in this video we're going to explore the idea of an indifference curve indifference indifference curve and what it is is it it describes all of the points all the combinations of things to which I am indifferent in the past we've thought about maximizing total utility now we're going to talk about all the combinations that essentially give us the same total utility so let's draw let's let's draw a graph that tells us all of the different combinations of two goods to which we are indifferent and like I've we've mentioned before we're focusing on two goods because we did three Goods we would have to do it in three dimensions and four Goods would get get very abstract so let's say in this axis the vertical axis this is going to be the quantity and we'll stay with the chocolate and the fruit tradeoff those are the only two things that we consume so this is going to be the quantity of chocolate in bars and in the horizontal axis this is going to be the quantity of fruit and this is going to be in pounds of fruit and this will go see this is 10 this is 20 this is 10 and this is 20 and this would be 15 five five and then 15 and let's say let's say that right now at some point I am consuming five pounds of fruit per month and 15 bars of chocolate per month so that would put me right there and if someone were to ask S how would you feel how how would you feel if instead of that instead of that I were to give you let's say 10 pound 10 bars of chocolate and 7 lb and 7 lb of fruit and I would say you know what I'm indifferent I wouldn't care whether I have so this right over here is I I wouldn't care whether I have 15 bars of chocolate and five lbs of fruit or whether I have 10 bars of chocolate and 7 lbs of fruit I am in different between these two I've introspected on what I like and what I derive benefit and satisfaction out of and I get the same total utility out of either of these out of either of these points so both of these are on the same indifference curve and in general I could plot all of the different combinations that give me the exact same total utility and it might look something like this it let me try to draw it as neatly as possible I'll do it in magenta it might look something something like this and then keep going all the way down like that so any point any point on this curve right over here I'm indifferent relative to my current predicament of 15 bars and 5 pounds of chocolate so that is my indifference curve indifference indifference curve now let's think about so obviously I if I go all over here 20 lbs of choc 20 lbs of fruit and I don't know that looks like about two bars of chocolate to me the same utility based on my preferences as where I started off with so if someone just swapped everything out I would just kind of I would kind of just you know shrug my shoulder and say yeah no big deal I'm exact I wouldn't be happy I wouldn't be sad I am indifferent now what about points what about points down here what about a point like this well that is clearly not preferable because for example that point I just I just showed I can show a point on the indifference curve where I'm better off for example that point that I just that's five pounds of fruit and about five bars of chocolate but assuming that the marginal benefit of more chocolate is positive and the way I've I've drawn this or the assumption is that it is then I'm obviously getting more benefit if I get even more chocolate per month and so anything down here below the indifference curve is not preferred not preferred preferred and using the same exact logic anything out here anything out out here anything out here well that would be good because we we're neutral between all of these points on the curve but this green point right over here I have the same number of bars as a point on the curve but I have a lot more I have a lot more pounds of fruit looks like I have 11 or 12 pounds of fruit so assuming that I'm getting marginal benefit from those incremental pounds of fruit and we will make that assumption then this right over here anything out here is going to be preferred so this whole area this whole area is going to be preferred to everything on the curve preferred and the whole area down here is obviously we've not preferred to anything on the curve and let me just to show you this not those points that so all of this and let me do that in a different color actually because our curve is purple everything in blue everything in blue is not preferred now the last thing I want to think about in this video is what the slope of this indifference curve tells us when I talk about the slope this is really kind of an idea out of calculus because we're used to thinking about slopes of lines so if you give me a a line like that the slope is how much how much does my vertical axis change for every change in my horizontal axis so in a typ typical algebra class that axis is your y AIS that is your x axis and when we think about slope we say okay when I have a I have a certain change in y when I change in X by one so we have something like this so when I change I get a certain change in y the triangle means change in Delta change in y when I get a certain change in X when I get a certain change in X and deltay the change in y over change in X is equal to the slope but this is when it's a line and the slope isn't changing at any point on this line if I do the same ratio between a change in y and a change in X I'm going to get the same value on a curve like this the slope is constantly changing so what we really do to figure out the slope exactly at a point you can imagine it's really the slope of the tangent line of that point a line that would just touch at that point so for example so for example let's say that I draw a tangent line I'll draw my best attempt at drawing a tangent line I'll do it in pink let's say I have a tangent line right from our starting predicament just like that and it looks something like that it looks something like that and so right where we are right where we are now exactly at this point exact you know if we Veer away it seems like our slope is is changing right fact it definitely is changing it's becoming less deep as we go forward to the right it's becoming more steep as we go to the left but right there the slope of the tangent line looks right like that or you can view that as the instantaneous slope right there and we can measure the slope of the tangent line we could say look if we want if we want an extra extra let's see this looks like about if we want an extra two if we want an extra two pounds of fruit how many bars are we going to have to give up how many bars are we going to have to give up well it looks like we're going to have to give up based on the slope right over there looks like we're going to have to give up F five bars so this is five and this is two so what is your change in what is the slope here the slope the slope here is going to be that your change in bars and I should actually say this this is a negative right over there it's going to be your change in bars your change in ch chocolate bars over the the your change in Fruit over your change in fruit and in this CA in this situation we it is5 five bars for every two fruit that you get so bars bars per fruit or you can say this is equal to -2.5 bars per fruit bars per fruit so it's essentially saying exactly at that Point how are you willing to trade off bars for fruit exactly that point it's going to change as things change along this curve but it's saying exactly where you're sitting right now you would be indifferent and and but it's only as you just slightly move or for an extra drop of fruit an extra ounce of fruit not even a whole pound you'd be willing to trade off two and a half bars per fruit and what this says so you're willing to give up since it's negative you're giving up 2 and 1 half bars of chocolate for every pound of fruit now it's going to be different once you have a lot more fruit you're going to be much less willing to give up bars of chocolate over here you have a lot of bars and not a lot of fruit so you're willing to give up a lot of bars for fruit over here if we go over here the slope looks a little bit different over here it is much flatter it is much flatter so let me draw it in a color we haven't used yet so over here the tangent line Looks something like this it looks something like this and let's say when you calculate it when you calculate it in in order to get in order to get I don't know this looks like about five pounds of fruit in order to get five pounds of fruit you are going to have to give up you're going to have to give up two bars so once again the slope is the change in the vertical axis over the change in the horizontal axis so over here at this point your change in bars over your change in fruit is going to be well you're going to give up two bars for every five fruit for every five fruit bars bars per fruit bars per fruit so this right over here is negative this is .4 0.4 I'll say B for f so over here you're willing to give up much fewer bars for every incremental fruit up here you were willing to give many bars away for every fruit and that made sense over here you had a lot of chocolate bars not a lot of fruit so you were willing to give up more bars for your fruit and over here you have many fewer bars so you're much you're much more resistant to giving up bars for fruit but this number this number how many bars you're willing to give up for an incremental fruit at any point at any point here or you could view it as the slope of the indifference curve the slope or the slope of a tangent line at that point of the indifference curve this right over here is called our marginal rate of substitution marginal rate of substitution it's a very fancy word but all it's really saying is how much you're willing to give up of the vertical axis for an increment of the horizontal axis right at that point it changes as soon as you move because this is a curve it changes a little bit but right at that point for a super super small amount how many how many bars are you willing to give up for fruit and obviously it changes as we go along this indifference curve