today we're going to start talking about what's under the demand curve so basically what we did last time and what you did in section Friday is talk about sort of the workhorse model of economics which is applying demand model and we always start the class with that because that's the D model in the course but I think is any good sort of scientists and inquisitive minds you're probably immediately asking well where do these supplying demand curves come from they're not just come out of thin air how how do we think about them where do they come from and that's what we'll spend the base of the first half of the course going through and so we're gonna start today with the demand curve and the demand curve is gonna come from how consumers make choices okay and that will help us derive the demand curve then we'll turn next to supply curve which would come from how firms make production decisions but let's start with the demand curve and we're gonna start by talking to you about people's preferences and then their utility functions okay so our model of consumer decision-making is going to be a model of utility maximization that's going to be our fundamental remember of course all about constrained maximization our model today's can model if utility maximization and this model is going to have two components there's going to be consumer preferences which is what people want and there's gonna be a budget constraint which is what they can afford and we're gonna put these two things together we're going to maximize people's happiness or their choice or their their happiness given their preferences subject to the budget constraint they face and that could be the constrained maximization exercise that actually through the magic of economics is going to yield the demand curve and its yield a very sensible domain curve that you'll understand intuitively now so we're gonna do is do this in three steps step one over the next two lectures step one is we'll talk about preferences how do we model people's tastes we'll do that today step two we'll talk about how we translate this to utility function how we mathematically represent people's preferences in the utility function we'll do that today as well and then next time we'll talk about the budget constraints that people face so today we're going to talk about the maxim and next time we'll talk about the budget constraint that means today's lecture is quite fun today's lectures about unconstrained choice we're not going to worry all about what you can afford what anything costs well worry about what things cost and a quarter of what you can afford okay today's the lecture where you won the lottery okay you won the lottery money is no object how do you think about what you want okay next time we'll say well you didn't win the lottery in fact is we run later in the semester no when's the lottery that's an incredibly bad deal but basic time will impose the budget constraints but for today we're just going to ignore that and talk about what do you want okay and to start this we're gonna start with the series of preference assumptions a series remember as I talked about last time models rely on simplifying assumptions otherwise we could never write down a model it'll go on forever okay and the key question is are those simplifying assumptions sensible do they do violence to reality in a way which makes you not believe the model or are they roughly consistent with reality in a way that allows you to go on with the model okay and we're gonna post three preference assumptions which I hope will not violate your sense of reasonableness the first is completeness what I mean by that is you have preferences over any set of goods you might choose from you might be indifferent you might say like a as much as B but you can't say I don't care or I don't know exact err that's a difference you can't say I don't know you can't literally say I don't know how I feel about this um you might say you're indifferent to things but you won't say I don't know how I feel about something that's completely okay the second is the assumption we've all become familiar with since kindergarten math which is transitivity if you prefer a to B and B to C you prefer A to C okay that's that's kind of I'm sure that's pretty clear you've done this a lot in other classes so these two are sort of standard assumption you might make any math class the third assumption is the one where the economics comes in which is the assumption of non-satiation or the assumption of more is better in this class we will assume more is always better than less okay we'll assume more is better than less now to be clear we're not going to say that the next unit makes you equally happy as the last unit in fact I'll talk about that in a few minutes well in fact assume it makes you less happy but we will say you always want more that face with a chance of more or less you'll always be happier with more okay and that's the non-satiation assumption okay and I'll talk about that some during a lecture but that's sort of what's going to give our models their power that's a sort of New Economics assumption that's going to give beyond our typical math assumptions this can you give our models their power okay so that's our assumptions so armed with those I want to start with the graphical representation of preferences when graphically represent people's preferences and I'll do so through something we call indifference curves indifference curves okay these are based indifference curves are basically preference maps especially difference curves are graphical Maps a preferences okay so for example suppose your parents gave you some money to begin a semester and you spend that money on two things your parents are rich to give you tons of money spend that money on two things buying pizza or C or um or eating cookies okay so consider your considered preferences between pizza and cookies that's your two things you can do once again there's constrain model obviously in life we can do a million things with your money but it turns out if we consider the contrast we can do a tutor for things with your money you get a rich set of intuition that you can apply to a month much more multi-dimensional decision case so let's start with a two dimensional decision case you've got your money either gonna have pizza or gonna have cookies okay now consider three choices okay choice a is two pizzas and one cookie choice B is one Pizza one pizza and two cookies and choice C is two pizzas two cookies okay that's the three packages I want to compare and I'm going to assume and I'll mathematically rationalize in a few minutes but for now I'm going to assume you are indifferent between these two packages I'm going to assume you're equally happy with two slices of pizza and one cookie or two cookies and one slice of pizza okay I'm gonna assume that but I'm also gonna assume you prefer option C to both of these in fact I'm not I'm gonna assume that because that is what more is better gives you okay so your different view nice this indifference doesn't come from any property road I'll buy that's an assumption that's just a just for this case I'm assuming that this comes to the third prop I rode up there you prefer package chic as more is always better than less okay so now let's graph your preferences and we do so in Figure two one OK in the handout okay so here's your indifference curve so we've graphed on the x-axis your number of number of cookies on the y-axis slices of pizza okay now you have we've graphed the three choices I laid here choice a which is two slices of pizza and one cookie choice B which is two cookies in one slice of pizza and choice C which is two of both and I've drawn on this graph here indifference curves the way indifference curves looks is there's one indifference curve between a and B because those are the points among which you're indifferent so when a difference curve represents is all combinations of consumption among which you are indifferent so why we call it a difference curve so a difference curve which will be sort of with the big warhorses of this course a difference curve represents all combinations along which you are indifferent you are indifferent between a and B therefore they lie on the same curve okay so that's sort of our preference map our indifference curves and these indifference curves are gonna have four properties four properties that you have two that follow naturally from this that's really three and a half the third and fourth are really pretty much the same but I like to write the minus four for properties that follow from the from these underlying assumptions property one is consumers prefer higher indifference curves consumers prefer higher indifference curves okay and that just fall for more is better that is an indifference curve that's higher goes to their package that has at least as much of one thing and more of the other thing therefore you prefer it okay so as a difference curve shift out people are happier okay so in that higher indifference curve Point C you are happier than points a and B because more is better okay the second is that indifference curves never cross indifference curves never cross okay actually that's I'm gonna that's third actually I want to come to that in order second third is the difference occurs whoever's second is indifference curves are downward sloping seconds and difference curves are downward sloping okay indifference curves are downward sloping let's talk about that first okay that simply comes from the principle of non-satiation so look at figure two - here's an upward sloping indifference curve okay why does that violate the principle non-satiation why does that violate that yeah they're yours less how do you have work like or yeah exactly so basically you're indifferent on this curve you're indifferent me one of each and two of each you can't be indifferent two of each has got to be better than one of each so an upward sloping and DIF curve would violate non-satiation so that's the second property of indifference curve the third property may discover the difference curves never cross okay we could see that in Figure two three okay someone else tell me why this violates the properties I wrote up their indifference curves crossing yeah what's that cuz the B and C P is strictly better that's right but but they're they're also but they're also both on the same curve is a so you're saying they're both you're indifferent with a for both B and C but you can't be because B is strictly better than C so violates transitivity okay so the problem with crossing indifference curves they violate transitivity and then finally the fourth is sort of a cute extra assumption but I think it's important to clarify which is that there is only one indifference curve through every possible consumption bundle only one I see through every bundle okay you can't have two indifference curves going through the same bundle okay and that's because of completeness if you have two and difference Coast wants the same bundle you wouldn't know how you felt okay so they can only be one going through every bundle cuz you know how you feel you may feel indifferent but you know how you feel you can't say I don't know okay so that's sort of a extra assumption sort of completes the link to the properties okay so that's basically how indifference curves work now I find when I took this course before you were God maybe before your parents were born I don't know certainly before you guys were born okay when I took this course I found this course full of a lot of light bulb moments that is stuff will just sort of these and then boom an example really make it work for me and the example that made indifference curves work to me was actually during my first UROP when my Europe was with a grad student and that grad student had to decide where he was can accept the job he'd a series of job obviously I decide and basically said here's the way I'm thinking about it I'm indifferent I haven't I have indifference map but I care about two things I care about school location and I care about Economics Department quality okay I care about the quality of my colleagues and the research that's done there in the location and basically his he had two offers one was from Princeton which he put up here no offense to New Jerseyans but Princeton as a young single person sucks okay fine when you're married to have kids but deadlies young single person and the other so that's Princeton down here was Santa Cruz okay awesome candidates the most beautiful University in America okay but not as good an economics department and he decided he was roughly and different between the two but he had a third offer from the IMF which is the research institution in DC which has he had a lot of good colleagues NDC's way better than Princeton New Jersey even it's not as good to see him to Cruz so he decided he would take the offer at the IMF okay even though the IMF had worse colleagues in Princeton and worse location of Santa Cruz it was still better in combination the two of them given his preferences and that's how he used in different skirts he'll make his decision okay so that's sort of an example of of applying and once again no offense to the New Jerseyans in the room of which I am one but believe me you'd rather be in Santa Cruz okay so now let's go from preferences to utility functions okay so now we're gonna move from preferences which we represent graphically to utility functions which we're gonna represent mathematically remember I want you understand everything in this course at three levels graphically mathematically and most importantly of all intuitively okay so graphic is indifference curves now we'll come to the mathematical representation which utility function okay and the idea is that every individual all of you in this room have a stable well behaved underlying mathematical representation of your preferences which we call utility function okay now once again that's to be very complicated your preference over lots of different things we're gonna make things simple by writing out two-dimensional representation for now of your indifference curve we're gonna say how do we a mathematically represent your feelings about Pizza versus cookies okay imagine that's all you care about in the world is pizza and cookies how do we a mathematically represent that so for example we could write down that your utility function is equal to the square root of the number of slice of pizza times the number of cookies we could write that down I'm not saying that's right I'm not saying it works for anyone in this room or even everyone this room but that is a possible way to represent utility okay what this would say this is convenient we will use we'll end up using square roots formal law for utility functions a lot of convenient mathematical properties and it happens to jibe with our example right because in this example you're different between two pizzas and one cookie or one pizza to cookie that both square root of two and you prefer two beats and two cookies that's two okay so this gives you a high utility for two pits and two cookies okay then one pizza then one Pete's and two cookie or two pizza and one cookie so now the question is what does this mean what is utility okay well utility doesn't actually mean anything there's not really a thing out there called noodles okay in other words utility is not a cardinal concept it is only an ordinal concept you cannot say your utility you are you cannot literally say my utilities X % higher than your utility but you can rank them so we're gonna assume that utility can be ranked to allow you to rank choices even if generally we might slip some and sort of pretend utilities Cardinal for some cute examples but by and large we're gonna think of utility as purely ordinal it's just a way to rank your choices it's just when you have a set of choices out there were many dimensions a if your choice in life was always over one dimension and more was better it would always be easier to rank it right you'd never have a problem once your choice over more than one dimension now if you want to rank them you need some way to combine them that's what this function does it allows you essentially to weight the different elements of your consumption bundle so you can rank them when it comes time to choose okay now this is obviously incredibly simple but it turns out to be amazingly powerful in explaining real world behavior okay and so I want to do today's work with the underlying mathematics of utility and then we'll come back we'll see in the next few lectures how it could actually be used to explain decisions so a key concept we're gonna talk about in this class is marginal utility margit hill is just the derivative of the utility function with respect to one of the elements so there marg utility for cookies of cookies is utility of the next cookie given how many cookies you've had this class can be very focused on marginal decision making in economics it's all about how you think about the next unit turns out that makes life a ton easier turns out it's way easier to say do you want the next cookie then they say how many cookies do you want because if you want the next we that's sort of a very isolated decision you say ok I've had this many cookies do I want the next cookie whereas before you start eating today how many cookies do you want that's sort of a harder more global decision so we're gonna focus on this stepwise decision making process of do you want the next unit the next cook your the next slice of pizza ok and the key feature of utility functions we'll work with throughout the semester is that they will feature diminishing diminishing marginal utility Mars utility will fall as you have more of a good the more of a good you've had the less happiness you'll derive from the next unit okay now we can see that graphically in Figure two for figure two for graphs on the x-axis the number of cookies holding constant pizza so let's say you're having two pizza slices and you want to say what's my benefit from the next cookie and I'm on the Left axis violating what I just said like 15 seconds ago we graph utility now once again the util numbers don't mean anything it's just to give you an ordinal sense what you see here is that if you have one cookie your utility is 1.4 square root of two times one if you have two cookies utility goes up to square root of four which is two you are happy with two cookies but you are less happy from the second cookie than the first cookie okay and you could see that in Figure if you flip back and forth 3 to 4 and 2/5 you can see that okay the first cookie going from zero to one cookie gave you one so in this case we're not graphing the margin utility so figure 2 4 is the level of utility which is not really something you can measure in fact figure 2 5 is something you can measure which is margin utility what's your happiness we'll talk about measuring this from the next cookie you see the first cookie gives you a utility and a utility increment of 1.4 okay you go for utility of zero two utility one point for the next cookie gives utility in current of 0.59 ok you go from utility of one point four one two utility of to the next cookie gives utility increment of 0.45 the square root of 3 so now we flip back to the previous page we're going from the square root of 4 so we're going from the square root of 4 I'm sorry to the square root of 6 square root of 6 is only 0.45 more than the square root of 4 and so on so each additional cookie makes you less and less happy it makes you happier it has to because more is better but makes you less and less happy okay and this makes sense just think about any decision in life starting with nothing of something and having the first one slice of pizza a cookie deciding on which movie to go to the first movie the one you want to see the most okay it's gonna make you happier then you want to see the one you want to see not quite as much the first cookie when you're hungry will make you happier than the second cookie the first slice of pizza make happen now you may be close to indifferent that second slice of pee she makes you almost as happy as the first but the first will make you happier okay if you think about that's really sort of that first step you were hungry in that first one makes you feel happier now but you got to remember you always want more cookies now you might say wait a second this is stupid okay once I've had 10 cookies I'm gonna barf the 11th cookie you can actually make me worse off because I don't like barfing but in economics we have to remember you don't have to eat the 11th cookie you could give it away so if I save you want the 11th cookie you can save it for later you could give it to a friend so you always want it in the worst case you throw it out it can't make you're worse off it could only make you better off and that's what we're sort of more is better assumption comes from obviously in the limit you know if you get a million cookies they're garbage game gets full you have no friends to give them to I understand the limit these things fall apart okay but that's a basic idea of Moore's better than the basic idea of diminishing marginal utility okay any questions about that yeah utility function can never be negative because we get well utility once again utility is not an ordinal concept you can set up utility functions such that the numbers negative you can set that up okay the margin utility is always positive you always get some benefit from the next unit utility once again the measurements are relevant so you can be negative to get set it up yeah I could write my utility function like this you know something like that so it could be negative that's just a sort of scaling factor but marginal utility is always positive you're always happier or it's not it's not negative you're always happy or at least indifferent to get in the next unit yeah uh I'm sorry you look think you're to five know the marginal because he can go down each fraction of a cookie the Marge utility marshal is always diminishing well it's really hard to do it from zero that's really tricky it's sort of much easy to start from one so corner solutions we'll talk a lot of corner solutions as class they get ugly think of it starting from one starving that first cookie every fraction of a cookie makes you happier but less and less happy with each fraction good question alright good questions alright so now let's let's talk about let's slip back from the math to the graphics and talk about where indifference curves come from I just drew them out but in fact indifference curves are the graphical representation of what comes out of utility function okay and indeed the slope of the indifference curve we're gonna call the marginal rate of substitution the rate essentially at which you're willing to substitute one good for the other larae willing to substitute cookies for pizza is your marginal rate of substitution and we'll define that as the slope of the indifference curve Delta P over Delta C that is your marginal rate of substitution little indifference curve tells you the rate should will in a substitute you just follow along and say look I'm willing to give up so in other words if you look at figure two six you say look I'm indifferent between point A and point B one cut one slice of pizza I'm sorry one cookie and four slices of pizza is the same to me as two cookies two slices to B so why is it the same because they both give me utility square root of four right so given this mathematical I'm not saying you are I'm saying give me this mathematical representation okay you aren't different between point a and point B so what that says and what's the slope with the indifference curve what's the arc slope between point a and point B the slope is negative two so your marginal rate of substitution is negative two you aren't different okay you're in different between 1/4 and 2 2 therefore you're willing to substitute or give away two slices of pizza to get one cookie Delta P Delta C is is negative 2 okay now it turns out you can define the margin rate of substitution over any segment of a difference curve and what's interesting is it changes it diminishes look what happens when we move from two pizzas and two cookies to from point B to Point C now the margeurite sub solution only negative 1/2 now I'm only willing to give up one slice of pizza to get two cookies what's happening first I was willing give up to slice of pizza get one cookie now only wouldn't give up willing to give up one slice apiece so to get two cookies what's happening yeah because of exactly diminishing margin Atilla T has caused the margin rate of substitution itself to itself to diminish for those who are really kind of better at math than I am it turns out technically mathematically large utilities and always diminishing you can drop cases mrs is always diminishing so you can think of margin is always diminishing it's fine for this class we get the higher-level math and economics you'll see Marge utility doesn't have to diminish mrs has to diminish okay mrs is always diminishing as you go along the indifference curve that slope is always falling okay so basically what we can right now is how the mrs relates utility function our first sort of mind-blowing result is that the mrs is equal to the negative of the Margy utility of cookies over the marge utility of pizza that's our first key definition its equal to the negative of the margit Ilia the good on the x-axis over the marge utility good although on the y-axis okay essentially the madre substitution tells you how your relative marginal utilities evolve as you move down the indifference curve when you start at Point a you have lots of Pizza and not a lot of cookies when you have lots of pizza your margin utility is small here's the key insight this is the thing which once again it's a light bulb thing if you get this and make your life so much easier margin utilities are negative functions of quantity the more you have of a thing the less you want the next unit of it that's why for example cookies is now in the numerator and pizzas in the denominator flipping from this side okay the more you have the good the less you want it so start at Point a you have lots of pizza and not a lot of cookies you don't really want more pizza you want more cookies that means the denominator is small the mores utility of pizza is small you don't really want it but the marginal if cookies is high you don't many of them so this is a big number now let's move to point B and think about your DX decision well now your margin Chile of Pizza if you're gonna go from two to one slice of pizza now Pizza is worth a lot more than cookies so now it gets smaller so essentially as you move along that indifference curve because of this you want because diminishing margin Atilla T it leads this issue of a diminishing marginal rate of substitution okay so basically as you along indifference curve you're more and more willing to give up the good on the x-axis to get the good on the y-axis as you move from the upper left to the lower right on that indifference map figure two six you're well you're more willing to give up the good on the on the x-axis to get the good on the y-axis and what this implies is that indifference curves are con indifference curves are convex to the origin indifference curves are convex to the origin it's very important okay that let's see that they are they are not concave theory the convex are straight let's say they're net they're not concave to the origin okay to be technical difference curves can be linear we'll come to that but they can't be concave the origin why well let's look at the next figure the last figure figure 2:7 what would happen if indifference curves were concave to the origin then that would say moving from one pizza so now I've drawn a concave indifference curve and with this is curved if it's curved move from point A to point B leaves you indifference so you're happy to give up one slice of pizza to get one cookie starting with four slice of beats in one cookie you are happy to give up one slice of pizza to get one cookie now starting from two and three you're now willing to give up two slices of pizza to get one cookie what does that violate why is that not make sense yeah yeah glad to vision margin utility here you were you were you were only you were happy to have one slice speeds to get one cookie now I really have to slice to pieces to get won't cook even though you have less pizza and more cookies that can't be right as you have less pizza more cookies cookies pizzas should become more valuable not less valuable and cookies should become less valuable not more valuable so a concave to the origin indifference curve would violate the principle diminishing marginal and diminishing marginal rate of substitution okay yeah okay that's very interesting so in some sense what that is saying is that your utility function is really over sets you're saying utility functions and over trading cards it's over sets so basically that's what sort of you know what's sort of a bit you know our models are flexible one way say they're loose another way say they're flexible so one but one of the challenges you'll face on this course is thinking about what is decision set over which I'm writing my utility function you're saying it's that's not trading cards so that's why it happens ok other questions good question yeah in the back what about like addictive things were like the more you have it the more you want to buy yeah that's that's a really religion question I spend a lot of my research life actually I do a lot of read a lot of research for a number of years on thinking about how you properly model just addictive decisions like smoking and making decisions like smoking essentially it really is that your utility function itself shifts as you get more addictive it's not that your margin utility the next cigarettes still worth less than the first cigarette it's just that as you get more addicted that first cigarette gets worth more and more to you so when you wake up in the morning feeling crappy that first cigarette still does more for you than the second cigarette it's just the next thing you wake up feeling crappy er okay so we model addiction it's something where essentially each day cigarettes do less and less for you get essentially adjusted to new you get habituated to higher levels and this is why you know I do a lot of work you know this is why unfortunately we saw last year the number the highest number of deaths from accidental overdose in US history 72,000 people died from drug overdose last year more than ever died traffic accidents in our nation's history okay why because people get habituated to certain levels and the exhibition a certain level so people get hooked on oxycontin they get obituaries I'm a be switched to heroin and their to a certain level and now have this thing called fentanyl which is a synthetic opioid brought over from China which is incredibly powerful and dealers are mixing the fentanyl in with the heroin and the people shoot up not realizing that they're habituated level not realizing they have this dangerous substances and they overdose and die and that's because they've gotten habituated to high level they don't realize that getting a different product so it's not about not diminishing marginal tea it's about different underlying different products all right other questions sorry for that depressing note but it's important to be thinking about that's why once again we're the dismal science we have to think about these things okay now let's come to a great example that I hope you've wondered about and maybe you've already figured out in your life but I hope you've at least stopped and wondered about which is the prices of different sizes of goods in a convenience store say okay take Starbucks you can get at all iced coffee for 225 or the next size whatever the hell they call it bigger okay you can get 470 more cents so 225 and you can double it for seventy more cents or take McDonald's a small drink is a dollar twenty two and the local McDonald's but for 50 more cents you can double the size okay what's going on here it why did it give you twice as much liquid or if you go for ice cream it's the same thing why do you view twice as much for much less than twice as much money what's going on yeah exactly that's a great way to explain it the point is it's all about diminishing margin utility okay when you come in to McDonald's on a hot day you are desperate for that soda but you're not as desperate to have twice as much soda you'd like it you're probably want to pay more for it but you don't like it nearly as much as that first Minnesota so those prices simply reflects the market's reaction to understanding diminishing marginal utility now we even talked about the supply side of the market yet I'm not getting top providers make decisions that's a much deeper issue I'm just saying that this is diminishing marginal in action how it works in the market and that's why you see this okay so basically um what you see is that that first bite of ice cream for example is worth more and that's why the ice cream is twice as big doesn't cost twice as much now so basically what this means is if you think about our semantic demand and supply model on a hot day or any day the demands for the first 16 ounces is higher than the demand for the second 16 ounces but the cost of perusing 16 ounces is the same so let's think about this it's always risky when I try to draw a graph in the board but let's bear with me okay so let's say that there's a simple supply and demand model you have this you have this supply function for soda and let's assume it's roughly flat okay let's assume sort of the cost of firm procedure you know within some range the firm basically every incremental 16 ounces cost of them the same so that's sort of their supply curve okay and then you have some demand curve okay you have some demand curve which is downward sloping okay and they set some price and this is the demand for 16 ounces now yeah what's the demand for the next 16 ounces okay yeah isn't gonna work we have to have an upward sloping supply curve sorry about that we have a slightly upward sloping supply curve okay now we have the demand for the next so so here's your here's your price here's dollar 22 okay now you say well what's my demand when I sell 32 ounces well it turns out demand as it shift out twice as much it just shifts out a little bit more so you can only charge a dollar 72 for the next 16 ounces probably if you want to go to the big if you can go to the 7-eleven where you can get sizes up to you know as big as your house okay they keep these curves keep getting closer and closer to each other so those price increments get smaller and smaller and that's why you get the monster you know ginormous gulp at 7-eleven is really just not that indict not that different from the price of getting the small little mini size okay because the diminishing margin utility all right and so that's how the market that's essentially how we can take this abstract concept this sort of crazy math and turn into literally what you see in the store you walk into okay questions about that yeah awesome awesome question and every single thing it was going to be your first granola right so I great great question yeah well I mean the risk of my going to this model is you know once we once we get nonlinear we do things in this class we have to start talking about supply factors I want to talk to but there's two answers one is packaging efficiencies but the other is if you actually go to Costco and look at their prices for many things they're not actually better than the supermarket so actually the price of buying the giant like eight thousand bars of granola is actually not that much more than not that much less than a thousand time buying a eight pack at eight granola bars it turns out it's less but it's not nearly as much less as these examples as sodas at McDonald's what's exactly your point utility diminishes less so they don't want to charge as much less in multiple packages so you can actually if you compare Parrish the gap in perishable product pricing by size it's much larger than the gap in non-perishable pricing by size great point yeah so there's a without recycle your awesome and that is why they don't let you walk back in with the same cup and refill it right that's exactly right and that comes to this point it's sort of like it's non-perishable as you get longer apart so um but you know it's all this really should think so at Fenway okay you can get you get like a regular-sized soda it's like crazy it's like six bucks then for like eight bucks you get a big soda then for ten bucks you get a refillable big soda okay now the question is can you bring that refillable soda back to additional games technically not but I do and and basically they sort of understand so so this interesting question of sort of the perishability of things and how that's and how that's gonna affect things going on it's a really it's a really it's an interesting question other comments okay I'm going to stop there those are great comments thanks everyone for participating and we will come back next time and talk about the sad reality that we haven't won the lottery and we have limited amounts of money