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Um

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Uh today we're going to start talking

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about what's underneath the demand

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curve.

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So, basically what we did last time and

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what you did in section on Friday is

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talk about sort of the workhorse model

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uh of economics, which is the supply and

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demand model. And we always start the

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class with that cuz that's the the model

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in the course. But, I think as any good

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sort of scientist and inquisitive minds,

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you're probably immediately asking,

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"Well, where do these supply and demand

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curves come from? They don't just come

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out of thin air. Uh

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how do we think about them? Where do

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they come from?" And that's what we'll

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spend the base of the first half of the

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course going through.

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And so, we're going to start today with

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the demand curve.

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And the demand curve is going to come

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from how consumers make choices.

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Okay? And that will help us derive the

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demand curve. Then we'll turn next to

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supply curve, which will come from how

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firms make uh production decisions.

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But, let's start with the demand curve.

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And we're going to start by talking

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today about people's preferences

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and then the utility functions.

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Okay?

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So, our model of consumer

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decision-making

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is going to be a model of utility

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maximization.

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That's going to be our fundamental

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Remember, this course is all about

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constrained maximization. Our model

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today is going to be a model of utility

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maximization.

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And this model is going to have two

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components.

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There's going to be consumer

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preferences,

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which is what people want, and there's

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going to be a budget constraint, which

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is what they can afford.

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And we're going to put these two things

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together. We're going to maximize

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people's happiness or their choice or

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their their happiness given their

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preferences subject to the budget

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constraint they face. And that's going

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to be the constrained maximization

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exercise that actually through the magic

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of economics is going to yield the

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demand curve. And it's going to yield a

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very sensible demand curve that you'll

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understand intuitively.

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Now, so what we're going to do is do

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this in three steps.

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Step one over the next two lectures.

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Step one is we'll talk about

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preferences.

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How do we model people's tastes?

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We'll do that today.

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Step two is we'll talk about how we

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translate this to utility function. How

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we mathematically represent people's

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preferences in the utility function.

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We'll do that today as well.

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And then next time, we'll talk about the

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budget constraints that people face.

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So, today we're going to talk about the

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maximand. Next time we'll talk about the

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budget constraint.

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That means today's lecture is quite fun.

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Today's lecture is about unconstrained

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choice. We're not going to worry at all

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about what you can afford, what anything

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costs.

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We'll worry about what things cost.

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We're not going to worry about what you

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can afford. Okay? Today's the lecture

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where you won the lottery.

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Okay? You won the lottery, money is no

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object. How do you think about what you

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want?

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Okay? Next time we'll say, "Well, you

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didn't win the lottery." In fact, as

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we'll learn later in the semester, no

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one wins the lottery. Uh that's an

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incredibly bad deal. Um uh but basically

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next time we'll impose the budget

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constraints. But for today, we're just

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going to ignore that and talk about what

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do you want?

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Okay? And to start this, we're going to

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start with the series of preference

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assumptions.

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A series Remember, as I talked about

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last time, models rely on simplifying

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assumptions. Otherwise, we could never

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write down a model. It would go on

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forever.

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Okay? And the key question is, are those

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simplifying assumptions sensible? Uh do

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they do violence to reality in a way

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which makes you not believe the model?

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Or do are they roughly consistent with

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reality in a way that allows you to go

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on with the model?

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Okay? And we're going to impose three

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preference assumptions, which I hope

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will not violate your sense of

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reasonableness.

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The first is completeness.

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What I mean by that is you have

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preferences over any set of goods you

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might choose from.

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You might be indifferent. You might say,

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"I like A as much as B." But, you can't

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say, "I don't care." or "I don't know."

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You say, "I don't care." That's

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indifference. You can't say, "I don't

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know." You can't literally say, "I don't

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know how I feel about this." Um you

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might uh say you're indifferent to

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things, but you won't say, "I don't know

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uh how I feel about something." That's

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completeness.

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Okay? The second is the assumption we've

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all become familiar with since

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kindergarten math, which is

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transitivity.

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If you prefer A to B and B to C, you

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prefer A to C.

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Okay?

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Uh

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that's that's kind of um

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uh I'm sure that's pretty clear. You've

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done this a lot in other classes.

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So, these two are sort of standard

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assumptions you might make in any math

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class.

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The third assumption is the one where

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the economics comes in,

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which is the assumption of

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non-satiation,

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or the assumption of more is better.

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In this class, we will assume more is

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always better than less.

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Okay? We'll assume more is better than

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less. Now, to be clear, we're not going

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to say that the next unit makes you

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equally happy as the last unit. In fact,

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I'll talk about that in a few minutes.

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We'll in fact assume it makes you less

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happy.

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But, we will say you always want more.

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The face of the chance of more or less,

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you'll always be happier with more.

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Okay? And that's the non-satiation

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assumption.

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Okay? I'll talk about that some during

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the lecture, but that's sort of what's

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going to give our models their power.

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That's the sort of new economics

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assumption that's going to give, beyond

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our typical math assumptions, that's

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going to give our models their power.

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Okay?

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So, that's our assumptions.

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So, armed with those,

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I want to start with the graphical

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representation of preferences.

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I want to graphically represent people's

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preferences. And I'll do so through

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something we call indifference curves.

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Indifference curves.

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Okay?

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These are base Indifference curves are

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basically preference maps.

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Essentially, indifference curves are

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graphical maps of preferences.

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Okay?

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So, for example,

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suppose your parents gave you some money

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at the beginning of the semester, and

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you can spend that money on two things.

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Your parents are rich. They give you

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tons of money. Spend that money on two

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things.

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Buying pizza

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or or um or eating cookies.

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Okay?

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So, consider your Consider preferences

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between pizza and cookies. That's your

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two things you can do. Once again, it's

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constrained model. Obviously, in life

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you can do a million things with your

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money. But, it turns out if we consider

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the contrast between doing two different

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things with your money, you get a rich

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set of intuition that you can apply to a

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much more multi-dimensional decision

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case.

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So, let's start with the two-dimensional

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decision case. You've got your money.

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You're going to have pizza or you're

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going to have cookies.

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Okay? Now, consider three choices. Okay?

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Choice A

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is two pizzas

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and one cookie.

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Choice B

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is one pizza,

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one pizza and two cookies, and choice C

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is two pizzas, two cookies.

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Okay? That's the three packages I want

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to compare.

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And I'm going to assume and I'll

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mathematically rationalize in a few

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minutes. But for now, I'm going to

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assume you are indifferent

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between these two packages.

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I'm going to assume you're equally happy

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with two slices of pizza and one cookie

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or two cookies and one slice of pizza.

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Okay?

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I'm going to assume that. But, I'm also

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going to assume you prefer option C to

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both of these.

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In fact, I'm not I'm going to assume

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that because that is what more is better

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gives you.

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Okay? So, you're indifferent between

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these.

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This indifference doesn't come from any

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property I wrote up there. That's an

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assumption. That's just a I just for

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this case I'm assuming that. This comes

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from the third property I wrote up

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there. You prefer package C cuz more is

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always better than less.

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Okay?

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So, now let's graph your preferences.

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And we do so in figure 2.1

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Okay? In the handout. Um

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Okay. So, um

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here's your indifference curve. So,

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we've graphed on the x-axis your number

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of number of cookies. On the y-axis,

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slices of pizza.

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Okay? Now, you have We've graphed the

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three choices I laid here. Choice A,

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which is two slices of pizza and one

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cookie.

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Choice B, which is two cookies and one

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slice of pizza. And choice C, which is

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two of both.

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And I have drawn on this graph your

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indifference curves. The way your

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indifference curves looks is there's one

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indifference curve between A and B

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because those are the points among which

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you're indifferent.

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So, what an indifference curve

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represents is all combinations of

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consumption among which you are

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indifferent. So, we call it indifference

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curve.

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So, an indifference curve, which will be

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sort of one of the big workhorses of

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this course. An indifference curve

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represents all combinations along which

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00:09:12,000 --> 00:09:15,440
you are indifferent. You are indifferent

280
00:09:13,919 --> 00:09:17,599
between A and B. Therefore, they lie on

281
00:09:15,440 --> 00:09:19,520
the same curve.

282
00:09:17,600 --> 00:09:21,000
Okay?

283
00:09:19,519 --> 00:09:23,519
So, that's sort of our our our

284
00:09:21,000 --> 00:09:24,799
preference map, our indifference curves.

285
00:09:23,519 --> 00:09:27,240
And these indifference curves are going

286
00:09:24,799 --> 00:09:30,759
to have four properties.

287
00:09:27,240 --> 00:09:32,200
Four properties that you have to that

288
00:09:30,759 --> 00:09:33,439
follow naturally from this It's really

289
00:09:32,200 --> 00:09:35,040
three and a half. The third and fourth

290
00:09:33,440 --> 00:09:36,720
are really pretty much the same, but I

291
00:09:35,039 --> 00:09:38,959
like to write them out as four.

292
00:09:36,720 --> 00:09:41,160
Four properties that follow from the

293
00:09:38,960 --> 00:09:42,800
from these underlying assumptions.

294
00:09:41,159 --> 00:09:45,240
Property one

295
00:09:42,799 --> 00:09:46,559
is consumers prefer higher indifference

296
00:09:45,240 --> 00:09:49,840
curves.

297
00:09:46,559 --> 00:09:51,679
Consumers prefer

298
00:09:49,840 --> 00:09:53,399
higher

299
00:09:51,679 --> 00:09:55,039
indifference curves.

300
00:09:53,399 --> 00:09:56,879
Okay? And that just follow from more is

301
00:09:55,039 --> 00:09:58,159
better. That is, an indifference curve

302
00:09:56,879 --> 00:10:00,559
that's higher goes through the package

303
00:09:58,159 --> 00:10:02,559
that has at least as much of one thing

304
00:10:00,559 --> 00:10:03,839
and more of the other thing. Therefore,

305
00:10:02,559 --> 00:10:05,719
you prefer it.

306
00:10:03,840 --> 00:10:08,080
Okay? So, as indifference curves shift

307
00:10:05,720 --> 00:10:09,639
out, people are happier.

308
00:10:08,080 --> 00:10:11,639
Okay? So, on that higher indifference

309
00:10:09,639 --> 00:10:13,639
curve

310
00:10:11,639 --> 00:10:15,879
point C, you are happier than points A

311
00:10:13,639 --> 00:10:17,960
and B because more is better.

312
00:10:15,879 --> 00:10:19,360
Okay?

313
00:10:17,960 --> 00:10:21,320
The second

314
00:10:19,360 --> 00:10:23,600
is that

315
00:10:21,320 --> 00:10:27,000
indifference curves

316
00:10:23,600 --> 00:10:27,000
never cross.

317
00:10:27,559 --> 00:10:31,919
Indifference curves

318
00:10:29,279 --> 00:10:33,480
uh never cross.

319
00:10:31,919 --> 00:10:35,199
Okay, actually that's

320
00:10:33,480 --> 00:10:37,639
I'm going to that's third actually. I

321
00:10:35,200 --> 00:10:38,520
want to come to that in order. Second,

322
00:10:37,639 --> 00:10:39,960
third is indifference curves never

323
00:10:38,519 --> 00:10:43,000
cross. Second is indifference curves are

324
00:10:39,960 --> 00:10:43,000
downward sloping.

325
00:10:44,200 --> 00:10:47,280
Second is indifference curves are

326
00:10:45,480 --> 00:10:48,560
downward sloping.

327
00:10:47,279 --> 00:10:51,079
Okay? Indifference curves are downward

328
00:10:48,559 --> 00:10:52,199
sloping. Let's talk about that first.

329
00:10:51,080 --> 00:10:54,960
Okay?

330
00:10:52,200 --> 00:10:57,040
That simply comes from the principle of

331
00:10:54,960 --> 00:10:59,320
non-satiation.

332
00:10:57,039 --> 00:11:00,838
So, look at figure 2.2.

333
00:10:59,320 --> 00:11:03,200
Here's an upward sloping indifference

334
00:11:00,839 --> 00:11:05,160
curve.

335
00:11:03,200 --> 00:11:06,400
Okay? Why does that violate the

336
00:11:05,159 --> 00:11:07,480
principle of non-satiation? Why does

337
00:11:06,399 --> 00:11:09,600
that violate that? Yeah.

338
00:11:07,480 --> 00:11:11,080
Well, either if you're either you're

339
00:11:09,600 --> 00:11:13,720
somehow less happy if you have more

340
00:11:11,080 --> 00:11:16,160
cookies, like or you're less happy if

341
00:11:13,720 --> 00:11:18,360
you have more pizza. Yeah, but

342
00:11:16,159 --> 00:11:20,360
And like there's

343
00:11:18,360 --> 00:11:22,039
and that violates non-satiation.

344
00:11:20,360 --> 00:11:23,600
Exactly. So, basically you're

345
00:11:22,039 --> 00:11:24,838
indifferent on this curve you're

346
00:11:23,600 --> 00:11:26,159
indifferent between one of each and two

347
00:11:24,839 --> 00:11:27,440
of each. You can't be indifferent. Two

348
00:11:26,159 --> 00:11:28,360
of each has got to be better than one of

349
00:11:27,440 --> 00:11:29,680
each.

350
00:11:28,360 --> 00:11:31,720
So, an upward sloping indifference curve

351
00:11:29,679 --> 00:11:32,838
would violate non-satiation.

352
00:11:31,720 --> 00:11:34,080
So, that's the second property of

353
00:11:32,839 --> 00:11:35,240
indifference curve.

354
00:11:34,080 --> 00:11:37,560
The third property of indifference curve

355
00:11:35,240 --> 00:11:40,039
is indifference curves never cross.

356
00:11:37,559 --> 00:11:42,399
Okay? We can see that

357
00:11:40,039 --> 00:11:44,199
in figure 2.3.

358
00:11:42,399 --> 00:11:45,559
Okay? Someone else tell me why this

359
00:11:44,200 --> 00:11:48,240
violates the properties I wrote up there

360
00:11:45,559 --> 00:11:49,359
indifference curves crossing.

361
00:11:48,240 --> 00:11:51,159
Yeah.

362
00:11:49,360 --> 00:11:53,279
Because B and C

363
00:11:51,159 --> 00:11:54,838
What's that? Because B and C are

364
00:11:53,279 --> 00:11:56,360
strictly better.

365
00:11:54,839 --> 00:11:58,880
Because the B and C, B is strictly

366
00:11:56,360 --> 00:12:00,800
better. That's right.

367
00:11:58,879 --> 00:12:03,559
But but they're they're also but they're

368
00:12:00,799 --> 00:12:04,519
also both on the same curve as A. So,

369
00:12:03,559 --> 00:12:06,439
you're saying they're both you're

370
00:12:04,519 --> 00:12:07,679
indifferent with A for both B and C, but

371
00:12:06,440 --> 00:12:09,200
you can't be because B is strictly

372
00:12:07,679 --> 00:12:10,679
better than C. So, it violates

373
00:12:09,200 --> 00:12:12,800
transitivity.

374
00:12:10,679 --> 00:12:13,838
Okay? So, the problem with crossing

375
00:12:12,799 --> 00:12:16,599
indifference curves they violate

376
00:12:13,839 --> 00:12:16,600
transitivity.

377
00:12:17,320 --> 00:12:22,400
And then finally, the fourth

378
00:12:20,120 --> 00:12:24,480
is sort of a cute extra assumption, but

379
00:12:22,399 --> 00:12:27,399
I think it's important to clarify,

380
00:12:24,480 --> 00:12:29,480
which is that there is only one

381
00:12:27,399 --> 00:12:33,039
indifference curve through every

382
00:12:29,480 --> 00:12:33,039
possible consumption bundle.

383
00:12:33,240 --> 00:12:36,360
Only one

384
00:12:34,799 --> 00:12:37,679
IC

385
00:12:36,360 --> 00:12:40,560
through

386
00:12:37,679 --> 00:12:40,559
every bundle.

387
00:12:42,279 --> 00:12:45,759
Okay? You can't have two indifference

388
00:12:43,839 --> 00:12:47,680
curves going through the same bundle.

389
00:12:45,759 --> 00:12:49,360
Okay? Uh and that's because of

390
00:12:47,679 --> 00:12:50,079
completeness. If you have two

391
00:12:49,360 --> 00:12:51,120
indifference curves going through the

392
00:12:50,080 --> 00:12:52,320
same bundle, you wouldn't know how you

393
00:12:51,120 --> 00:12:54,039
felt.

394
00:12:52,320 --> 00:12:55,160
Okay? So, there can only be one going

395
00:12:54,039 --> 00:12:56,199
through every bundle cuz you know how

396
00:12:55,159 --> 00:12:57,600
you feel.

397
00:12:56,200 --> 00:12:59,080
You may feel indifferent, but you know

398
00:12:57,600 --> 00:13:00,240
how you feel. You can't say I don't

399
00:12:59,080 --> 00:13:01,920
know.

400
00:13:00,240 --> 00:13:03,240
Okay? So, that's sort of a extra

401
00:13:01,919 --> 00:13:05,360
assumption that sort of completes the

402
00:13:03,240 --> 00:13:06,360
link to the properties.

403
00:13:05,360 --> 00:13:08,759
Okay?

404
00:13:06,360 --> 00:13:10,000
So, that's basically how indifference

405
00:13:08,759 --> 00:13:11,559
curves work.

406
00:13:10,000 --> 00:13:14,279
Now,

407
00:13:11,559 --> 00:13:15,759
I find when I I took this course

408
00:13:14,279 --> 00:13:16,879
before you were

409
00:13:15,759 --> 00:13:18,200
God, maybe before your parents were

410
00:13:16,879 --> 00:13:19,679
born. I don't know. Certainly before you

411
00:13:18,200 --> 00:13:20,800
guys were born. Okay, when I took this

412
00:13:19,679 --> 00:13:22,279
course,

413
00:13:20,799 --> 00:13:23,599
I found this course full of a lot of

414
00:13:22,279 --> 00:13:24,799
lightbulb moments. That is stuff was

415
00:13:23,600 --> 00:13:26,600
just sort of confusing then boom an

416
00:13:24,799 --> 00:13:27,719
example really make it work for me. And

417
00:13:26,600 --> 00:13:29,600
the example that made indifference

418
00:13:27,720 --> 00:13:31,080
curves work to me was actually during my

419
00:13:29,600 --> 00:13:33,000
first year up.

420
00:13:31,080 --> 00:13:34,680
When my year up was with a grad student

421
00:13:33,000 --> 00:13:35,759
and that grad student had to decide

422
00:13:34,679 --> 00:13:36,959
where he was going to accept a job. He

423
00:13:35,759 --> 00:13:38,838
had a series of job offers and he had to

424
00:13:36,960 --> 00:13:40,320
decide. And basically said, here's the

425
00:13:38,839 --> 00:13:42,080
way I'm thinking about it. I'm

426
00:13:40,320 --> 00:13:44,080
indifferent I've I've indifference map

427
00:13:42,080 --> 00:13:47,440
and I care about two things. I care

428
00:13:44,080 --> 00:13:47,440
about school location

429
00:13:47,839 --> 00:13:52,240
and I care about economics department

430
00:13:49,679 --> 00:13:52,239
quality.

431
00:13:53,000 --> 00:13:55,839
Okay? I care about the quality of my

432
00:13:54,480 --> 00:13:57,839
colleagues and the research that's done

433
00:13:55,839 --> 00:13:59,800
there and the location. And basically

434
00:13:57,839 --> 00:14:02,040
he's he had two offers.

435
00:13:59,799 --> 00:14:03,439
One was from Princeton, which he put up

436
00:14:02,039 --> 00:14:04,759
here. No offense to New Jerseyans, but

437
00:14:03,440 --> 00:14:06,800
Princeton as a young single person

438
00:14:04,759 --> 00:14:08,559
sucks. Okay, fine when you're married

439
00:14:06,799 --> 00:14:10,439
and have kids, but deadly as a young

440
00:14:08,559 --> 00:14:13,439
single person. And the other so, that's

441
00:14:10,440 --> 00:14:15,160
Princeton. Down here was Santa Cruz.

442
00:14:13,440 --> 00:14:17,360
Okay? Awesome can have the most

443
00:14:15,159 --> 00:14:19,199
beautiful university in America. Okay?

444
00:14:17,360 --> 00:14:20,480
But not as good an economics department.

445
00:14:19,200 --> 00:14:23,079
And he decided he was roughly

446
00:14:20,480 --> 00:14:25,360
indifferent between the two.

447
00:14:23,078 --> 00:14:27,559
But he had a third offer

448
00:14:25,360 --> 00:14:29,919
from the IMF, which is a research

449
00:14:27,559 --> 00:14:31,559
institution in DC, which as he had a lot

450
00:14:29,919 --> 00:14:32,838
of good colleagues and DC is way better

451
00:14:31,559 --> 00:14:34,679
than Princeton, New Jersey even if it's

452
00:14:32,839 --> 00:14:35,880
not as good as Santa Cruz. So, he

453
00:14:34,679 --> 00:14:37,399
decided he would take the offer at the

454
00:14:35,879 --> 00:14:39,759
IMF.

455
00:14:37,399 --> 00:14:41,480
Okay? Even though the IMF had worse

456
00:14:39,759 --> 00:14:43,879
colleagues than Princeton

457
00:14:41,480 --> 00:14:45,519
and worse location than Santa Cruz,

458
00:14:43,879 --> 00:14:47,720
it was still better in combination the

459
00:14:45,519 --> 00:14:48,879
two of them given his preferences.

460
00:14:47,720 --> 00:14:50,879
And that's how he used indifference

461
00:14:48,879 --> 00:14:52,279
curves to help make his decision.

462
00:14:50,879 --> 00:14:54,360
Okay?

463
00:14:52,279 --> 00:14:55,720
So, that's sort of an example of uh of

464
00:14:54,360 --> 00:14:57,720
applying it. Let's see no offense to the

465
00:14:55,720 --> 00:14:59,639
New Jerseyans in the room, of which I'm

466
00:14:57,720 --> 00:15:00,720
one, but believe me you'd rather be in

467
00:14:59,639 --> 00:15:02,919
Santa Cruz.

468
00:15:00,720 --> 00:15:05,879
Um okay. Uh

469
00:15:02,919 --> 00:15:09,838
so, now let's go from preferences

470
00:15:05,879 --> 00:15:09,838
to utility functions.

471
00:15:12,480 --> 00:15:15,079
Okay? So, now we're going to move from

472
00:15:13,679 --> 00:15:17,519
preferences,

473
00:15:15,078 --> 00:15:19,639
which we've represented graphically,

474
00:15:17,519 --> 00:15:21,799
to utility functions, which we're going

475
00:15:19,639 --> 00:15:22,799
to represent mathematically. Remember, I

476
00:15:21,799 --> 00:15:23,838
want you to understand everything in

477
00:15:22,799 --> 00:15:25,838
this course at three levels:

478
00:15:23,839 --> 00:15:28,320
graphically, mathematically, and most

479
00:15:25,839 --> 00:15:30,400
importantly of all intuitively. Okay?

480
00:15:28,320 --> 00:15:31,400
So, graphic is indifference curves. Now

481
00:15:30,399 --> 00:15:34,120
we'll come to the mathematical

482
00:15:31,399 --> 00:15:36,519
representation, which utility function.

483
00:15:34,120 --> 00:15:38,679
Okay? And the idea is that every

484
00:15:36,519 --> 00:15:41,879
individual, all of you in this room,

485
00:15:38,679 --> 00:15:43,559
have a stable, well-behaved underlying

486
00:15:41,879 --> 00:15:44,919
mathematical representation of your

487
00:15:43,559 --> 00:15:47,399
preferences,

488
00:15:44,919 --> 00:15:49,319
which we call utility function.

489
00:15:47,399 --> 00:15:50,199
Okay? Now, once again, that's going to

490
00:15:49,320 --> 00:15:51,240
be very complicated and you have

491
00:15:50,200 --> 00:15:52,680
preference over lots of different

492
00:15:51,240 --> 00:15:54,120
things. We're going to make things

493
00:15:52,679 --> 00:15:56,120
simple by writing out two-dimensional

494
00:15:54,120 --> 00:15:58,078
representation for now of your

495
00:15:56,120 --> 00:16:00,959
indifference curve. We're going to say,

496
00:15:58,078 --> 00:16:03,919
how do we mathematically represent your

497
00:16:00,958 --> 00:16:05,599
feelings about pizza versus cookies?

498
00:16:03,919 --> 00:16:07,599
Okay? Imagine that's all you care about

499
00:16:05,600 --> 00:16:09,519
in the world is pizza and cookies.

500
00:16:07,600 --> 00:16:11,639
How do we mathematically represent that?

501
00:16:09,519 --> 00:16:14,039
So, for example, we could write down

502
00:16:11,639 --> 00:16:15,799
that your utility function is equal to

503
00:16:14,039 --> 00:16:18,480
the square root of the number of slices

504
00:16:15,799 --> 00:16:19,599
of pizza times the number of cookies.

505
00:16:18,480 --> 00:16:21,360
We could write that down. I'm not saying

506
00:16:19,600 --> 00:16:22,600
that's right. I'm not saying it works

507
00:16:21,360 --> 00:16:25,279
for anyone in this room or even everyone

508
00:16:22,600 --> 00:16:28,360
in this room, but that is a possible way

509
00:16:25,279 --> 00:16:30,559
to represent utility.

510
00:16:28,360 --> 00:16:32,159
Okay? What this would say, this is

511
00:16:30,559 --> 00:16:33,879
convenient. We will use we'll end up

512
00:16:32,159 --> 00:16:34,919
using square root form a lot for utility

513
00:16:33,879 --> 00:16:36,720
functions, a lot of convenient

514
00:16:34,919 --> 00:16:39,039
mathematical properties.

515
00:16:36,720 --> 00:16:40,639
And it happens to jive with our example,

516
00:16:39,039 --> 00:16:42,078
right? Because in this example you're

517
00:16:40,639 --> 00:16:44,000
indifferent between two pizza and one

518
00:16:42,078 --> 00:16:45,759
cookie or one pizza and two cookie.

519
00:16:44,000 --> 00:16:47,000
They're both square root of two.

520
00:16:45,759 --> 00:16:48,600
And you prefer two pizza and two

521
00:16:47,000 --> 00:16:50,600
cookies, that's two.

522
00:16:48,600 --> 00:16:53,560
Okay? So, this gives you a higher

523
00:16:50,600 --> 00:16:55,800
utility for two pizza and two cookies

524
00:16:53,559 --> 00:16:57,838
okay? Um uh

525
00:16:55,799 --> 00:16:59,679
then uh one pizza

526
00:16:57,839 --> 00:17:02,000
than one pizza and two cookie or two

527
00:16:59,679 --> 00:17:03,838
pizza and one cookie.

528
00:17:02,000 --> 00:17:05,920
So, now the question is what does this

529
00:17:03,839 --> 00:17:08,799
mean? What is utility?

530
00:17:05,920 --> 00:17:10,560
Okay? Well, utility doesn't actually

531
00:17:08,799 --> 00:17:12,919
mean anything. There's not really a

532
00:17:10,559 --> 00:17:14,039
thing out there called utils.

533
00:17:12,920 --> 00:17:15,600
Okay?

534
00:17:14,039 --> 00:17:18,039
In other words, utility is not a

535
00:17:15,599 --> 00:17:19,838
cardinal concept. It is only an ordinal

536
00:17:18,039 --> 00:17:23,279
concept.

537
00:17:19,838 --> 00:17:26,119
You cannot say your utility you are you

538
00:17:23,279 --> 00:17:27,838
cannot literally say my utility is X%

539
00:17:26,119 --> 00:17:29,119
higher than your utility, but you can

540
00:17:27,838 --> 00:17:31,279
rank them.

541
00:17:29,119 --> 00:17:33,079
So, we're going to assume that utility

542
00:17:31,279 --> 00:17:34,720
can be ranked to allow you to rank

543
00:17:33,079 --> 00:17:36,720
choices.

544
00:17:34,720 --> 00:17:38,319
Even if generally we might slip some and

545
00:17:36,720 --> 00:17:41,319
sort of pretend utility is cardinal for

546
00:17:38,319 --> 00:17:42,319
some cute examples, but by and large

547
00:17:41,319 --> 00:17:44,559
we're going to think of utility as

548
00:17:42,319 --> 00:17:46,279
purely ordinal. It's just a way to rank

549
00:17:44,559 --> 00:17:47,720
your choices. It's just when you have a

550
00:17:46,279 --> 00:17:49,799
set of choices out there over many

551
00:17:47,720 --> 00:17:51,679
dimensions. Like if your choice in life

552
00:17:49,799 --> 00:17:53,200
is always over one dimension

553
00:17:51,679 --> 00:17:54,840
and more was better, it would always be

554
00:17:53,200 --> 00:17:56,960
easy to rank it, right? You never ever

555
00:17:54,839 --> 00:17:58,519
problem. Once your choice over more than

556
00:17:56,960 --> 00:18:00,039
one dimension,

557
00:17:58,519 --> 00:18:01,839
now if you want to rank them, you need

558
00:18:00,039 --> 00:18:03,599
some way to combine them. That's what

559
00:18:01,839 --> 00:18:05,359
this function does. It allows you

560
00:18:03,599 --> 00:18:07,439
essentially to weight the different

561
00:18:05,359 --> 00:18:09,199
elements of your consumption bundle so

562
00:18:07,440 --> 00:18:11,759
you can rank them um

563
00:18:09,200 --> 00:18:14,319
when it comes time to choose.

564
00:18:11,759 --> 00:18:15,679
Okay? Now, this is obviously incredibly

565
00:18:14,319 --> 00:18:17,200
simple,

566
00:18:15,679 --> 00:18:19,200
but it turns out to be amazingly

567
00:18:17,200 --> 00:18:20,480
powerful in explaining real world

568
00:18:19,200 --> 00:18:21,840
behavior.

569
00:18:20,480 --> 00:18:23,240
Okay?

570
00:18:21,839 --> 00:18:24,519
And so, what I want to do today is work

571
00:18:23,240 --> 00:18:25,720
with the underlying mathematics of

572
00:18:24,519 --> 00:18:26,879
utility

573
00:18:25,720 --> 00:18:28,319
and then we'll come back we'll see in

574
00:18:26,880 --> 00:18:31,240
the next few lectures how it could

575
00:18:28,319 --> 00:18:33,519
actually be used to explain decisions.

576
00:18:31,240 --> 00:18:34,839
So, a key concept we're going to talk

577
00:18:33,519 --> 00:18:38,119
about

578
00:18:34,839 --> 00:18:39,678
in this class is marginal utility.

579
00:18:38,119 --> 00:18:41,719
Marginal utility is just the derivative

580
00:18:39,679 --> 00:18:43,560
of the utility function with respect to

581
00:18:41,720 --> 00:18:45,880
one of the elements. So, the marginal

582
00:18:43,559 --> 00:18:48,279
utility for cookies of cookies is

583
00:18:45,880 --> 00:18:50,560
utility of the next cookie

584
00:18:48,279 --> 00:18:52,480
given how many cookies you've had.

585
00:18:50,559 --> 00:18:55,039
This class can be very focused on

586
00:18:52,480 --> 00:18:56,679
marginal decision making.

587
00:18:55,039 --> 00:18:58,559
In economics, it's all about how you

588
00:18:56,679 --> 00:19:00,679
think about the next unit. Turns out

589
00:18:58,559 --> 00:19:02,039
that makes life a ton easier. Turns out

590
00:19:00,679 --> 00:19:03,720
it's way easier to say, do you want the

591
00:19:02,039 --> 00:19:06,200
next cookie? Than to say, how many

592
00:19:03,720 --> 00:19:07,159
cookies do you want?

593
00:19:06,200 --> 00:19:09,159
Because if you want the next cookie,

594
00:19:07,159 --> 00:19:10,159
that's sort of a very isolated decision.

595
00:19:09,159 --> 00:19:12,159
You say, okay, I've had this many

596
00:19:10,159 --> 00:19:13,400
cookies, do I want the next cookie?

597
00:19:12,159 --> 00:19:14,360
Whereas before you start eating you say,

598
00:19:13,400 --> 00:19:16,759
how many cookies do you want? That's

599
00:19:14,359 --> 00:19:18,799
sort of a harder more global decision.

600
00:19:16,759 --> 00:19:20,720
So, we're going to focus on the stepwise

601
00:19:18,799 --> 00:19:22,399
decision making process of do you want

602
00:19:20,720 --> 00:19:24,440
the next unit, the next cookie or the

603
00:19:22,400 --> 00:19:28,120
next slice of pizza?

604
00:19:24,440 --> 00:19:29,559
Okay? And the key feature of utility

605
00:19:28,119 --> 00:19:31,000
functions we'll work with throughout the

606
00:19:29,559 --> 00:19:35,440
semester

607
00:19:31,000 --> 00:19:35,440
is that they will feature diminishing

608
00:19:36,359 --> 00:19:41,599
diminishing marginal utility.

609
00:19:39,079 --> 00:19:43,319
Marginal utility will fall as you have

610
00:19:41,599 --> 00:19:45,439
more of a good.

611
00:19:43,319 --> 00:19:47,079
The more of a good you've had, the less

612
00:19:45,440 --> 00:19:48,799
happiness you'll derive from the next

613
00:19:47,079 --> 00:19:50,599
unit.

614
00:19:48,799 --> 00:19:52,839
Okay?

615
00:19:50,599 --> 00:19:55,199
Now, we can see that graphically in

616
00:19:52,839 --> 00:19:58,039
figure 2-4.

617
00:19:55,200 --> 00:20:00,200
Figure 2-4 graphs on the x-axis the

618
00:19:58,039 --> 00:20:01,720
number of cookies holding constant

619
00:20:00,200 --> 00:20:04,279
pizza. So, let's say you're having two

620
00:20:01,720 --> 00:20:05,799
pizza slices and you want to say,

621
00:20:04,279 --> 00:20:07,559
"What's my benefit from the next

622
00:20:05,799 --> 00:20:09,879
cookie?"

623
00:20:07,559 --> 00:20:11,799
And on the on the left axis, violating

624
00:20:09,880 --> 00:20:13,360
what I just said like 15 seconds ago, we

625
00:20:11,799 --> 00:20:14,799
graph utility.

626
00:20:13,359 --> 00:20:16,000
Now, once again, the util numbers don't

627
00:20:14,799 --> 00:20:18,039
mean anything. It's just to give you an

628
00:20:16,000 --> 00:20:19,519
ordinal sense.

629
00:20:18,039 --> 00:20:20,960
What you see here is that if you have

630
00:20:19,519 --> 00:20:23,879
one cookie,

631
00:20:20,960 --> 00:20:25,400
your utility is 1.4, square root of 2 *

632
00:20:23,880 --> 00:20:26,760
1.

633
00:20:25,400 --> 00:20:28,200
If you have two cookies, your utility

634
00:20:26,759 --> 00:20:30,119
goes up

635
00:20:28,200 --> 00:20:32,039
to square root of 4, which is 2. You are

636
00:20:30,119 --> 00:20:34,599
happier with two cookies.

637
00:20:32,039 --> 00:20:36,440
But you are less happy from the second

638
00:20:34,599 --> 00:20:39,119
cookie than the first cookie.

639
00:20:36,440 --> 00:20:40,600
Okay? And you can see that in figure if

640
00:20:39,119 --> 00:20:43,519
you flip back and forth between 2-4 and

641
00:20:40,599 --> 00:20:46,159
2-5, you can see that.

642
00:20:43,519 --> 00:20:48,440
Okay? The first cookie,

643
00:20:46,160 --> 00:20:50,400
going from zero to one cookie, gave you

644
00:20:48,440 --> 00:20:53,440
one So, in this case, we're not graphing

645
00:20:50,400 --> 00:20:56,200
the marginal utility. So, figure 2-4 is

646
00:20:53,440 --> 00:20:57,480
the level of utility,

647
00:20:56,200 --> 00:20:59,559
which is not really something you can

648
00:20:57,480 --> 00:21:00,519
measure, in fact. Figure 2-5 is

649
00:20:59,559 --> 00:21:02,079
something you can measure, which is

650
00:21:00,519 --> 00:21:03,680
marginal utility. What's your happiness?

651
00:21:02,079 --> 00:21:05,240
And we'll talk about measuring this from

652
00:21:03,680 --> 00:21:06,880
the next cookie. You see, the first

653
00:21:05,240 --> 00:21:08,640
cookie

654
00:21:06,880 --> 00:21:10,960
gives you

655
00:21:08,640 --> 00:21:13,040
um a utility and a utility increment of

656
00:21:10,960 --> 00:21:15,480
1.4.

657
00:21:13,039 --> 00:21:17,480
Okay? You go from utility of zero

658
00:21:15,480 --> 00:21:18,640
to utility of 1.4.

659
00:21:17,480 --> 00:21:21,120
The next cookie gives you a utility

660
00:21:18,640 --> 00:21:23,600
increment of 0.59.

661
00:21:21,119 --> 00:21:25,239
Okay, you go from utility of 1.41

662
00:21:23,599 --> 00:21:26,519
to utility of 2.

663
00:21:25,240 --> 00:21:28,960
The next cookie gives you a utility

664
00:21:26,519 --> 00:21:30,759
increment of 0.45, the square root of 3.

665
00:21:28,960 --> 00:21:32,360
So, now we flip back to the previous

666
00:21:30,759 --> 00:21:34,359
page. We're going from the square root

667
00:21:32,359 --> 00:21:35,439
of 4 to We're going from the square root

668
00:21:34,359 --> 00:21:36,839
of 4, I'm sorry, to the square root of

669
00:21:35,440 --> 00:21:39,080
6.

670
00:21:36,839 --> 00:21:40,799
Square root of 6 is only 0.45 more than

671
00:21:39,079 --> 00:21:42,279
the square root of 4.

672
00:21:40,799 --> 00:21:44,440
And so on.

673
00:21:42,279 --> 00:21:46,480
So, each additional cookie

674
00:21:44,440 --> 00:21:48,519
makes you less and less happy. It makes

675
00:21:46,480 --> 00:21:50,400
you happier. It has to cuz more is

676
00:21:48,519 --> 00:21:51,879
better. But it makes you less and less

677
00:21:50,400 --> 00:21:54,640
happy.

678
00:21:51,880 --> 00:21:56,360
Okay? And this makes sense.

679
00:21:54,640 --> 00:21:58,080
Just think about any decision in life

680
00:21:56,359 --> 00:22:00,479
starting with nothing of something and

681
00:21:58,079 --> 00:22:02,480
having the first one. Slice of pizza, a

682
00:22:00,480 --> 00:22:03,319
cookie, deciding on which movie to go

683
00:22:02,480 --> 00:22:04,880
to.

684
00:22:03,319 --> 00:22:06,599
The first movie, the one you want to see

685
00:22:04,880 --> 00:22:08,720
the most,

686
00:22:06,599 --> 00:22:09,919
okay, is going to make you happier than

687
00:22:08,720 --> 00:22:11,360
you want to see the one you want to see

688
00:22:09,920 --> 00:22:12,640
not quite as much.

689
00:22:11,359 --> 00:22:15,039
The first cookie when you're hungry will

690
00:22:12,640 --> 00:22:16,120
make you happier than the second cookie.

691
00:22:15,039 --> 00:22:17,960
The first slice of pizza will make you

692
00:22:16,119 --> 00:22:19,159
happier. Now, you may be close to

693
00:22:17,960 --> 00:22:20,600
indifferent where that second slice of

694
00:22:19,160 --> 00:22:21,840
pizza makes you almost as happy as the

695
00:22:20,599 --> 00:22:23,759
first.

696
00:22:21,839 --> 00:22:25,639
But the first will make you happier.

697
00:22:23,759 --> 00:22:27,000
Okay, if you think about that's really

698
00:22:25,640 --> 00:22:27,960
sort of that first step. You were hungry

699
00:22:27,000 --> 00:22:29,519
and that first one makes you feel

700
00:22:27,960 --> 00:22:32,160
happier.

701
00:22:29,519 --> 00:22:33,920
Now, but you got to remember you always

702
00:22:32,160 --> 00:22:35,080
want more cookies.

703
00:22:33,920 --> 00:22:36,400
Now, you might say, "Wait a second, this

704
00:22:35,079 --> 00:22:38,119
is stupid. Okay, once I've had 10

705
00:22:36,400 --> 00:22:39,480
cookies, I'm going to barf."

706
00:22:38,119 --> 00:22:42,079
The 11th cookie could actually make me

707
00:22:39,480 --> 00:22:43,360
worse off cuz I don't like barfing.

708
00:22:42,079 --> 00:22:45,480
But

709
00:22:43,359 --> 00:22:47,240
in economics, we have to remember you

710
00:22:45,480 --> 00:22:49,000
don't have to eat the 11th cookie. You

711
00:22:47,240 --> 00:22:50,120
could give it away.

712
00:22:49,000 --> 00:22:52,240
So, if I say you want to buy the 11th

713
00:22:50,119 --> 00:22:53,959
cookie, you could save it for later. You

714
00:22:52,240 --> 00:22:56,039
could give it to a friend.

715
00:22:53,960 --> 00:22:57,880
So, you always want it. In the worst

716
00:22:56,039 --> 00:22:59,799
case, you throw it out.

717
00:22:57,880 --> 00:23:01,880
It can't make you worse off.

718
00:22:59,799 --> 00:23:03,159
It can only make you better off.

719
00:23:01,880 --> 00:23:04,640
And that's what where our sort of more

720
00:23:03,160 --> 00:23:05,840
is better assumption comes from.

721
00:23:04,640 --> 00:23:07,160
Obviously, in the limit, you know, if

722
00:23:05,839 --> 00:23:08,678
you get a million cookies, your garbage

723
00:23:07,160 --> 00:23:09,759
can gets full, you have no friends to

724
00:23:08,679 --> 00:23:12,240
give them to. I understand the limit

725
00:23:09,759 --> 00:23:13,640
these things fall apart. Okay? But

726
00:23:12,240 --> 00:23:15,000
that's the basic idea of more is better

727
00:23:13,640 --> 00:23:16,640
and the basic idea of of diminishing

728
00:23:15,000 --> 00:23:17,960
marginal utility. Okay, any questions

729
00:23:16,640 --> 00:23:20,320
about that?

730
00:23:17,960 --> 00:23:20,319
Yeah.

731
00:23:20,880 --> 00:23:25,520
Utility function can never be negative

732
00:23:22,559 --> 00:23:26,879
because we have Well, utility Once

733
00:23:25,519 --> 00:23:28,119
again, utility is not an ordinal

734
00:23:26,880 --> 00:23:29,200
concept. You can set up utility

735
00:23:28,119 --> 00:23:31,678
functions such that the number is

736
00:23:29,200 --> 00:23:34,360
negative. You can set that up. Okay? The

737
00:23:31,679 --> 00:23:35,920
marginal utility is always positive. You

738
00:23:34,359 --> 00:23:37,079
always get some benefit from the next

739
00:23:35,920 --> 00:23:38,400
unit.

740
00:23:37,079 --> 00:23:39,480
Utility, once again, the measurement is

741
00:23:38,400 --> 00:23:40,759
irrelevant. So, it can be negative. You

742
00:23:39,480 --> 00:23:42,240
can set it up. Yeah, I could write my

743
00:23:40,759 --> 00:23:43,920
utility function like this, you know,

744
00:23:42,240 --> 00:23:45,440
something like that. So, it could be

745
00:23:43,920 --> 00:23:47,279
negative. That's just a sort of scaling

746
00:23:45,440 --> 00:23:49,440
factor. But marginal utility is always

747
00:23:47,279 --> 00:23:51,240
positive. You're always happier or it's

748
00:23:49,440 --> 00:23:53,160
not it's not negative. You're always

749
00:23:51,240 --> 00:23:54,640
happier at least indifferent to getting

750
00:23:53,160 --> 00:23:56,840
the next unit.

751
00:23:54,640 --> 00:23:58,240
Yeah. So, when you're looking at 2-5,

752
00:23:56,839 --> 00:23:59,839
you can't look at the function of the

753
00:23:58,240 --> 00:24:02,039
pizza and the marginal utility, so it's

754
00:23:59,839 --> 00:24:04,678
going to go down.

755
00:24:02,039 --> 00:24:05,519
Uh I'm sorry. You look Figure 2-5, no,

756
00:24:04,679 --> 00:24:06,640
the marginal utility is going to go

757
00:24:05,519 --> 00:24:07,960
down.

758
00:24:06,640 --> 00:24:09,200
Each fraction of cookie, the marginal

759
00:24:07,960 --> 00:24:11,000
utility Marginal utility is always

760
00:24:09,200 --> 00:24:12,840
diminishing. So, if you start with zero,

761
00:24:11,000 --> 00:24:14,279
then you can get half of the pizza in

762
00:24:12,839 --> 00:24:15,720
this graph.

763
00:24:14,279 --> 00:24:17,279
Well, it's really hard to do it from

764
00:24:15,720 --> 00:24:19,000
zero. That's really tricky. It's sort of

765
00:24:17,279 --> 00:24:20,720
much easier to start from one.

766
00:24:19,000 --> 00:24:21,759
So, corner solutions, we'll talk a lot

767
00:24:20,720 --> 00:24:23,519
about corner solutions in this class.

768
00:24:21,759 --> 00:24:25,000
They get ugly. Think of it starting from

769
00:24:23,519 --> 00:24:26,240
one. Starting from that first cookie,

770
00:24:25,000 --> 00:24:27,559
every fraction of a cookie makes you

771
00:24:26,240 --> 00:24:29,799
happier but less and less happy with

772
00:24:27,559 --> 00:24:31,919
each fraction. It's a good question.

773
00:24:29,799 --> 00:24:35,720
All right. Good questions. All right.

774
00:24:31,920 --> 00:24:38,920
So, now let's let's talk about Let's

775
00:24:35,720 --> 00:24:40,640
flip back from the math to the graphics

776
00:24:38,920 --> 00:24:42,600
and talk about where indifference curves

777
00:24:40,640 --> 00:24:44,640
come from. I just drew them out. But in

778
00:24:42,599 --> 00:24:46,519
fact, indifference curves are the

779
00:24:44,640 --> 00:24:49,000
graphical representation of what comes

780
00:24:46,519 --> 00:24:51,359
out of utility function.

781
00:24:49,000 --> 00:24:54,480
Okay? And indeed, the slope of the

782
00:24:51,359 --> 00:24:58,439
indifference curve we are going to call

783
00:24:54,480 --> 00:24:59,920
the marginal rate of substitution.

784
00:24:58,440 --> 00:25:02,600
The rate essentially at which you're

785
00:24:59,920 --> 00:25:04,240
willing to substitute

786
00:25:02,599 --> 00:25:05,919
one good for the other. The rate at

787
00:25:04,240 --> 00:25:09,559
which you're willing to substitute

788
00:25:05,920 --> 00:25:11,160
cookies for pizza is your marginal rate

789
00:25:09,559 --> 00:25:14,480
of substitution.

790
00:25:11,160 --> 00:25:16,519
And we'll define that as the slope of

791
00:25:14,480 --> 00:25:18,679
the indifference curve, delta P over

792
00:25:16,519 --> 00:25:19,720
delta C.

793
00:25:18,679 --> 00:25:20,960
That is your marginal rate of

794
00:25:19,720 --> 00:25:22,839
substitution. Literally, the

795
00:25:20,960 --> 00:25:23,880
indifference curve tells you the rate at

796
00:25:22,839 --> 00:25:25,959
which you're willing to substitute. You

797
00:25:23,880 --> 00:25:28,480
just follow along and say, "Look, I'm

798
00:25:25,960 --> 00:25:30,920
willing to give up um So, in other

799
00:25:28,480 --> 00:25:33,679
words, if you look at figure 2-6,

800
00:25:30,920 --> 00:25:35,720
you say, "Look, I'm indifferent between

801
00:25:33,679 --> 00:25:37,759
point A and point B.

802
00:25:35,720 --> 00:25:39,120
One cook- one slice of pizza and I'm

803
00:25:37,759 --> 00:25:40,160
sorry, one cookie and four slices of

804
00:25:39,119 --> 00:25:42,479
pizza

805
00:25:40,160 --> 00:25:44,560
is the same to me as two cookies and two

806
00:25:42,480 --> 00:25:45,799
slices of pizza. Why is it the same?

807
00:25:44,559 --> 00:25:47,759
Because they both give me utility square

808
00:25:45,799 --> 00:25:49,079
root of 4, right? So, given this

809
00:25:47,759 --> 00:25:50,480
mathematical rep- I'm not saying you

810
00:25:49,079 --> 00:25:52,000
are. I'm saying given this mathematical

811
00:25:50,480 --> 00:25:54,079
representation,

812
00:25:52,000 --> 00:25:55,440
okay, you are indifferent between point

813
00:25:54,079 --> 00:25:57,119
A and point B.

814
00:25:55,440 --> 00:25:58,519
So, what that says and what's the slope

815
00:25:57,119 --> 00:26:01,039
of the indifference curve? What's the

816
00:25:58,519 --> 00:26:04,119
arc slope between point A and point B?

817
00:26:01,039 --> 00:26:05,440
The slope is -2.

818
00:26:04,119 --> 00:26:07,439
So, your marginal rate of substitution

819
00:26:05,440 --> 00:26:09,279
is -2.

820
00:26:07,440 --> 00:26:10,279
You are indifferent.

821
00:26:09,279 --> 00:26:13,240
Okay?

822
00:26:10,279 --> 00:26:15,079
Um you're indifferent between 1-4 and

823
00:26:13,240 --> 00:26:18,200
2-2. Therefore, you're willing to

824
00:26:15,079 --> 00:26:22,119
substitute or give away

825
00:26:18,200 --> 00:26:24,120
two slices of pizza to get one cookie.

826
00:26:22,119 --> 00:26:25,639
Delta P delta C

827
00:26:24,119 --> 00:26:28,399
is uh

828
00:26:25,640 --> 00:26:31,240
is -2.

829
00:26:28,400 --> 00:26:32,440
Okay? Now, it turns out you can define

830
00:26:31,240 --> 00:26:34,519
the marginal rate of substitution over

831
00:26:32,440 --> 00:26:36,920
any segment of indifference curve. And

832
00:26:34,519 --> 00:26:39,119
what's interesting is it changes. It

833
00:26:36,920 --> 00:26:42,640
diminishes. Look what happens when we

834
00:26:39,119 --> 00:26:44,919
move from two pizzas and two cookies

835
00:26:42,640 --> 00:26:46,280
to from point B to point C.

836
00:26:44,920 --> 00:26:47,920
Now, the marginal rate of substitution

837
00:26:46,279 --> 00:26:50,039
is only -1/2.

838
00:26:47,920 --> 00:26:52,320
Now, I'm only willing to give up one

839
00:26:50,039 --> 00:26:53,839
slice of pizza to get two cookies.

840
00:26:52,319 --> 00:26:55,359
What's happening? First, I was willing

841
00:26:53,839 --> 00:26:57,000
to give up two slices of pizza to get

842
00:26:55,359 --> 00:26:58,319
one cookie.

843
00:26:57,000 --> 00:27:00,000
Now, I'm only willing to give up willing

844
00:26:58,319 --> 00:27:02,240
to give up one slice of pizza to get two

845
00:27:00,000 --> 00:27:03,880
cookies. What's happening?

846
00:27:02,240 --> 00:27:05,640
Yeah. You don't want a cookie as much.

847
00:27:03,880 --> 00:27:07,679
Because of? Diminishing marginal

848
00:27:05,640 --> 00:27:10,400
utility. Exactly. Diminishing marginal

849
00:27:07,679 --> 00:27:12,840
utility has caused the marginal rate of

850
00:27:10,400 --> 00:27:13,960
substitution itself itself to diminish.

851
00:27:12,839 --> 00:27:15,720
For those of you who are really kind of

852
00:27:13,960 --> 00:27:17,960
better at math than I am, it turns out

853
00:27:15,720 --> 00:27:19,799
technically, mathematically, marginal

854
00:27:17,960 --> 00:27:22,000
utility isn't always diminishing. You

855
00:27:19,799 --> 00:27:23,279
can draw cases. MRS is always

856
00:27:22,000 --> 00:27:24,640
diminishing.

857
00:27:23,279 --> 00:27:25,678
So, you can think of marginal utility as

858
00:27:24,640 --> 00:27:27,040
always diminishing. It's fine for this

859
00:27:25,679 --> 00:27:28,080
class. When you get to higher level math

860
00:27:27,039 --> 00:27:30,200
and economics, you'll see marginal

861
00:27:28,079 --> 00:27:32,039
utility doesn't have to diminish. MRS

862
00:27:30,200 --> 00:27:35,000
has to diminish.

863
00:27:32,039 --> 00:27:36,519
Okay? MRS is always diminishing.

864
00:27:35,000 --> 00:27:40,200
As you go along the indifference curve,

865
00:27:36,519 --> 00:27:40,200
that slope is always falling.

866
00:27:40,319 --> 00:27:43,759
Okay?

867
00:27:41,679 --> 00:27:46,640
So, basically,

868
00:27:43,759 --> 00:27:48,559
what we can write now is how the MRS

869
00:27:46,640 --> 00:27:50,600
relates to utility function,

870
00:27:48,559 --> 00:27:53,720
our first sort of mind-blowing result,

871
00:27:50,599 --> 00:27:56,599
is that the MRS is equal to the negative

872
00:27:53,720 --> 00:27:59,519
of the marginal utility of cookies over

873
00:27:56,599 --> 00:28:02,119
the marginal utility of pizza.

874
00:27:59,519 --> 00:28:04,279
That's our first key definition.

875
00:28:02,119 --> 00:28:05,599
It's equal to the negative of the

876
00:28:04,279 --> 00:28:07,720
marginal utility of the good on the

877
00:28:05,599 --> 00:28:10,519
x-axis over the marginal utility of the

878
00:28:07,720 --> 00:28:13,079
good on the y-axis.

879
00:28:10,519 --> 00:28:16,240
Okay? Essentially, the marginal rate of

880
00:28:13,079 --> 00:28:19,039
substitution tells you how your relative

881
00:28:16,240 --> 00:28:22,039
marginal utilities evolve as you move

882
00:28:19,039 --> 00:28:25,720
down the indifference curve.

883
00:28:22,039 --> 00:28:28,599
When you start at point A,

884
00:28:25,720 --> 00:28:30,799
you have lots of pizza and not a lot of

885
00:28:28,599 --> 00:28:33,119
cookies.

886
00:28:30,799 --> 00:28:36,879
When you have lots of pizza,

887
00:28:33,119 --> 00:28:38,839
your marginal utility is small.

888
00:28:36,880 --> 00:28:40,560
Here's the key insight. This is the

889
00:28:38,839 --> 00:28:41,678
thing which, once again, it's a light

890
00:28:40,559 --> 00:28:43,799
bulb thing. If you get this, it'll make

891
00:28:41,679 --> 00:28:46,320
your life so much easier. Marginal

892
00:28:43,799 --> 00:28:47,759
utilities are negative functions of

893
00:28:46,319 --> 00:28:50,279
quantity.

894
00:28:47,759 --> 00:28:53,079
The more you have of a thing, the less

895
00:28:50,279 --> 00:28:54,879
you want the next unit of it.

896
00:28:53,079 --> 00:28:55,918
That's why, for example, cookies is now

897
00:28:54,880 --> 00:28:58,440
in the numerator and pizza is in the

898
00:28:55,919 --> 00:29:00,679
denominator, flipping from this side.

899
00:28:58,440 --> 00:29:02,120
Okay? The more you have a good, the less

900
00:29:00,679 --> 00:29:04,679
you want it.

901
00:29:02,119 --> 00:29:07,199
So, start at point A. You have lots of

902
00:29:04,679 --> 00:29:09,120
pizza and not a lot of cookies.

903
00:29:07,200 --> 00:29:10,640
You don't really want more pizza. You

904
00:29:09,119 --> 00:29:13,479
want more cookies.

905
00:29:10,640 --> 00:29:16,800
That means the denominator is small.

906
00:29:13,480 --> 00:29:18,319
The marginal utility of pizza is small.

907
00:29:16,799 --> 00:29:19,759
You don't really want it.

908
00:29:18,319 --> 00:29:21,559
But the marginal utility of cookies is

909
00:29:19,759 --> 00:29:24,279
high. You don't have many of them. So,

910
00:29:21,559 --> 00:29:26,720
this is a big number.

911
00:29:24,279 --> 00:29:28,599
Now, let's move to point B.

912
00:29:26,720 --> 00:29:30,240
And think about your next decision.

913
00:29:28,599 --> 00:29:33,119
Well, now

914
00:29:30,240 --> 00:29:34,200
your marginal utility of pizza,

915
00:29:33,119 --> 00:29:35,759
if you're going to go from two to one

916
00:29:34,200 --> 00:29:37,519
slice of pizza, now pizza is worth a lot

917
00:29:35,759 --> 00:29:38,879
more than cookies. So, now it gets

918
00:29:37,519 --> 00:29:40,960
smaller.

919
00:29:38,880 --> 00:29:43,080
So, essentially, as you move along that

920
00:29:40,960 --> 00:29:44,400
indifference curve, because of this you

921
00:29:43,079 --> 00:29:45,678
want because diminishing marginal

922
00:29:44,400 --> 00:29:47,519
utility,

923
00:29:45,679 --> 00:29:49,720
it leads this issue of a diminishing

924
00:29:47,519 --> 00:29:52,000
marginal rate of substitution.

925
00:29:49,720 --> 00:29:53,559
Okay? So, basically, as you move along

926
00:29:52,000 --> 00:29:55,640
the indifference curve, you're more and

927
00:29:53,559 --> 00:29:57,480
more willing to give up

928
00:29:55,640 --> 00:29:59,280
the good on the x-axis to get the good

929
00:29:57,480 --> 00:30:00,960
on the y-axis. As you move from the

930
00:29:59,279 --> 00:30:03,599
upper left to the lower right on that

931
00:30:00,960 --> 00:30:04,960
indifference map, figure 2.6,

932
00:30:03,599 --> 00:30:06,199
you're more you're more willing to give

933
00:30:04,960 --> 00:30:08,680
up

934
00:30:06,200 --> 00:30:11,000
the good on the on the x-axis to get the

935
00:30:08,680 --> 00:30:13,160
good on the y-axis.

936
00:30:11,000 --> 00:30:16,039
And what this implies is that

937
00:30:13,160 --> 00:30:17,759
indifference curves are con-

938
00:30:16,039 --> 00:30:21,119
indifference curves

939
00:30:17,759 --> 00:30:22,680
are uh convex to the origin.

940
00:30:21,119 --> 00:30:23,959
Indifference curves are convex to the

941
00:30:22,680 --> 00:30:26,720
origin.

942
00:30:23,960 --> 00:30:28,440
It's very important. Okay, the

943
00:30:26,720 --> 00:30:29,799
Let's see. The They are They are not

944
00:30:28,440 --> 00:30:31,240
concave. They're either convex or

945
00:30:29,799 --> 00:30:33,079
straight. Let's say they're They're not

946
00:30:31,240 --> 00:30:34,960
concave to the origin.

947
00:30:33,079 --> 00:30:36,159
Okay, to be technical.

948
00:30:34,960 --> 00:30:37,799
Indifference curves can be linear. We'll

949
00:30:36,160 --> 00:30:39,160
come to that.

950
00:30:37,799 --> 00:30:40,919
But they can't be concave to the origin.

951
00:30:39,160 --> 00:30:43,480
Why? Well, let's look at the next

952
00:30:40,920 --> 00:30:44,840
figure, the last figure, figure 2.7.

953
00:30:43,480 --> 00:30:47,640
What would happen if indifference curves

954
00:30:44,839 --> 00:30:51,879
were concave to the origin?

955
00:30:47,640 --> 00:30:54,280
Then that would say moving from

956
00:30:51,880 --> 00:30:55,920
one pizza, so now I've drawn a a concave

957
00:30:54,279 --> 00:30:57,440
indifference curve. And with this

958
00:30:55,920 --> 00:31:00,200
indifference curve, moving from point A

959
00:30:57,440 --> 00:31:02,920
to point B leaves you indifferent.

960
00:31:00,200 --> 00:31:04,720
So, you're happy to give up one slice of

961
00:31:02,920 --> 00:31:06,400
pizza to get one cookie.

962
00:31:04,720 --> 00:31:07,720
Starting with four slices of pizza and

963
00:31:06,400 --> 00:31:09,920
one cookie,

964
00:31:07,720 --> 00:31:12,480
you were happy to give up one slice of

965
00:31:09,920 --> 00:31:15,519
pizza to get one cookie.

966
00:31:12,480 --> 00:31:16,920
Now, starting from two and three, you're

967
00:31:15,519 --> 00:31:19,160
now willing to give up two slices of

968
00:31:16,920 --> 00:31:20,519
pizza to get one cookie.

969
00:31:19,160 --> 00:31:23,080
What does that violate? Why Why does

970
00:31:20,519 --> 00:31:25,000
that not make sense? Yeah.

971
00:31:23,079 --> 00:31:26,119
Law of diminishing marginal returns.

972
00:31:25,000 --> 00:31:28,799
Yeah, it's law of diminishing marginal

973
00:31:26,119 --> 00:31:30,319
utility. Here, you were you were you

974
00:31:28,799 --> 00:31:31,879
were only You were happy to have one

975
00:31:30,319 --> 00:31:32,799
slice of pizza to get one cookie. Now

976
00:31:31,880 --> 00:31:33,760
you were willing to have two slices of

977
00:31:32,799 --> 00:31:35,799
pizza to get one cookie, even though you

978
00:31:33,759 --> 00:31:37,720
have less pizza and more cookies. That

979
00:31:35,799 --> 00:31:40,200
can't be right. As you have less pizza

980
00:31:37,720 --> 00:31:42,480
and more cookies, cookies pizza should

981
00:31:40,200 --> 00:31:43,960
become more valuable, not less valuable.

982
00:31:42,480 --> 00:31:45,480
And cookies should become less valuable,

983
00:31:43,960 --> 00:31:47,559
not more valuable.

984
00:31:45,480 --> 00:31:49,519
So, a concave to the origin indifference

985
00:31:47,559 --> 00:31:50,519
curve would violate the principle of

986
00:31:49,519 --> 00:31:51,279
diminishing marginal utility and

987
00:31:50,519 --> 00:31:53,079
diminishing marginal rate of

988
00:31:51,279 --> 00:31:55,359
substitution.

989
00:31:53,079 --> 00:31:56,480
Okay? Yeah. What if it's like trading

990
00:31:55,359 --> 00:31:58,719
cards?

991
00:31:56,480 --> 00:32:00,000
Okay. I mean, theory and

992
00:31:58,720 --> 00:32:01,000
I mean, I think you get more of trading

993
00:32:00,000 --> 00:32:03,240
cards,

994
00:32:01,000 --> 00:32:04,079
you you you have fewer cards than you

995
00:32:03,240 --> 00:32:05,200
want to

996
00:32:04,079 --> 00:32:06,639
trade that.

997
00:32:05,200 --> 00:32:08,000
That's very interesting. So, in some

998
00:32:06,640 --> 00:32:10,160
sense,

999
00:32:08,000 --> 00:32:11,720
what that is saying is that your utility

1000
00:32:10,160 --> 00:32:12,720
function is really over sets. You're

1001
00:32:11,720 --> 00:32:15,319
saying your utility function is over

1002
00:32:12,720 --> 00:32:17,480
trading cards. It's over sets.

1003
00:32:15,319 --> 00:32:19,720
So, basically, that's what sort of you

1004
00:32:17,480 --> 00:32:22,039
know, what's sort of a bit

1005
00:32:19,720 --> 00:32:23,400
you know, our models are flexible. One

1006
00:32:22,039 --> 00:32:26,279
way to say they're loose, another way to

1007
00:32:23,400 --> 00:32:27,920
say they're flexible. So, one But one of

1008
00:32:26,279 --> 00:32:30,119
the challenges you'll face on this

1009
00:32:27,920 --> 00:32:31,480
course is thinking about what is

1010
00:32:30,119 --> 00:32:32,879
decision set over which I'm writing my

1011
00:32:31,480 --> 00:32:34,880
utility function. You're saying it's

1012
00:32:32,880 --> 00:32:36,440
sets, not trading cards. So, that's why

1013
00:32:34,880 --> 00:32:38,240
it happens.

1014
00:32:36,440 --> 00:32:39,759
Okay? Other questions? Good question.

1015
00:32:38,240 --> 00:32:41,599
Yeah, in the back. What about like

1016
00:32:39,759 --> 00:32:43,759
addictive things where like the more you

1017
00:32:41,599 --> 00:32:45,399
have of it, the more you want to buy?

1018
00:32:43,759 --> 00:32:46,920
Yeah, that's that's a really really good

1019
00:32:45,400 --> 00:32:48,759
question. I spent a lot of my research

1020
00:32:46,920 --> 00:32:50,640
life, actually. I do a lot of I did a

1021
00:32:48,759 --> 00:32:52,559
lot of research for a number of years on

1022
00:32:50,640 --> 00:32:54,800
thinking about how you properly model

1023
00:32:52,559 --> 00:32:56,759
addictive decisions like smoking.

1024
00:32:54,799 --> 00:32:59,960
Addictive decisions like smoking,

1025
00:32:56,759 --> 00:33:02,359
essentially, it really is that your

1026
00:32:59,960 --> 00:33:03,920
utility function itself shifts as you

1027
00:33:02,359 --> 00:33:06,519
get more addictive.

1028
00:33:03,920 --> 00:33:07,960
It's not that your marginal utility, the

1029
00:33:06,519 --> 00:33:09,720
next cigarette is still worth less than

1030
00:33:07,960 --> 00:33:10,799
the first cigarette. It's just that as

1031
00:33:09,720 --> 00:33:12,079
you get more addicted, that first

1032
00:33:10,799 --> 00:33:13,359
cigarette gets worth more and more to

1033
00:33:12,079 --> 00:33:14,678
you.

1034
00:33:13,359 --> 00:33:16,559
So, when you wake up in the morning

1035
00:33:14,679 --> 00:33:17,880
feeling crappy, that first cigarette

1036
00:33:16,559 --> 00:33:19,559
still does more for you than the second

1037
00:33:17,880 --> 00:33:21,600
cigarette. It's just the next day you

1038
00:33:19,559 --> 00:33:23,119
wake up feeling crappier.

1039
00:33:21,599 --> 00:33:26,559
Okay? So, we model addiction as

1040
00:33:23,119 --> 00:33:28,079
something where essentially each day

1041
00:33:26,559 --> 00:33:29,799
cigarettes do less and less for you. You

1042
00:33:28,079 --> 00:33:31,960
get essentially adjusted to new You get

1043
00:33:29,799 --> 00:33:33,119
habituated to higher levels.

1044
00:33:31,960 --> 00:33:34,400
And this is why, you know, I do a lot of

1045
00:33:33,119 --> 00:33:36,559
work, you know, this is why,

1046
00:33:34,400 --> 00:33:37,960
unfortunately, we saw last year the

1047
00:33:36,559 --> 00:33:39,440
number of the highest number of deaths

1048
00:33:37,960 --> 00:33:42,160
from accidental overdose in US history,

1049
00:33:39,440 --> 00:33:43,279
72,000 people died from drug overdoses

1050
00:33:42,160 --> 00:33:44,840
last year, more than ever died in

1051
00:33:43,279 --> 00:33:45,920
traffic accidents in our nation's

1052
00:33:44,839 --> 00:33:47,799
history.

1053
00:33:45,920 --> 00:33:49,400
Okay? Why?

1054
00:33:47,799 --> 00:33:51,119
Because people get habituated to certain

1055
00:33:49,400 --> 00:33:52,360
levels. And they used to be used to

1056
00:33:51,119 --> 00:33:54,119
certain levels. So, people get hooked on

1057
00:33:52,359 --> 00:33:55,479
OxyContin.

1058
00:33:54,119 --> 00:33:57,039
They get habituated to a certain level.

1059
00:33:55,480 --> 00:33:58,400
They maybe switch to heroin. And they're

1060
00:33:57,039 --> 00:33:59,960
habituated to a certain level. And now

1061
00:33:58,400 --> 00:34:01,720
there's this thing called fentanyl,

1062
00:33:59,960 --> 00:34:03,360
which is synthetic opioid brought over

1063
00:34:01,720 --> 00:34:05,519
from China, which is incredibly

1064
00:34:03,359 --> 00:34:07,799
powerful. And dealers are mixing the

1065
00:34:05,519 --> 00:34:09,878
fentanyl in with the heroin.

1066
00:34:07,799 --> 00:34:11,159
And the people shoot up not realizing at

1067
00:34:09,878 --> 00:34:12,279
their habituated level, not realizing

1068
00:34:11,159 --> 00:34:14,159
they have this dangerous substance, and

1069
00:34:12,280 --> 00:34:15,000
they overdose and die.

1070
00:34:14,159 --> 00:34:16,280
And that's because they've got

1071
00:34:15,000 --> 00:34:17,159
habituated to higher levels. They didn't

1072
00:34:16,280 --> 00:34:18,320
realize they're getting a different

1073
00:34:17,159 --> 00:34:19,760
product. So, it's not about not

1074
00:34:18,320 --> 00:34:22,399
diminishing marginal utility. It's about

1075
00:34:19,760 --> 00:34:23,560
different underlying different products.

1076
00:34:22,398 --> 00:34:25,599
All right?

1077
00:34:23,559 --> 00:34:27,279
Other questions?

1078
00:34:25,599 --> 00:34:28,319
Sorry for that depressing note, but it's

1079
00:34:27,280 --> 00:34:29,240
important to be thinking about That's

1080
00:34:28,320 --> 00:34:30,600
why, once again, we're the dismal

1081
00:34:29,239 --> 00:34:33,519
science. We have to think about these

1082
00:34:30,599 --> 00:34:34,918
things. Okay. Now, let's come to a great

1083
00:34:33,519 --> 00:34:36,519
example

1084
00:34:34,918 --> 00:34:37,759
that I hope you've wondered about, and

1085
00:34:36,519 --> 00:34:39,679
maybe you've already figured out in your

1086
00:34:37,760 --> 00:34:41,200
life. But I hope you've at least stopped

1087
00:34:39,679 --> 00:34:44,679
and wondered about,

1088
00:34:41,199 --> 00:34:45,878
which is the prices of different sizes

1089
00:34:44,679 --> 00:34:48,480
of goods

1090
00:34:45,878 --> 00:34:49,519
in a convenience store, say.

1091
00:34:48,480 --> 00:34:51,519
Okay?

1092
00:34:49,519 --> 00:34:53,440
Take Starbucks.

1093
00:34:51,519 --> 00:34:55,358
You can get a tall iced coffee for

1094
00:34:53,440 --> 00:34:56,679
$2.25.

1095
00:34:55,358 --> 00:35:00,119
Or the next size, whatever the hell they

1096
00:34:56,679 --> 00:35:03,000
call it, bigger. Okay? You can get for

1097
00:35:00,119 --> 00:35:05,279
70 more cents. So, $2.25 and you can

1098
00:35:03,000 --> 00:35:09,119
double it for 70 more cents. Or take

1099
00:35:05,280 --> 00:35:11,519
McDonald's. A small drink is $1.22

1100
00:35:09,119 --> 00:35:14,079
at the local McDonald's. But for 50 more

1101
00:35:11,519 --> 00:35:16,320
cents, you can double the size.

1102
00:35:14,079 --> 00:35:18,400
Okay? What's going on here?

1103
00:35:16,320 --> 00:35:19,640
It Why do they give you twice as much

1104
00:35:18,400 --> 00:35:20,800
liquid?

1105
00:35:19,639 --> 00:35:22,519
Or if you go for ice cream, it's the

1106
00:35:20,800 --> 00:35:25,080
same thing. Why do they give you twice

1107
00:35:22,519 --> 00:35:26,320
as much for much less than twice as much

1108
00:35:25,079 --> 00:35:27,679
money?

1109
00:35:26,320 --> 00:35:30,519
What's going on? Yeah.

1110
00:35:27,679 --> 00:35:33,079
Um since your marginal utility is is

1111
00:35:30,519 --> 00:35:34,880
diminishing as you have more coffee

1112
00:35:33,079 --> 00:35:37,799
available to you, you're willing to pay

1113
00:35:34,880 --> 00:35:39,599
less for it. So, they make like the

1114
00:35:37,800 --> 00:35:41,280
additional coffee cheaper.

1115
00:35:39,599 --> 00:35:43,079
Exactly. That's a great way to explain

1116
00:35:41,280 --> 00:35:45,080
it. The point is it's all about

1117
00:35:43,079 --> 00:35:47,119
diminishing marginal utility.

1118
00:35:45,079 --> 00:35:48,960
Okay? When you come in to McDonald's on

1119
00:35:47,119 --> 00:35:50,358
a hot day, you are desperate for that

1120
00:35:48,960 --> 00:35:51,400
soda.

1121
00:35:50,358 --> 00:35:52,960
But you're not as desperate to have

1122
00:35:51,400 --> 00:35:54,200
twice as much soda. You'd like it.

1123
00:35:52,960 --> 00:35:56,159
You're probably willing to pay more for

1124
00:35:54,199 --> 00:35:58,358
it. But you don't like it nearly as much

1125
00:35:56,159 --> 00:36:00,239
as that first bit of soda.

1126
00:35:58,358 --> 00:36:02,759
So, those prices simply reflect the

1127
00:36:00,239 --> 00:36:04,759
market's reaction to understanding

1128
00:36:02,760 --> 00:36:06,120
diminishing marginal utility.

1129
00:36:04,760 --> 00:36:07,760
Now, we haven't talked about the supply

1130
00:36:06,119 --> 00:36:09,000
side of the market yet. I'm not getting

1131
00:36:07,760 --> 00:36:11,080
to how providers make decisions. That's

1132
00:36:09,000 --> 00:36:12,719
a much deeper issue. I'm just saying

1133
00:36:11,079 --> 00:36:14,000
that this is diminishing marginal

1134
00:36:12,719 --> 00:36:17,239
utility in action, how it works in the

1135
00:36:14,000 --> 00:36:21,280
market. And that's why you see this.

1136
00:36:17,239 --> 00:36:23,559
Okay? So, basically, um what you see is

1137
00:36:21,280 --> 00:36:25,440
that uh that first bite of ice cream,

1138
00:36:23,559 --> 00:36:27,000
for example, is worth more, and that's

1139
00:36:25,440 --> 00:36:30,440
why the ice cream is twice as big

1140
00:36:27,000 --> 00:36:34,000
doesn't cost uh twice as much.

1141
00:36:30,440 --> 00:36:36,079
Now, so basically, what this means is if

1142
00:36:34,000 --> 00:36:37,480
you think about our demand and supply

1143
00:36:36,079 --> 00:36:40,358
model,

1144
00:36:37,480 --> 00:36:43,679
on a hot day, or any day,

1145
00:36:40,358 --> 00:36:46,239
the demand for the first 16 oz

1146
00:36:43,679 --> 00:36:48,559
is higher than the demand for the second

1147
00:36:46,239 --> 00:36:50,719
16 oz.

1148
00:36:48,559 --> 00:36:52,840
But the cost of producing 16 oz is the

1149
00:36:50,719 --> 00:36:54,358
same. So, let's think about this. It's

1150
00:36:52,840 --> 00:36:56,358
always risky when I try to draw a graph

1151
00:36:54,358 --> 00:36:57,759
on the board, but let's bear with me.

1152
00:36:56,358 --> 00:36:59,759
Okay? So, let's say we have this sort of

1153
00:36:57,760 --> 00:37:01,960
simple supply and demand model.

1154
00:36:59,760 --> 00:37:04,240
You have this You have this supply

1155
00:37:01,960 --> 00:37:06,679
function for soda. And let's assume it's

1156
00:37:04,239 --> 00:37:08,319
roughly flat. Okay, let's assume sort of

1157
00:37:06,679 --> 00:37:10,358
the cost of firm producing each, you

1158
00:37:08,320 --> 00:37:13,039
know, within some range, the firm

1159
00:37:10,358 --> 00:37:14,759
basically every incremental 16 oz costs

1160
00:37:13,039 --> 00:37:17,159
them the same. So, that's sort of their

1161
00:37:14,760 --> 00:37:18,800
supply curve. Okay? And then you have

1162
00:37:17,159 --> 00:37:20,599
some demand curve.

1163
00:37:18,800 --> 00:37:23,240
Okay? You have some demand curve, which

1164
00:37:20,599 --> 00:37:25,319
is downward sloping. Okay? And they set

1165
00:37:23,239 --> 00:37:27,358
some price. And this is the demand for

1166
00:37:25,320 --> 00:37:29,039
16 oz.

1167
00:37:27,358 --> 00:37:31,519
Now, you have What's the demand for the

1168
00:37:29,039 --> 00:37:32,880
next 16 oz?

1169
00:37:31,519 --> 00:37:34,280
Okay?

1170
00:37:32,880 --> 00:37:35,400
Yeah, this isn't going to work.

1171
00:37:34,280 --> 00:37:36,680
We have to have an upward sloping supply

1172
00:37:35,400 --> 00:37:38,800
curve. Sorry about that. We have a

1173
00:37:36,679 --> 00:37:40,839
slightly upward sloping supply curve.

1174
00:37:38,800 --> 00:37:42,560
Okay? Now we have the demand for the

1175
00:37:40,840 --> 00:37:46,519
next So, So, here's your Here's your

1176
00:37:42,559 --> 00:37:46,519
price. Here's your $1.22.

1177
00:37:46,559 --> 00:37:52,440
Okay? Now you say, "Well, what's my

1178
00:37:49,358 --> 00:37:53,759
demand when I sell 32 oz?"

1179
00:37:52,440 --> 00:37:55,200
Well, it turns out demand doesn't shift

1180
00:37:53,760 --> 00:37:56,920
out twice as much. It just shifts out a

1181
00:37:55,199 --> 00:38:00,119
little bit more. So, you can only charge

1182
00:37:56,920 --> 00:38:01,480
$1.72 for the next 16 oz. Probably, if

1183
00:38:00,119 --> 00:38:03,358
you want to go to the big If you go to

1184
00:38:01,480 --> 00:38:05,559
the 7-Eleven where you can get sizes up

1185
00:38:03,358 --> 00:38:07,840
to, you know, as big as your house,

1186
00:38:05,559 --> 00:38:09,679
okay? They keep These curves keep

1187
00:38:07,840 --> 00:38:11,079
getting closer and closer to each other.

1188
00:38:09,679 --> 00:38:12,759
So, those price increments get smaller

1189
00:38:11,079 --> 00:38:14,719
and smaller. And that's why you get the

1190
00:38:12,760 --> 00:38:16,080
monster, you know, ginormous gulp at

1191
00:38:14,719 --> 00:38:18,599
7-Eleven

1192
00:38:16,079 --> 00:38:20,000
is really just not that not that

1193
00:38:18,599 --> 00:38:21,880
different from the price of getting the

1194
00:38:20,000 --> 00:38:23,480
small little mini size.

1195
00:38:21,880 --> 00:38:24,880
Okay? Because of diminishing marginal

1196
00:38:23,480 --> 00:38:27,079
utility.

1197
00:38:24,880 --> 00:38:29,840
All right? And so, that's how the market

1198
00:38:27,079 --> 00:38:32,480
That's essentially how we can take this

1199
00:38:29,840 --> 00:38:34,400
abstract concept, this sort of crazy

1200
00:38:32,480 --> 00:38:36,559
math, and turn it into literally what

1201
00:38:34,400 --> 00:38:38,760
you see in the store you walk into.

1202
00:38:36,559 --> 00:38:39,719
Okay? Questions about that?

1203
00:38:38,760 --> 00:38:41,600
Yeah.

1204
00:38:39,719 --> 00:38:44,000
Um so, how does

1205
00:38:41,599 --> 00:38:45,759
this play into buying in bulk versus

1206
00:38:44,000 --> 00:38:48,039
buying like a single item?

1207
00:38:45,760 --> 00:38:49,359
Like if, for example, like you wanted to

1208
00:38:48,039 --> 00:38:51,320
buy a snack, but you were going to have

1209
00:38:49,358 --> 00:38:52,960
the breakfast every day. Awesome.

1210
00:38:51,320 --> 00:38:54,359
Awesome question. And then every single

1211
00:38:52,960 --> 00:38:57,960
day it was going to be your first

1212
00:38:54,358 --> 00:39:00,159
granola bar, right? So, so it I I think

1213
00:38:57,960 --> 00:39:02,199
that its utility would be diminished

1214
00:39:00,159 --> 00:39:04,079
like every single time. But it's still

1215
00:39:02,199 --> 00:39:06,358
cheaper to buy in bulk than it would be

1216
00:39:04,079 --> 00:39:08,319
to buy a single granola bar every Great

1217
00:39:06,358 --> 00:39:10,199
great question. Yeah. I think that has

1218
00:39:08,320 --> 00:39:11,720
more to do with packaging costs than

1219
00:39:10,199 --> 00:39:13,159
with utility.

1220
00:39:11,719 --> 00:39:15,079
Well, I mean,

1221
00:39:13,159 --> 00:39:16,519
the risk of my going to this model is,

1222
00:39:15,079 --> 00:39:17,639
you know, once we once we get non-linear

1223
00:39:16,519 --> 00:39:18,599
in the world we do things in this class,

1224
00:39:17,639 --> 00:39:20,239
we have to start talking about supply

1225
00:39:18,599 --> 00:39:21,880
factors I want to talk to. But there's

1226
00:39:20,239 --> 00:39:24,639
two answers. One is packaging

1227
00:39:21,880 --> 00:39:27,119
efficiencies. But the other is if you

1228
00:39:24,639 --> 00:39:28,879
actually go to Costco

1229
00:39:27,119 --> 00:39:29,920
and look at their prices, for many

1230
00:39:28,880 --> 00:39:31,519
things they're not actually better than

1231
00:39:29,920 --> 00:39:33,440
the supermarket.

1232
00:39:31,519 --> 00:39:36,358
So, actually, the price of buying the

1233
00:39:33,440 --> 00:39:40,079
giant like 8,000 bars of granola

1234
00:39:36,358 --> 00:39:41,799
is actually not that much more

1235
00:39:40,079 --> 00:39:43,519
than not that much less than a thousand

1236
00:39:41,800 --> 00:39:44,519
time buying eight pack of eight granola

1237
00:39:43,519 --> 00:39:46,199
bars.

1238
00:39:44,519 --> 00:39:47,599
It turns out it's less.

1239
00:39:46,199 --> 00:39:49,679
But it's not nearly as much less as

1240
00:39:47,599 --> 00:39:51,920
these examples as sodas and McDonald's.

1241
00:39:49,679 --> 00:39:53,839
Which is exactly your point. Utility

1242
00:39:51,920 --> 00:39:55,920
diminishes less.

1243
00:39:53,840 --> 00:39:57,840
So, they don't want to charge as much

1244
00:39:55,920 --> 00:39:59,440
less for multiple packages.

1245
00:39:57,840 --> 00:40:01,120
So, you can actually if you compare

1246
00:39:59,440 --> 00:40:03,800
perish the gap in perishable product

1247
00:40:01,119 --> 00:40:05,239
pricing by size, it's much larger than

1248
00:40:03,800 --> 00:40:07,600
the gap in non-perishable pricing by

1249
00:40:05,239 --> 00:40:09,639
size. Great point. Yeah. Is there also

1250
00:40:07,599 --> 00:40:11,400
just like a different time frame for

1251
00:40:09,639 --> 00:40:13,279
which the utilities start diminishing

1252
00:40:11,400 --> 00:40:15,360
for every product? Cuz like you gave the

1253
00:40:13,280 --> 00:40:17,120
example of soda, but it's like would

1254
00:40:15,360 --> 00:40:19,120
that reset like later in the day if you

1255
00:40:17,119 --> 00:40:20,719
wanted like were thirsty then? Or

1256
00:40:19,119 --> 00:40:22,039
Awesome. And that is why they don't let

1257
00:40:20,719 --> 00:40:23,439
you walk back in with the same cup and

1258
00:40:22,039 --> 00:40:25,239
refill it.

1259
00:40:23,440 --> 00:40:27,119
Right? That's exactly right. And that

1260
00:40:25,239 --> 00:40:29,919
comes this point. It's sort of like it's

1261
00:40:27,119 --> 00:40:32,799
non-perishable as you get longer apart.

1262
00:40:29,920 --> 00:40:34,639
Uh so, um but you know, it's all this

1263
00:40:32,800 --> 00:40:37,519
really interesting thing. So, at Fenway,

1264
00:40:34,639 --> 00:40:39,359
okay? You can get You get like a regular

1265
00:40:37,519 --> 00:40:40,800
size soda. It's like crazy. It's like

1266
00:40:39,360 --> 00:40:42,920
six bucks.

1267
00:40:40,800 --> 00:40:44,760
Then for like eight bucks, you get a big

1268
00:40:42,920 --> 00:40:48,079
soda. Then for 10 bucks, you get a

1269
00:40:44,760 --> 00:40:49,040
refillable big soda. Okay? Now, the

1270
00:40:48,079 --> 00:40:50,400
question is can you bring that

1271
00:40:49,039 --> 00:40:51,559
refillable soda back to additional

1272
00:40:50,400 --> 00:40:54,800
games?

1273
00:40:51,559 --> 00:40:57,880
Technically not, but I do.

1274
00:40:54,800 --> 00:40:59,160
Uh and um and basically they sort of

1275
00:40:57,880 --> 00:41:00,119
understand. So, so there's an

1276
00:40:59,159 --> 00:41:02,199
interesting question of sort of the

1277
00:41:00,119 --> 00:41:04,079
perishability of things and how that's

1278
00:41:02,199 --> 00:41:05,480
and how that's going to affect uh things

1279
00:41:04,079 --> 00:41:07,239
going on. It's a really it's it's a

1280
00:41:05,480 --> 00:41:08,719
really it's an interesting question.

1281
00:41:07,239 --> 00:41:10,119
Other comments?

1282
00:41:08,719 --> 00:41:11,399
Okay, I'm going to stop there. Those are

1283
00:41:10,119 --> 00:41:13,359
great comments. Thanks everyone for

1284
00:41:11,400 --> 00:41:14,960
participating and we'll come back next

1285
00:41:13,360 --> 00:41:16,480
time and talk about the sad reality that

1286
00:41:14,960 --> 00:41:19,360
we haven't won the lottery and we have

1287
00:41:16,480 --> 00:41:19,360
limited amounts of money.