welcome back so as promised we're gonna go through another example of uh maximizing utility uh when uh during consumer choice um so in this example we have uh samantha and she buys two items for lunch tacos and meatball subs a taco cost two dollars and meatball sub costs four dollars just 22 to spend on lunch every week the utility she receives from subs and tacos is depicted in the table below okay so there you go there you have it that is all the information we need to solve the following problems if samantha had an unlimited budget so you're just told she can spend 22 dollars but suppose she didn't suppose she had all the money in the world she had an unlimited budget how many subs and tacos would you want to purchase okay so this question isn't take any calculation rather this just takes you to ask you to look at this table and examine your understanding of what utility means so we look at samantha's utility we see that her margin utility is positive every with every extra taco she gets more utility and at some point it maximizes and goes down so what is this telling us this is telling us that this seventh taco here actually doesn't make her happier it doesn't provide more satisfaction in fact it provides dissatisfaction as we can see with her total utility decreasing and the same thing is true here with the subs after five subs if she goes any farther she gets dissatisfaction from her sixth and seventh sub for a week right and you can imagine this could happen with you if you ate the same lunch every day eventually like i don't really want any more sandwiches so this tells me that her satisfaction is maximized if she has five subs and six tacos and all i looked for there is where does total utility maximize in each individual column okay but back to our typical problem sorry does it you know what i am there we go sorry this is the side i was looking for i didn't realize i slipped i must have clicked over at one point with her 22 budget how many of each good will she purchased so with her actual 22 hour budget what would she purchase purchase so i slipped in this empty table into these notes you're not going to see this when you're looking back at the slot no at the powerpoint um because i just wanted to be able to calculate this for you so the first thing i'm going to do is calculate marginal utility and remember the way we calculate margin utility it's the excess or extra utility from each additional unit of each good so for her first taco she goes from no utility no tacos to 12 so the margin utility is 12. and then she goes from 12 to 21. that tells me that second taco brought her 21 minus 12 nine additional units of utility you can always check your work in these cut these cases be if i added the marginal utility here 12 plus 9 equals 21 that's going to be my total utility of two of two tacos which makes sense my first taco gave me gives me 12. my second taco gives me nine then two tacos must give me 21. 27 minus 21 is six so that's the utility from the third taco 32 through minus 27 is five 35 minus 32 is 3 36 minus 35 is 1. and now don't forget this is 34 minus 36. this has got to be a negative number to represent that she gets disutility or un she gets less satisfaction when she purchases that taco let's do the same thing for subs 28 44 minus 28 is 16 58 minus 44 is 14. 70 minus 58 is 12. 74 minus 70 is four and then it turns negative 70 minus 74 is negative four 62 minus 70 is negative eight okay and to complete our table we're gonna calculate the marginal utility per dollar which just means i'm gonna take my margin utility column and divide by two dollars which is the price of a sub so 12 divided by two dollars is six four and a half three five divided by two is two and a half one and a half zero point five and negative one i'll do the same thing over here but remember the price of a sub was four dollars so take that into consideration 28 divided by four is seven sixteen divided by four is four fourteen divided by four is three and a half twelve divided by four is eight no it's not sorry twelve divided by four is three four divided by four is one negative four divided by four is negative 1 and negative 2. okay so now we have this table complete we can go through our exercise to figure out what samantha's optimal bundle is remember she starts out with 22 so i'm going to put this here in the margin she's twenty two dollars i wanna ask herself what is she gonna buy first her first sub seven or her first taco six seven is more than six so she buys a sub so her amount of money goes down from 22 and she now has 18 dollars left what is she gonna buy next her first taco is six dollars or her second sub at four dollars well six is more than four so she's gonna buy a taco she now has remember tacos are two dollars sixteen dollars left now we're gonna pair four and a half the second taco to four the second sub four and a half is more so she buys her second taco that's two dollars so she has 14 left now is she gonna buy her second sub four or her third taco three well four is more than three so she's gonna buy a sub that cost her four dollars and so it's just ten dollars left i probably should have started this at the beginning you can always look at the answer by looking at what you've crossed off at the end but i'm also going to put tally marks here so she started out their first sub and then she got two tacos and then she just got her second sub and she has ten dollars left three dollars for the third taco or three sorry not three dollars three utils per dollar for the third taco or three and a half utils per dollar for the third sub three and a half is more so she buys another set and now we're left with three for the fourth sub three for the third taco three versus three that means she's indifferent you can do either one or you could recognize that she has enough to do both i'm just going to kind of flip a coin it was heads i didn't say what heads meant so let's say she buys a taco tacos cost two dollars remember that's what indifferent means it means she honestly doesn't care so you can pick either of them and that leaves us with four dollars left two and a half versus three she buys that last sub she has zero dollars left she's purchased four subs and three tacos and again you can look at what you've crossed out if you don't make the tally marks so three tacos four subs and that's our answer that's our optimal bundle and again that is the margin utility per dollar method and that's the one i want you to do in your homework and eventually on the exam okay we're not gonna we're not gonna stop there in this example i'm gonna ask another question imagine the price of a taco goes up imagine it's risen to three dollars but our budget is still 22. what is her new optimal consumption bundle well we got to do it again so all i've changed here and i brought this table back the only thing i changed here is i fixed this column to represent three dollars so now 12 divided by 3 is 4 9 divided by 3 is 3 6 divided by 3 is 2 etc and let's do it again so i'm going to tally in the number of tacos i'm going to tell you the number of subs and samantha still starts out with the 22 budget okay seven is the biggest so we're going to start with the sub and she's left with 18 left okay looks like she's already indifferent between a taco and a sub so i'm going to flip a coin i don't actually even have a coin she buys the sub first right four and four means she's indifferent i'm saying she does the sub first for no good reason that means she has 14 left and she's bought two subs now i have four versus three and a half four is the bigger number so she's gonna buy a taco remember tacos cost three dollars now so she has eleven dollars left and she's bought a taco three versus three and a half she's seven dollars left and she's bought three subs three versus three she's indifferent flip a coin she buys the taco first tacos cost three dollars just four dollars left two versus three she buys the sub this is zero four subs and two tacos okay so what changed the price of a taco went up from three dollars to two dollars from two dollars to three dollars and her optimal consumption bundle went from four subs and three tacos to four subs and two tacos so i asked this question a couple semesters ago and then followed up with this considering the optimal consumption bundles in the last two examples does samantha's preference follow the law of demand and again this just calls you back to an earlier chapter is this consistent with the law of demand so when the price was two dollars we saw that she bought four subs and three tacos when the price of a taco went up to three dollars she brought four subs and two tacos that's what the law of demand predicts the law of demand says when the price of a taco rose or quantity demand would fall precisely what the law of demand says obviously it's just two points but i could plot a little baby demand curve here which shows a downward sloping relationship at a price of two dollars she bought three subs sorry three tacos at a price of three dollars she bought two tacos and we put together it slopes downward so that's it from this chapter let me know if you have any questions you're going to see another example like this in your practice uh assignment so please do the practice assignment on your own before you look at the answers because this is the sort of thing that will take practice you can also see some practice problems in the book and in the back of the book you have example problems okay good luck and let me know if you have any questions