, that is not necessarily a sign that its prior success was random. Business has a selfcorrecting cycle that fosters mean reversion. Success attracts competitors. Some readers will object that Kahneman’s is an overly Cartesian world, barren of human intuition. He recommends using formulae even for predicting the future value of wines. Thinking, Fast and Slow is nonetheless rife with lessons on how to overcome bias in daily life. Kahneman advises that you “recognize the signs that you are in a cognitive minefield, slow down, and ask for reinforcement from System 2.” The next time a relative pops off about the stock market or President Obama, I will wonder: Does he or she know? Or is this just their reflexive self? I will never think about thinking quite the same. It’s a monumental achievement. See also: Bias, Blindness, and How We Truly Think: Part 1, Part 2, Part 3, Part 4 __________________________________________________________________________________________ 4. Representing Rational Preferences by a “Utility” Function To model consumer choice using math, we will need to represent consumer preferences (rankings, actually) by a mathematical equation. Such an equation – a “utility function” -- should have two desirable properties: ❶ The preferred bundle must have a higher utility value: 𝑥 ≻ 𝑦 if and only if 𝑈(𝑥) > 𝑈(𝑦)

❷ Indifferent bundles must have the same utility value:

For example, suppose:

𝑥 ~ 𝑦 if and only if 𝑈(𝑥) = 𝑈(𝑦)

Then we can represent Ajax’s (rational) preferences by any utility values (“function”) so long as: 7 ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

𝑈(Seth) > 𝑈(Art Department) = 𝑈(Tiesto) Here, for example, are five “utility functions” representing Ajax’s preferences:

In fact, there are an infinite number of “utility functions” representing Ajax’s preferences because there are an infinite number of utility values satisfying: 𝑈(Seth) > 𝑈(Art Department) = 𝑈(Tiesto)

Here’s an example which shows that there is more than one utility function representing rational preferences: Suppose a consumer tells you that in her “mind”: ≻ ~ ≻ Bundle

Ranking

1 2 2 3 𝐶=

𝑈( )

,

≥0

0

𝑈( ) 𝑈( )

𝑈( )

As in the previous example, we can come up with another utility function (green mapping) which represents this consumer’s preferences:

8 ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

Suppose a consumer tells you that in her “mind”: ≻ ~ ≻ Bundle

Ranking 1 2 2 3

𝑈( )

0

0

𝑈( )

𝑈( ) 𝑈( )

𝑈( )

𝑈( ) 𝑈( )

𝑈( )

How can there be an infinite number of “utility functions” representing a set of rational preferences? The answer is that “utility number” does not measure the level of “satisfaction/felicity”. Utility is not a cardinal number (measuring something physical like height, weigh, or speed) but rather it is an ordinal number in that the order represents preference rankings. For example, the WSJ score and its variations below is an ordinal number in the sense that they all say Harvard is #1 and Columbia is #2:

9 ECO 204 CHAPTER: CONSUMER THEORY – PART ONE. © Ajaz Hussain, [email protected]

University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute.

Rankings, like utility values, are ordinal numbers in that only the order matters. Note that rankings are unaffected if “WSJ score/utility” are multiplied by a positive number, or if we add a positive number to “WSJ score/utility”, or if we raise the “WSJ score/utility” by a positive number, or if we take natural logs of the “WSJ score/utility”. This means, if we have one utility function representing a consumer’s rational preferences, we can go on to find an infinite number of other utility functions representing the same set of preferences by performing any one, or combination, of mathematical operations known as positive monotonic transformations or PMT: 1. Adding a positive constant to the right hand...