Consumer preferences, utility functions, and indifference curves explained

so today we are going to uh talk about where consumer decisions come from remember last lecture we built a supply

curve and demand curve and I just sort of made them up and I said now we're going to start to go back and build up

where they come from and today we'll start with the demand curve and start by talking about consumer preferences okay

so um the first thing we're going to do is we're going to understand how consumers make choices now essentially

as I mentioned last time consumers make constrained choices they essentially make themselves as well as off as

possible subject to a limited budget what we're going to start with today is forget the limited budget imagine we

just all won the Mega Millions okay there's no budget we're just going to ask what to Consumers want and not worry

about how they're going to pay for it okay so today we're going to talk about preferences we're talk about what

consumers want and how we translate those wants and desires into a mathematical formulation that allows us

to derive demand curves okay the so basically we're going to do this we're going to ultimately for Consumer demand

proceed in three steps the first step is we're going to write down our underlying assumptions about consumer preferences

we're going to talk about how consumers talk about a set of axioms that determine the rules of consumer

preferences across Goods we'll then translate those set of a into a mathematical function we call

the utility function which is a mathematical expression of consumer preferences and then next time we'll

introduce the budget constraint and talk about how consumers make choices given this mathematical utility function and

given the budget constraint they face okay so that's the road map of where we're going okay so today we're going to

talk about pref es axiomatic rules of preferences and how they translate into the mathematical rules that govern

individual decisions so do this let's start by talking about

preferences and let's talk about the key assumptions we are going to make in modeling consumer

preferences so remember all models make simplifying assumptions we're going to make um inexact models make simplifying

assumptions we're going to make three assumptions here the first assumption we're going to make so what are the key

assumptions the first assumption we're going to make is completeness that is we are going to

assume that when consumers are faced with two choices they're either going to prefer one or prefer the other or be

indiff but they're going to have an opinion they're not going to say I don't know

okay consumers will have opinions over all possible choices they'll like one by another they'll be indifferent but

they'll have opinions over all possible choices it's a complete set of preferences the second thing is the same

ass subject we've been making since kindergarten in all our math classes which is

transitivity okay which is the classic if you prefer a to B and B to C you must prefer a to c I'm pretty sure all MIT

students know transitivity by now okay um so that is uh the second key assumption which is once again not a

great not a big deal the third assumption is where economics gets its power the third assumption is a new one

which we call the Assumption of nons satiation or new to you the Assumption of

non-satiation or basically more is always better okay the third assumption so

these assumptions are standard assumptions make in math class complete Choice sets transitivity nons satiation

is new to you that's the assumption that basically more is always better now it doesn't mean more makes you equally

happy it doesn't mean the 10th thing makes you as happy is the ninth thing it just means the 10th thing is always

better than not having it more is always better okay so basically if you're offered something for free you'll always

take it okay it's always better than not having it that's because we live in a world of goods you might be thinking to

yourself well if someone offered me for free you know to stick me in the eye with a needle I wouldn't take that and

you're right cuz that's a bad for most people I guess but uh we're going to operate in the world of goods

so as long as things are Goods we always want more now with those in mind we can

develop what we call indifference curves which are essentially preference Maps we're going

to map people's preferences into a set of what we call indifference curves so to do this let's start with a simple

example okay imagine at the beginning of semester and your parents are going to give you some money to buy

the two things you care about slice of pizza and cookies that's all you care about in this world once again as

someone asked last time work was simplifying two-dimensional assumptions in reality of course you care about

buying 20 different things but the underlying logic won't change the math will just get harder and the graphs will

become multi-dimensional hard to see so we're going to start with two goods but everything we do here works with three

four five six Etc Goods okay just harder math and Graphics so so let's say have two goods and let's say you're going to

face three choices choice a is you can have two slices of pizza and one cookie Choice B is you can have two cookies you

can have I'm sorry one slice of pizza and two cookies or Choice C is you can have two slices of pizza and two cookies

those are your three choices you're facing okay and let's assume given my preferences that I'm

indifferent between A and B let's assume that given my preference I'm indifferent between those two now

where does that come from well we are going to take preferences as Primitives we're not going to question where

preferences come from people going to have their preferences it's genetics or nature nurture whatever that's something

we deep delve more deeply into when we think about deeper economics but for now for this class preference is given so I

have a set of preferences such that I'm indifferent between those two choices but I prefer opt C to both okay I'm a

different between A and B but I prefer C okay so we can now graph my preferences Andrew can I get a copy the

handout uh so we can now graph my preferences and the graph of my preferences is shown in figure

21 okay everyone should have a handout remember they'll always be in the back when you come in please make sure you

grab them as you come in figure 2 one is a map of my preferences okay on the x axis okay is I believe let me just I'm

going to look at yours for a second you can look at your neighbors on the x- axis is cookies on the y axis is slices

of pizza okay so indiff maps are essentially maps of how you choose between two goods you're choosing from

okay so basically this is your indifference map thank you um this is your indifference map and what you see

is we have mapped the three points a b and c a is one uh two slice of pizza in one

cookie B is two cookies and one slice of pizza C is two of both and we have drawn a curve between A and B we label this an

indifference curve it's an indifference curve because I said you're indifferent between A and B so there's a one

indifference curve goes through both A and B because you're indifferent between those choices remember completeness says

you can't not care complet completeness says you have to choose but it's okay to be indiff okay but Point C is on a

higher indifference curve because you prefer Point C to both okay so there's going to be four

properties of indifference curves these indifference curs which you're going to work with extensively throughout the

semester are going to have four properties properties of indifference curves first property okay is consumers

prefer higher indifference curves so the further out the indifference curve is the more preferred it is okay

and that just follows from non-satiation more is better so quantities that are further out away from the away from the

uh uh away from the origin are better okay the second property is indifference curves are downward

sloping we're not say anything about the sheet yet just the slope that indifference curves are downward

sloping and once again this follows from non-satiation why because if indifference curves were upward sloping

it wouldn't sat you wouldn't satisfy non-satiation look at figure 2 two with an upward sloping indifference curve an

upward this is just one particular kind of upward sloping IND difference curve but true for all of them if the differ

curve is upward sloping that mean you'll be a different between one cookie and one slice of pizza and two cookies and

two slices a pizza that would violate non-satiation you can't be indifferent between less and more you have to always

like more better so difference cures have to be downward sloping through non-satiation

Okay the third is indifference curves never cross indifference curves never

cross and the reason because the difference curves can't cross is because that would violate transitivity and more

is better so let's look at figure 2 three with Crossing indifference curves

okay in this graph figure 2 three A and B are on the same indifference curve and A and C are on the same indifference

curve that means you must be a different between a and b and different between a and C well if you're different between A

and B and A and C by transitivity you must be IND different between B and C but that can't be true you can't be

different B and C because B is more than C okay B is is a dominant you get the same amount of cookies and more pizza so

you by definition have to like B better than C so you can't be you violates jointly transitivity and

non-satiation okay so that's the third property and the fourth property is basically completeness which is which we

express as only one indifference curve through any given point you can't have two indifference curves that cross

through one Point okay so one I see through any given point per Point per precise allocation

going be one because otherwise you wouldn't know how to feel okay there has to be one IND difference curve through

precise Point okay so let's with these rules in mind

let's talk about how you can use IND difference curves here's how I learned about difference curves when I was

student in 1401 here's how I learned difference curves actually a semester later I still didn't quite understand

how I left 1401 cuz I was as smart as you all okay but I had a year op and my year op was with a graduate student and

this graduate student was trying to decide on where to go for their job and they said to me look we can express it

in difference curve this is one of a few graphs I'll draw for you this semester he said look there's two things I care

about I care about school quality like how highly ranked is where I'm going to go are my colleagues the smartest Etc

and I care about location which is how's the weather really this is weather okay and he had two choices his choices

were Princeton great quality mediocre weather or Santa Cruz not as good quality great weather to Santa Cruz I

don't know how anybody studies there you can like walk out steps out and surf okay and he basically said look at this

point I'm indifferent I'm indifferent between better job at Princeton but you know

mediocre weather and a worst job at Santa Cruz no offense to Santa Cruz Princeton's an amazing place Santa Cruz

is still a great place but it's not Princeton okay a worst job at Santa Cruz uh and awesome weather and being able to

Surf every day so he said I'm indifferent he said in the end what did he decide to do in

the end he decided to go to a place called The IMF which is not the thing from the Tom

Cruz movies but actually uh the international monetary fund because that was in DC which had better

weather and was so it wasn't as good a job as Princeton this is Princeton this is Santa Cruz

but it was better weather it wasn't as good weather as Santa Cruz but it was a better job and he decided that

combination made him happier is he right no he's not right there's no sense of right preferences or your

preferences okay you might all feel very differently about this set of choices does anybody's preferences are correct

or wrong okay this is just how we thought about this job choice and how we used an indifference map to explain

it okay questions about that question about how these indifference curves work yeah

speak loudly so everyone can hear thanks that's a great question so basically once again the the question is

how do you put quality into this framework well essentially what you would do is you would say then I have

two Dimensions be quality and quantity of one good you'd have to add either a third dimension or you say it's a

different choice so it we'll do a lot in this course you could think of sequential choices so let's say for

example you want to decide between uh cook and pizza you decide and now within cookies you want to decide you decide I

want to allocate $6 to cookies now I say my choice is one unbelievable $6 cookie or six terrible $1 cookies that's a new

indifference curve you've already decided first how many you're going to spend on cookies then you decide so

that's we can always break any monster decision to a set of sequential two-dimensional decisions so that's how

you do it okay good question other questions yeah yeah yeah I I always get that question

it's technically different but effectively the same okay good if I don't see your hand

by the way shout out it's a big classroom okay so now we're going to move on move on from preferences and go

on to talking about utility okay point two topic two utility okay so basically underlying where preferences

come from is a mathematical function we call the utility function it's basically how we mathematically represent these

graphical indifference curves okay so it set so for example a common form of utility function will use

a lot this semester okay is is the log utility function which is the which we express the form

utility is the square root in this case of pizza slices times the number of cookies that is a mathematical

representation of preferences it says my utility is a square root of the number of slices of pizza times the number of

cookies s stands for pizza because it's slices because we use P Elsewhere for prices I don't be confusing okay so that

says note this is consistent with what I wrote up there about indifference curse two slice of pizza and one cookie

gives me square root of two utility one slice of pizza and two cookies gives me square root of two utility so I'm

indifferent two slice pizza in two cookies gives me two utility so I'm happier so this is consistent with the

indifference curves yeah that's a different IND that you could write down like I said I'm not

judging anybody's preferences but that would be a different mathematical function this is one of an infinite set

of mathematical functions right down this is not a true representation this is an example you can write any utility

function you guys want to think of we can write it down and we'll write down many of them this semester but I need to

work with this one first till we understand the rules yeah what well no but it shows your

indiffer between s and C but it would show that you it would show that you are you prefer uh more of both but it's true

it shows you're indifferent between s time C that's absolutely right between

what same as what oh oh that's a great Point uh that's an excellent point the reason

we're going to need square root is because it's going to it's it's a form of preferences that's it's a a a rule on

preference going to help us do a lot of things well in this semester I'll explain that in one minute it's a good

question now I understand thank you yes in fact that question leads to a natural next question which is what the hell is

utility what does it mean and the answer is utility means nothing cardinally it only is meanings ordinally that's what I

mean is a utility of three is a meaningless concept utility only matters in an ordinal sense in the sense of

ranking choices so utility functions will simply be mappings that we use to rank choices not mappings that we used

say this choice is 50% better than that choice it's only for ranking so the number itself doesn't matter and by that

same question well the ranking of s time C was the same as ranking of square s time C so why do we write it that way

okay and the reason we write it that way is because the utility functions of this general form of this power form of less

than one um will deliver an important rear World consequence and we see that through the notion of marginal

utility okay so once again this is just one form of preferences the question is absolutely right this mapping would work

just fine as s time C or S2 time c s or s to the millionth time C to the millionth because the because the

numbers don't matter it's the ranking that matters all those little the same ranking but those functions deliver

something very different which would violate the way we think about the real world which is that basically the

fundamental driver of all consumer decision will make this semester remember I said everything I'm going to

tell you a hundred times things are really important this is really important okay the fundamental driver is

the key assumption that we make of diminishing margin utility that is we assume more is

better but the next unit is not quite as good as the one before we assume marginal utility diminishes we assume

each additional unit makes you less happy than the one before which wouldn't be true if we didn't have the square

root function there okay why do we assume that because it makes sense okay it makes sense that basically 10th slice

of pizza makes you less happy in the ninth slice of pizza it makes sense that the fifth cookie makes you less happy in

the fourth cookie it makes sense that your fifth favorite movie makes you less happy than your fourth favorite movie

now it could be tiny increments between them but it makes sense that when you rank things the next one is worth less

okay so for example let's go to figure 24 and let's hold the number of pizza slices by the way Andrew we should

change that instead of holding pizza say hold pizza slices okay let's change the number of pizza slices constant at two

let's assume you you for sure decide you want two slices of pizza now you're going to ask yourself how does my

utility vary as I uh have additional cookies the answer is if I have one cookie

my utility is 1.4 of two if I have two cookies my utility is two if I have three cookies it's 2.45 and so on okay

basically what you see is that the incremental utility from each additional cookie is falling that's shown in figure

2-5 figure 2-5 illustrates diminishing margin utility each additional cookie makes you less happy holding constant

the number of pizzas okay so

basically this is an enormously sensible uh assumption it's an assumption as I said no one can tell you

what your preferences should be but it turns out we think most in we think most people's preferences satisfy the

principle of diminishing margin utility and that is going to drive a lot of the mathematics we're going to do this

semester it's not we will we will give you examples where it's not true we'll give you examples of increasing margin

utility and constant margin utility and have you discuss them but we're going to generally soon diminishing

question that's a great question that would be that's um essentially in this with these

preferences it would say that essentially your preferen are such that if you can't have a cookie you don't

care how much pizza get that doesn't violate non-satiation because basically that is uh non-satiation says more of

everything is better it doesn't say more of one thing is better more of any one thing is better non says more of

everything is better it can't be true that you get more of everything you're better off it can be true getting more

one thing doesn't make you better off so think about left shoes and right shoes okay it doesn't matter how many once you

have if you only have one left shoe it doesn't matter how many right shoes you have so it doesn't violate more as

better it's just but you'll be better off with two left shoes and two right shoes than one left shoe and one right

shoe yeah good question good I love these questions thank you so much okay so

basically with that in mind let's talk about how do we can now go back and ask well what drives the shape and slope of

indifference curves okay so what is the slope of the indifference curve the slope of the

indifference curve is the rate at which we're willing to trade off just definitionally mathematically the rate

which we're willing to trade off slices of pizza for cookies okay the rate which you're

willing to trade off trade off basically one good for another okay so we'll call that Delta s

Delta C is the slope at any point that's the slope of the indifference curve the rate at which you're willing to trade

the good on the Y AIS for the good on the x-axis we're going to just Define it this way for convenience obviously you

can invert it doesn't change anything but for convenience we'll always think of it this way the rate at which you're

willing to trade the good on the y- axis for the good on the x- axis okay and we're going to call

this the marginal rate of substitution the mrss a key concept for this class the mrss the marginal rate of

substitution okay that is the rate at which you're willing to trade off the good on the y- axis for the good on the

x-axis okay now you're not really trading we're not in some ancient barter system where you're trading pizza for

cookies but effectively you are because of opportunity cost given a budget we haven't given you a budget yet but next

time we will given a budget any money you spend on Pizza you can't spend on cookies and vice versa so effectively

it's a trade by buying a slice of pizza you're essentially trading away cookies not the only trading away but you're

trading away the money you could use to buy cookies okay so in the world with only two goods whenever you buy one

you're trading away the other now doesn't operate directly operates through the budget constraint but that's

the way to think about it so you're substituting pizza for cookies now how does this

relate to the utility function well here's what's kind of cool okay think about an incremental Move Along an

indifference curve an incremental Move Along indifference curve is essentially you're

giving up a little slice a little slice of piece to get a little more cookie on the margin so that's saying you are you

give up Delta s times the Marg utility of slice so you give up a little bit of slice of pizza

which you liked mu that's your margin utility for pizza and you're getting a little more

cookie which you value at your margin utility for cookies okay that's the equation of that's a Delta along that

curve okay you give up a little pizza which cost you margin utility of pizza you get some cookies which which gains

you marginality of cookies okay rewriting this we get get that Delta s Delta C which I said is the

mrss is equal to minus mu C over muu the mrss is the ratio of margin utilities that is the slope of

the indifference curve is the ratio of the margin utilities and that's how we tie the math and the graph

together that's how the math the graph together that basically the slope of the indifference curve is the mrss is the

negative opposite of the ratio of margin utilities now this is very tricky here's the one thing you need to keep in mind

which is to remember that Marg the reason there's a negative sign is that margin utilities are negative functions

of quantity the more you get the lower your margin utility is utility is a positive

function of quantity but because of diminishing margin utility margin utility is a negative function of

quantity got to keep embed that in your brain okay moris better says utility is a positive function of quantity except

of course in this important case was pointed out there positive function of both things going up but margin utility

is a negative function of quantity okay you're less Happy by the next incremental unit than you were by the

ones before okay so basically as you get fewer slices and more cookies what is happening well the Marg ility of slices

is rising you're giving up pizza slices so your Marg utility is going up the

marginality of cookies is falling okay so what you get is basically a decline in the value of the

mrss the margil of pizzas is slightly Rising okay margil cookies is slightly falling this ratio Falls so the mrss

Falls so you get this downward sloping indifference curve okay so this is sort of hard so let's see this

mathematically and graphically let's start with the math okay let's start with the

math okay we said utility is the square root of s * C okay so what is the margin utility of cookies well we're just going

to differentiate this with respect to C differentiate this function with respect to C what do you get so Delta U Delta C

you get 0.5 time the number of slices of pizza over the square root of s *

C okay what is the margin utility of pizza slice of pizza you get du

DS equals 0.5 * C over Square < TK of s * C and once again I apologize for the handwriting please ask if it's not clear

okay so I'm just differing this function to get the two Marge utilities okay if I take based on these

two Marge utilities the mrss which is the the negative of the ratio the mrss equals minus s over C for this

particular example don't these aren't general rules I'm deriving here for this example the mrss is minus s over

C so basically what the Mrs is showing you is that the mrss for slice of cookies for

slice of pizza opposed to cookies is rising as you get more slices and foll as you get more cookies so let's see

this in figure 26 okay figure 26 shows the indifference curve again but now with the mrss is

plotted remember the indifference curve is not linear in this case so mrss changes along the indifference curve so

I'm giving you local approximations to the mrss at different points to the indiference curve but it's

very important to remember this is key because the DI Mission utility you are going to get

yeah right yeah yeah figure 2.5 is just giving you local approximations those

points are solved by differentiation but those are local approximations okay yep so basically um

that's the thing our graphs are never going to be as precise as our math because we of because we essentially

want to use linear mathematics for nonlinear for nonlinear graphs and so we're going to end up with a lot of

local local approximations okay so basically in other words at Point

a okay um at Point a um you have four slices of pizza in one cookies at point B you have two of each and at Point C

you have four cookies and one slice of pizza and according to this utility function you're indifferent right all

those give two as the utility all those combinations give utility of two you're indifferent okay now but at Point a even

though you're different between all three points they have very different mrs's at Point a the mrss is minus four

you would be willing to give up four slices of pizza to get one cookie at Point C the mrss is minus

one4 you'd be willing to give up only one slice of pizza to get four cooked why what's changed between points A and

C why is the Mrs changed so radically between points A and C

yeah what sorry you have you have fewer slices of pizza exactly so basically what's

happening is as your slice of pizza Falls and then by definition your cookies goes up your margin utility of

pizza Rises and your Mar utility cookies fall when you're point a you really want pizza you're happy to give cookies to

get pizza because you get I'm sorry you really want want cookies I'm sorry my bad at Point a you really want cookies

you got four slices of pizza you're full already you want a cookie okay when you're at Point C it's like what do you

do with four cookies you're not going to have enough protein in your dinner your mom will be upset okay so you basically

want to trade some of those cookies back for some pizza okay and then at point B you see the mrss is minus one because

given this utility function at that point you're essentially indifferent you're indifferent between

pizza and cookies at point B Okay so so that that is why we graph we graph the um we graph the

indifference curves uh in this way as concave uh as concave indifference curves concave to the origin because

basically we want um we want to satisfy this principle diminishing marginal rate of substitution for those you who really

want to be technical the real technical definition is diminishing margin substitution you

don't always have to have diminishing utility we generally you could write down functions which don't have dimin

utility but do have diminishing Margate of substitution if you are so inclined the technical definition is is that what

drives what what drives utility theory is diminishing margin R of substitution but almost always we'll have diminishing

margin utility as well that's all I'll say about it you can forget it if you want but if it's bugging you that's why

okay now consider what would be like I'm sorry so it's it's convex to the origin

my bad I'm sorry convex to the origin in difference curves convex in difference curves consider what would be like with

a concave to the origin and difference curve as in figure 27 consider what life would be like we

often do proes by the negative okay this is for the utility function figure 27 is for is drawn for the utility function

X2 plus y^2 = 65 that's utility function that's graph there well uh I should say S2 Plus I

shouldn't say X and Y I should say S2 S2 Plus C s equal 65 okay now once again you can't tell me

that utility function is wrong people have different preferences but it doesn't satisfy what we could think is a

common sense principle which is that would say that when you have eight slices of pizza in one

cookie you you'd be willing to give up um when you have eight slices of pizza uh and one cookie you would give up only

an eighth of a slice of pizza to get a cookie so you really wouldn't give up much pizza to get a cookie and yet when

you're down all the way of having seven cookies and four slices of pizza then you give up almost two slices of pizza

to have a cookie it doesn't make sense why would you give up more pizza when you have less Pizza when you already

have eight slices of pizza why are you less L of a a pizza for a cookie than when you have more slices of pizza uh

when you have fewer slices of pizza and more cookies it doesn't make sense that's why we gener now it doesn't make

sense let's be clear I'm not saying it's inconsistent with reality okay like I said we don't have strict laws like

equal MC s in this class there's someone out there who has these preferences I guarantee it what I'm saying is most

people do not and so we're going to try to in this class like I said make a series of simplifying assumptions that

explain most of reality even they explain 100% of reality okay and diminishing mrss is one of those

assumptions okay and that's why um diminishing mrss makes sense uh because it delivers the fact

that the more you have of one good the less you care about having the next unit of it okay let me stop there questions

about that this is really really important for all of consumer Theory it's actually going to be important for

production Theory too this General notion of diminishing production the we call it diminishing marginal product but

it's going to be the same sort of thing so questions about how this where this all comes

from okay you know throughout this class you want to ask yourself does this pass the mom

test that is could you go home and explain this to your non-economist mom and you should understand this well

enough that you can I don't know if she'd be interested but it doesn't matter she's your mom she has to listen

to you so basically make sure you understand it that well okay now let's go to an example yeah I'm sorry go

ahead uh the only point of a concave disc would to represent the set of preferences I wrot there I mean there's

no there's no point or not point it's just simply saying that there exists someone in the world who has that

utility function this is their preferences but you won't generally ever see one does that make

sense all right okay so let's go to an example there's actually a wonderful example of

diminishing margin utility and how it operates in the real world which is um different

sizes of consumer goods of consumer uh consumption Goods so for example at Starbucks according to Alex's detailed

research you can get a tall ice coffee for $455 or you can get twice as much coffee

whatever the hell they call the big one for 90 more cents so $455 for the smallest 90 cents more to double your

amount of coffee or McDonald's a small Coke is 229 a large Coke which is more than

twice as big is 299 so essentially you are paying much less to increase the quantity why is

that yeah loudly so we can here go ahead exactly so you think about yourself walking to McDonald's on a on a

hot day okay or Starbucks on a cold day and you really need to be saded you're you're you're either very very cold or

very hot you need to be SED but a small will get you most of the way there now a large is better buy more is better but

it's not as much better you just needed to be Sav you need to make sure you got your your liquids in so you're not

willing to pay as much for the incremental quantity you're not willing to pay as much and the key thing is that

basically um uh that companies recognize this and this is where we start to dip into producer

Theory companies are making their business decision based on what they know about consumer

preferences this is why someone asked you know why we ever have a concave indifference curve this is why companies

don't believe they're concave uh uh concave indifference curves because they price this way they know that most

people care less about the additional 16 ounces they do about the first 16 ounces now if if maybe you all thought that was

common sense or maybe you never thought about why that is but this is once again an illustration of how a common

phenomenon in society that exists everywhere can be explained by what's an incredibly

simple model remember we came into this class knowing nothing about utility and all that stuff we' already got an

explained an incredibly important phenomenon in the world and there's many other choices and things that you'll see

that that can be explained by this model OKAY questions about that

yeah great question someone to answer that how does it benefit Starbucks and McDonald's yeah

Yeah so basically if they McDonald's if if they price essentially the calculation we ar going to producer

Theory yet but I'll give you a heads up the calculation McDonald's and Starbucks are doing are I want to you're right the

next let's say the next let's say the first I mean the cost the inputs of stuff is so cheap I mean you'd be

disgusted how McDonald's for their sodas it's like probably about three three to four cents for them to make a soda in

terms of the marginal cost of a soda Okay so let's say it's 3 cents for a small and 4 cents for a large okay so

basically they're if if they couldn't get if preferences were such and you can write preference this way where I never

want anything more than a small like literally our stomachs can't hold more than a small then they nobody pay a

penny more for a large and they wouldn't make it but nobody's that way every most people pay a penny more for a large so

then your question is how much more can I charge before people don't want the larges anymore and that's essentially

the calculation they're doing is there they comput and they've got people hundreds of people doing this all the

time saying look if we charge 69 cents people buy the large if we buy if we charge 70 cents people buy a couple

fewer larges but we make one cent more but once it go about 71 no longer makes sense and that's essentially the

business decision making we'll talk about in a few lectures which is how to businesses decide how to set their

prices here we're just showing this set their prices and response to a principle we now know is generally true which

diminishing marginal rate of substitution other questions good question other

questions all right well let's stop there um we will it's a little early but that's all I got for today so we will uh

come back on Wednesday and we'll talk about what happens when you actually have a limit on how much you can spend