Alright, so now let's discuss some special cases for indifference curves. Perfect substitutes and perfect complements. So let's start here with perfect substitutes and we're gonna see that perfect substitutes have same. Excuse me? Straight line straight line indifference curves. Okay. And perfect substitutes are kind of silly to see in the real world, just like you're gonna see what these perfect complements. Um But a perfect substitute we could say is fivers and tenors. Right? When you've got a $5 bill? Well, you would want to $5 bills for 1 $10 bill. Right? So they're perfect substitutes for every $25 bills you're gonna get 1 $10 bill. So that would be right here. You would be indifferent between two fibers or one tenor right there. Right? Just as you would be indifferent between four fibers worth $20.02 tenors worth $20 also. Right. So that would keep happening here and we would keep having the straight line indifference curves. Right, Let me do that a little better. And they're all just like that. Right? They're all just gonna be straight line indifference curves based on that rate of substitution. And note that in this case the M. R. S. Is constant. This is a specific case where that marginal rate of substitution is constant because you would only trade $25 bills for one for 1 $10 bill. So that M. R. S. In this case is gonna equal to for fibers and tenders. Okay, so pretty simple there with the perfect substitutes. You're gonna be indifferent between these fibers and tenders. Right? Because of the perfect substitution. Let's move on to perfect complements down here. So perfect compliments are gonna have what I'm going to call a right angled Indifference curve. Okay, so perfect compliments are kind of silly to what you're gonna see is something like left shoes and right shoes right there. Perfect compliments when you have, you wouldn't want to have 10 left shoes and zero right shoes. Right. That would be kind of silly. So you're always gonna want to have equal amounts of these. You're gonna want to have the same amount of left shoes as right shoes. And you're gonna end up in this situation where let's say you have uh two, let's start here with two left shoes and two right shoes. That's the ideal situation, right? You wanna have two and two, but you would be indifferent with anything up going this way and anything out going this way as well. Right. So why would you be indifferent for that? Let's think about it. So, if you had two right shoes right now, right. If you had two right shoes, you would want at least two left shoes. Right. You want to have two left shoes? But you'd be indifferent if you had three left shoes or four left shoes or five left shoes, it's not really gonna make a difference to you because you only have two right shoes. So you need two left shoes. So you're indifferent whether a situation where you have two and two or two and 10, right? Because you only have the two shoes to match with the two others. So you end up in this situation with the right angle, same thing with the left shoes. If we say we definitely have two left shoes. Well, you're indifferent whether you're gonna have to write shoes. Three right shoes, four right shoes, you're gonna get the same level of satisfaction because you can only match two pairs of shoes in that case, no matter what. So the same thing is gonna happen with three. We would have a situation here where this is in another indifference curve. Right? But now we've got three pairs of shoes, another one out here at four. So we're gonna keep having these right angles right and it's just gonna keep going out like that. So perfect complements have these right angles because you don't care if you have more of something as long as you have enough to make that compliment. Alright, so we get the right angle, the different skirts with perfect complements and the straight lines with perfect substitutes. Cool, let's go ahead and move on to the next topic.