Types of indifference curves

I've been drawing my indifference curves to look something like this so that's a vertical axis that's one good so this is the quantity of good a this is the quantity of good B and I've been drawing the indifference curves like this so it might look like that that's one indifference curve then another indifference curve would look like that and I could keep drawing indifference curves and this is what an indifference curve would look like for two normal Goods let me write that down normal these are normal goods and the reason why normal Goods indifference curves would look like that or what I'm trying to figure out the combinations of two normal Goods is because if I have a lot of one good so this point right over here I have a lot of good a and I have very little of good B I would be willing to trade off a lot of a to get one extra B but if all of a sudden I have a lot of B and a lot less a I you would have to give you I would be willing to trade off very little a to get an incremental B so that's why we have kind of this this inward bow shaped curve right over here or you could you know mathematically it looks like it's part of a hyperbola and so that's what normal Goods the indifference curves between if you're trading up between normal Goods would look like I was think about the indifference curve so it'd be this kind of curve thing but the marginal rate of substitution would constantly be changing now let's think about different types of goods let's say that this was let's say that this is the quantity quantity of five dollar bills five dollar bills and let's say that this is the quantity the quantity of ten dollar bills ten dollar bills and we're talking about the actual the good now is actually the dollar bills so let's say so let's say that this right over here is 10 10 five-dollar bills well that's 50 bucks I'd be indifferent between that and five ten dollar bills so this is five right over here and any point in between I would be indifferent because I'm always willing to trade off to five dollar bills for one ten dollar bill so it would look my indifference curve would be linear in this case my difference curve would would be linear so no matter what on this indifference curve I'm always willing if I want to get one extra $10 bill I'm always willing to give up to $5 bills which makes complete sense because to $5 bills are completely equivalent to one $10 bill and we could take it to another extreme let's say I have let's say I have an indifference well let me draw the quantity the quantity of I don't know the quantity of MMS quantity of MMS of let's say let's say red mms red red mms and I should have done that in red but I won't and then let's say this is the quantity of blue mms and let's say that I actually am indifferent between red and blue M&M some people aren't red mms and blue M&Ms so having 10 red mms is to me is completely equivalent of having ten blue mms so I I'm willing to trade them off one for one I don't care I get the same total utility I get the same total utility so in this case assuming that I really don't care but the color of my mmm I am completely indifferent as I swap them out and so this is a case of perfect substitutes perfect perfect substitutes substitute now I'd always be happy to have more mms so another indifference curve might look something like this might look something like this but it's always going to have a slope of negative one I always giving up one a red mmm to get one blue M&M then I would be indifferent and likewise over here you could have another indifference curve between between $5 bills and $10 bills that looks like this that looks like this but the slope would be the exact same thing now the last situation I want to think about is what we'll call perfect complements so goods that if you have one of them you really need the other one otherwise one of one of the two is somewhat useful and maybe the most pure version of perfect complements let me write it over here perfect perfect complements complements so let's say that this is the quantity of right shoes so the quantity of right shoes and this is the quantity of left of left shoes so obviously you if we're talking about just one pair you have one of each now do you care if you really get more left shoes no you have the exact same preference it doesn't really change your life you have the same total utility in fact it might even be negative because you have to store a role but let's just say assume you have the same total utility and you don't get any benefit of having those spare shoes in case your shoe gets destroyed or anything like that in terms of what you can get out of it what you can wear you get the same utility and so you're really indifferent no matter how many extra no matter how many extra left shoes someone gives you and you'd also be indifferent no matter how many extra right shoes how many right shoes someone gives you now you would be happier if you had maybe two right shoes and two left shoes because now you have two pairs so this would be another indifference curve and once again if you have two right shoes you really don't care how many more than two left shoes you get and if you have two left shoes you really don't care how many more than two right shoes you get so this in this indifference curve in green is clearly preferable to the one in white but along each indifference curve it doesn't benefit you to have three left shoes and only two right shoes so this is what perfect complements would look like this is perfect substitutes and this is normal goods