All right. So now let's discuss some special cases for indifference curves, perfect substitutes, and perfect complements. So let's start here with perfect substitutes. We're going to see that perfect substitutes have, excuse me, straight-line indifference curves. Okay? Perfect substitutes are kind of hard to spot in the real world, just like you're going to see with perfect complements, but a perfect substitute we could consider is fivers and tenors, right? When you've got a $5 bill, you would want 2 $5 bills for 1 $10 bill, right? So they're perfect substitutes. For every 2 $5 bills, you're going to get 1 $10 bill, so that would be right here. You would be indifferent between 2 fivers or 1 tenor. Right there. Right? Just as you would be indifferent between 4 fivers worth $20 and 2 tenors worth $20 also. Right? So that would keep happening here, and we would keep having these straight-line indifference curves, right? Let me do that a little better. And they're all just like that, right? They're all just going to be straight-line indifference curves based on that rate of substitution and note that in this case, the MRS is constant. This is a specific case where that marginal rate of substitution is constant because you would only trade 2 $5 bills for 1 $10 bill, so that MRS in this case is going to equal 2 for fivers and tenors. Okay? So pretty simple there with the perfect substitutes, you're going to be indifferent between these fivers and tenors, right, because of the perfect substitution.

Let's move on to perfect complements down here. So perfect complements are going to have what I'm going to call a right-angled indifference curve. Okay? Perfect complements are kind of hard to spot too. What you're going to see is something like left shoes and right shoes, right? They're perfect complements. When you have, you wouldn't want to have 10 left shoes and 0 right shoes, right? That would be rather illogical, so you're always going to want to have equal amounts of these. You're going to want to have the same amount of left shoes as right shoes, and you're going to end up in this situation where, let's say, you have 2 left shoes and 2 right shoes. That's the ideal situation, right? You want to have 2 and 2, but you would be indifferent with anything going this way and anything going this way as well, right? So why would you be indifferent for that? Let's think about it. So if you had 2 right shoes right now, Right? If you had 2 right shoes, you would want at least 2 left shoes, right? You'd want to have 2 left shoes, but you'd be indifferent if you had 3 left shoes or 4 left shoes or 5 left shoes. It’s not really going to make a difference to you, because you only have 2 right shoes, so you need 2 left shoes. So you're indifferent whether a situation where you have 2 and 2 or 2 and 10, right? Because you only have the 2 shoes to match with the others, so you end up in this situation with a right angle. The same thing with the left shoes. If we say we definitely have 2 left shoes, well, you're indifferent whether you're going to have 2 right shoes, 3 right shoes, 4 right shoes—you're going to get the same level of satisfaction because you can only match 2 pairs of shoes in that case no matter what. So the same thing is going to happen with 3. We would have a situation here where this is another indifference curve, right, but now we've got 3 pairs of shoes, another one out here at 4, so we're going to keep having these right angles, right, and it's just going to keep stretching 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 complement. Alright? So we get the right-angle indifference curves with perfect complements and the straight lines with perfect substitutes. Cool. Let's go ahead and move on to the next topic.