ECON B251 Class Recording 4/30 9:35am

追加: 2026-05-07

[00:00:02]All right. So, couple things for you going. Um, on Canvas, I now have it set. So, the grades that you're seeing are Oh, that would help. Is dropping your lowest module reading score.

[00:00:27]There we go. and then dropping kind of your two lowest quizzes and then your four lowest in-class quizzes. Okay, so the grades you see should be up to date in those categories. The only grade that kind of is still out there is that Canvas discussion that was turned in last night. I'll have my TAs help me get these graded hopefully by the end of the week. If not, by the end of the weekend, so start of next week. Those should be kind of up to date as well. You can then use that hypothetical grade tool, input your grades in each of those categories as well as your first two midterms, and then play around with hypothetical grades on the final to see what your final grade in the class would be. Now, that hypothetical grade tool also has a column for your CL points. So, I uploaded those yesterday. There's sometimes a lag. If you went to this last week, kind of my the leaders getting the attendants entered in. I'll upload them again um on Monday.

[00:01:21]So on Monday, those should all be up to date. Uh there are one more.

[00:01:28]There is one more available CL session to earn extra credit. Kind of replacing that uh snowstorm. So I put up an announcement on Canvas the other day. It's very similar to the same times and locations that are usually available on Thursday.

[00:01:42]They're a little different based off the CL leaders availability. Um, so they might be different than the leaders that they usually are, but there will be someone at each one of these times and locations this evening. Uh, if you want kind of a last CL session to go to. Now, there's nothing that they have kind of scripted to go. It's just a time to go ask them questions. So, this could be over the practice finals and they'll kind of do the best to kind of help you out with these. Um, other than that, the next week on Monday, I'll have kind of office hours as I usually would. So, 9:30 to 12:30. Um, so if you have last minute questions, you can stop by. My guess is it'll be relatively busy, so the earlier you get there, probably the better. Um, so those are kind of two last times where you can kind of go and ask questions. Of course, today as well, we'll just be doing review. You can ask questions today. Um, other than that, that should kind of cover most of the housekeeping stuff that we have before we just jump into doing review today.

[00:02:37]Uh, although I wanted to mention a couple other things. So, I put up also an announcement and I'll post another one um just so that's at the very top and kind of has it in one, but we're going to be split into two rooms. So, we'll be in Hodgej Hall. These rooms are like right next to each other. Um but just to kind of uh to avoid one getting too busy, if you have last names A through L, you'll be in 155. If your last names M through Z, you'll be in 159. Okay. So that makes sure I have kind of an equal number of students in each room so there's not, you know, you know, we don't end up with an issue where there's no available seats. So the procedure will look very similar to the midterms, right? All you can have is something to write with, right? A non-graphing calculator. You'll need your ID when you hand in the exam to verify it's you. If there's a phone out at any time, I will take your exam or the proctor will take your exam and you'll receive a zero. Okay? So, do not have your phone out or other materials.

[00:03:37]The only thing you should need is something to write with and a non-graphing calculator. It'll be 30 multiple choice questions, a little bit longer than the midterm, but we've got two hours. So, it'll be next Wednesday.

[00:03:48]I think it's the 6th. Do I have it on here? Uh, I'll make sure I put that in the additional. So, it's Oh, yeah. Wednesday 6. It'll be the same time class starts usually. So, 8:00, we'll end at 10:00.

[00:04:02]So, once again, a little bit more time.

[00:04:03]in two hours opposed an hour and 15 minutes. Um, other than that, I think that should kind of cover everything. Um, and my other announcement I'll post up. If you have an accommodation for this exam, I've sent you an email. You need to confirm with me that you received that email.

[00:04:21]Okay. Um, other than that, I put up a link to the kind of video I I post or I recorded just doing some additional review. I think I mainly focused on practice exam A there. But any questions you have today over practice exam A, B, old quiz questions we can kind of work through. Uh any other questions about the final or anything logistically about the class before we just jump into review questions?

[00:04:47]Okay, now is the time to ask them.

[00:04:51]All right. Okay. So we will start with anyone has a question they want to see work through here.

[00:05:08]So we're all ready for the finals. Just showed up to Nobody has a question.

[00:05:18]Quicker I get responses, the more questions we get through.

[00:05:23]So, if we look at exam A, come down here, question 29.

[00:05:29]So, this is one where I've gotten a handful of emails. Um, quiz was not wrong. You just solved it wrong. Um, so if I have a question like this and I gave you the quantity, marginal revenue, marginal cost, average total, average variable, and the price. So, in the long run, right, we're going to try to determine what firms would do and what will be true about the quantity they produce. So, I'll add an additional question here. Um, kind of solve for 28 along the way. So, I'll kind of start with 29. I'll then go back to 28 since they're similar because it's a concept that a lot of people missed on this last quiz. So, if I've got 29, I've got my average total cost and my price. So, if I stay open, this is true for any firm that we're looking at. Our profit equation is going to be the price, sorry, the quantity they sell times the difference between their price and average total cost. So the price I was given in this problem I believe was 85.

[00:06:30]The average total cost I was told is 100. Okay. So what is going to be true about my profits?

[00:06:39]Price is below average total cost. This value will be negative. So, I have something else I need to check. If profits are negative, what's the next thing I need to check to see if I do? Do I shut down? Our shutdown rule for monopolistically or perfectly competitive firms would be I shut down if the price is ever below my average variable costs. So, my average variable costs here were 80. My price is 85. So, do I shut down?

[00:07:09]No. I'm going to stay open. Okay. So if I stay open, I know my profits are negative. Moving towards the long run, what are s some firms going to choose to do? Well, I can't hemorrhage money forever. So some firms are going to choose to exit the market. As they exit the market, the remaining firms, the demand they face, well overall demand for the product hasn't changed. It's just that each firm is getting a higher proportion. So their demand curves increase. they can set a higher price.

[00:07:43]This continues until profits are equal to zero. So firms will exit this market.

[00:07:49]Now as they exit the market, so if we'll think about a scenario here where we started out here was the demand, they face a twice as steep marginal revenue curve. They set the quantity. How do I set that profit maximizing quantity? Doesn't matter what firm we're looking at. It's going to be where We have to have this burned into our memory. Marginal revenue is equal to marginal cost. We then go up to the demand curve to set the price. So we started out with a scenario where price was below my average total cost. Okay. As firms exit, I said each remaining firm is going to have a higher proportion of the overall demand curve.

[00:08:36]So that would look something like this.

[00:08:39]Right?

[00:08:42]You see, I want marginal revenue to kind of have the same slope.

[00:08:48]Now, that profit maximizing quantity as they exit. Eventually, it results in a price that's exactly equal to average total cost. So, if it was exactly equal to average total cost, my profits would be zero. So as firms exit, the remaining firms produce a higher quantity and their profits increase until they're equal to zero. Okay, questions on that idea.

[00:09:23]Okay, now we'll go back to 28 where I changed things a little bit. Okay, so I think I had all the same values, but instead I told you that my average variable cost was 90.

[00:09:40]So if I have a difference between my average total and average variable cost, I know that I'm in what? Short run because I must have some fixed costs, right? Average total is the sum of my average variable plus my average fixed.

[00:09:55]Now in this scenario, price is still below my average total cost, right? I haven't changed those values. So profits are negative. So do I shut down? Well, now is my price below average variable cost?

[00:10:17]Yes. So the firm is going to shut down, which now this was only my profit equation. If the firm stays open, if I shut down, my revenues are zero. I'm not making anything, but I still have to pay my fixed costs. We said if I'm not given my fixed costs, how can I calculate them? Well, it' be at a given quantity, what's the difference? So, actually, I'll start out here. You wouldn't have to do this every time, but this is where it comes from. Fixed costs are the quantity I'm producing times the average fixed cost. How can I find my average fixed cost? It's the difference between my average total and my average variable. So I was told here at a quantity of 25 my average total cost would be 100. My average variable cost is 90. So my profits would be -250.

[00:11:13]Okay. Now a lot of you on the quiz or had kind of a confusion.

[00:11:18]If instead I made the wrong decision, where is it at? There it is. And I didn't shut down. If they stayed open, well, we would use that profit equation, which was our profit equation only if I stayed open. So, this would have been what? 25, 85, and 100. So, I would have had what? 25 * 15 what? Oh, 250 plus 125. So, -375 if I'm doing mental math correct there. Notice if I stay open, my profits are a larger negative value than if I shut down, which is why we should shut down. Now, you don't have to go through and calculate these every single time.

[00:12:03]you can just rely on this shutdown rule which is if the price is below average variable costs I know I should shut down which means my profits are simply those negative fixed costs. Okay, so I kind of did 28 and 29 there. Okay, any questions over anything there?

[00:12:29]Okay.

[00:12:33]Any other questions people want to see work through?

[00:12:45]Now is the time to ask.

[00:12:48]You feel comfortable with all the questions. Not sure why you showed up to the app.

[00:12:52]>> Number 10 on exam.

[00:12:53]>> Okay. So we've got exam A here.

[00:13:00]Go all the way up to question 10.

[00:13:03]So here I've got an example. I given you the demand curve. I gave you a constant marginal cost. I asked you to calculate the quantity and the price if I'm profit maximizing. If I'm a single price monopolist. Now I could also ask you what the level of profits are here. um if I gave you average total cost, but you'll notice in most of them I I don't do that in this type of a question. So really here when you have the equation, I'm just going to be asking you how do you solve for that profit maximizing quantity and price. Okay? So so I'll give you a visual to go along with this as we look at the equations. So I've got my demand curve was 300 The slope was -6 and I told you there's a constant marginal cost of 60. So in these equation examples, I simplify a little bit and give you this nice constant marginal cost. So if I'm a single price monopouist, I make decisions based off of a twice as steep demand curve. So if my or sorry, twice as steep marginal revenue curves, twice as steep as demand. So if my demand curve was 300 minus 6 Q, my marginal revenue equation would be 300 minus twice as steep. So 2 * 6 or - 12 Q. So how do I find that profit maximizing quantity where marginal revenue is equal to marginal cost? I set those two equal to each other. I would have 60 is equal to 300 - 12 Q. One equation, one unknown. This is just a little bit of algebra, right? So I subtract 60 from both sides. I move 12 Q over. Got what? 240.

[00:14:58]Divide both sides by 12 and I get what?

[00:15:02]A quantity of 20. If I'm doing math in my head correct there. Okay. Now once I have that equilibrium quantity or that sorry, I shouldn't say equilibrium. a profit maximizing quantity of 20. How do I set the price? I go up to that demand curve. So if I have the quantity, how do I go up to the demand curve using equations?

[00:15:26]I simply plug that quantity into my demand curve. So this would give me what? Um 300us 120.

[00:15:39]No. Yes. Right. So 180.

[00:15:43]>> Okay.

[00:15:44]>> So the quantity would be 200. The price they set is 180.

[00:15:49]>> Okay.

[00:15:51]Any questions on that?

[00:15:55]Now what if I had a followup or a similar question where I asked you for a perfectly competitive firm's price and quantity?

[00:16:03]Well, the price part should be easy. if I have a perfectly competitive market and this will kind of answer some other questions and I think it might be a good concept to review since we're here at this point in the long run right and actually the same would be true about the short run what I I want to make a point about the long run first so if I have a perfectly competitive market where does it end up where supply is equal to demand supply represents my marginal costs so here the profit maximizing quantity for a perfectly competitive market and the price would be right here. Okay.

[00:16:41]Now, what ends up being true is the price they don't have any control. So, whatever that equilibrium price in the market is, they have to take that as given that becomes their marginal revenue curve.

[00:16:53]So, when we're looking at a firm, what ends up being true in the long run for these perfectly competitive firms, profits should be equal to zero. So what's going to be true? Well, their marginal revenue curve is equal to marginal cost here. So marginal revenue will be equal to marginal cost.

[00:17:14]What is their marginal revenue? Simply the equilibrium price they perfectly competitive market. They have to take that price as given. If profits are equal to zero, what's the only way that that's true?

[00:17:32]So a quantity I'm producing something what's the only way profits are zero price has to be what would this if I have 10 what's the only way I get zero if this difference is zero so what has to be true price has to be equal to average total cost so that price would also be equal to my average total cost now we also said in the long run. What happens to fixed costs?

[00:18:05]There's zero. So my average total cost would actually be entirely composed of variable cost or my average total is my average variable cost in the long run.

[00:18:17]So all of these things are equal for a perfectly competitive firm in the long run.

[00:18:22]And what will also end up being true is these perfectly competitive markets, not only do they end up where price is equal to average total cost, but it ends up being the minimum of that average total cost as well.

[00:18:36]So if I was thinking about this as a perfectly competitive market, what am I actually looking at where that demand curve hits the marginal cost of the firm? So where would that be? out here at a higher quantity.

[00:18:52]So if I'm thinking about where marginal cost is equal to marginal revenue for a perfectly competitive firm, well marginal revenue, the price they're setting is based off the demand curve.

[00:19:03]So I simply say where does that marginal cost hit my demand curve? I do a little bit of algebra here. I get what? uh 240 / 6. So this should be wait am I doing this right? 240 / 6 should be not 24. I'm writing quickly right 40. Okay.

[00:19:32]Any questions on that idea?

[00:19:34]So the perfectly competitive market ends up at a higher quantity. Now what should also be true? Monopolies have market power. So they can get away with setting a not lower price, lower quantity, but a higher price. Now what would the price be in a perfectly competitive market?

[00:19:53]I have constant marginal costs exactly equal to that value, right? Where marginal cost hits marginal revenue will be at that value of 60. So the price they set is 60 quite a bit lower than the monopouist. Okay.

[00:20:12]Let me think if there's another point I want to make here. I had something in my mind. Um, oh, so are we okay with this before I keep moving? Another point I wanted to make here.

[00:20:25]Now, the questions you would likely see wouldn't be with a constant marginal cost if I asked you this. So if I instead think about this single price monopolist, let's just complicate it a little bit and I won't have a constant marginal cost.

[00:20:42]I would still make the profit maximizing quantity decision based off where marginal revenue is equal to marginal cost. I go up to the demand curve to set that price.

[00:20:54]What is the difference at that profit maximizing quantity between price and marginal cost? What did we call that?

[00:21:07]My markup, >> right?

[00:21:09]>> So, monopolists will have a markup, right? Now, what about a perfectly competitive market?

[00:21:16]Well, they actually set or we see the price end up where supply is equal to demand.

[00:21:23]So, what is true about the price of a perfectly competitive market relative to marginal costs?

[00:21:31]Well, what did we just say? Everything is equal. So, what's going to be true about these? They're equal to each other. What is the markup in a perfectly competitive market?

[00:21:44]Zero. There is no markup, right? Because firms compete with price down to the point where economic profits are zero.

[00:21:53]Okay. Um, just kind of thinking about some of these concepts comparing singlepric monopolists to perfectly competitive markets. I know that wasn't the original question. We worked through some additional things, but I've got the exam written and printed, so I might know some things that are worthwhile to go through. Okay.

[00:22:11]Any other questions here before we keep moving?

[00:22:17]>> Okay.

[00:22:19]Any other questions people want to see work through? Yeah.

[00:22:40]I know there's a question. So, let me see it. again.

[00:22:52]>> Yeah. So, if I'm looking here, why do I know this is depiction of the short run?

[00:23:01]>> There's a difference between average total and average variable costs. So, if instead I was thinking about the long run, what ends up happening? I start to eliminate my fixed costs until all of my costs are variable. So in the long run, my average total cost, we had it drawn earlier, becomes my average variable, or I should say really the other way around. My average variable cost become my average total cost, right? It's just two different ways of saying the same thing. So when I'm thinking about eight, if I'm looking at the long run, I know I end up at that minimum point of my average total cost curve. So that's a quantity of 300. And I know the value of my average variable cost. Well, I wouldn't go down to this average variable cost curve because this must be a depiction of the short run. There's a difference between average total and average variable. In the long run, my average total becomes my average variable. So my average variable cost at that point would also be 300. Mean the quantity and price or quantity in that don't have to be the same value. They just happen to be in this case.

[00:24:06]Does that answer your question? Yep.

[00:24:09]Um, let me think if there's anything else I'm gonna say here. So, that should be should be good for that question.

[00:24:26]>> Okay. So, I've got 15 and 16. I'm thinking about a single price monopoulos. Now, what I could do, and this is um I put an announcement up on Canvas. I actually updated practice exam A. I think the original one I accidentally switched whoops these values. Right now, you could have solved through it and you conceptually would have been the same thing. But just to kind of be more accurate in terms of what you'd see on the exam, this is kind of, you know, what those quantities or total revenue should be because how would I come up with total revenue? It's simply the price I'm selling the good for times the quantity I'm selling. So these should be the correct values if you go ahead and do all that math. Now if I'm thinking about a single price monopoulos, they find that profit maximizing quantity where >> marginal revenue is equal to marginal cost. Well, I've got a constant marginal cost here of five. What do I need?

[00:25:21]I need my marginal revenue. Okay, so how would I calculate marginal revenue? So, this is where the exam and I've said this many times and I'm still getting emails. Is the exam cumulative?

[00:25:34]No. All right. It's comprehensive in that we're using some old concepts, but I'm not going to go back and ask you module six type questions. It's just the modules we've covered since the last exam. So, 10, 11, 12, and 13.

[00:25:46]So, marginal revenue is the change in my total revenue divided by a change in the number of units I'm producing or quantity. So 45 over 5 would be what? 9.

[00:25:59]Change in total revenue here is 35 / 5 is 7. So to save yourself some time, what's true about marginal revenue relative to demand? It is twice as steep. So notice every time I go up by five units, what is my demand curve?

[00:26:19]It's the combinations of price and quantity. So every time quantity goes up by five, price is falling by one, which means every time quantity goes up by five, my marginal revenue should be falling by two. Sure enough, it does. I can go through and calculate all these if I want to. Taking the change in total revenue divide by the change in quantity. What I'll end up finding is that decrease is always that it goes down by two. I don't know why this must have accidentally hit tab there.

[00:26:51]Okay, so if I have my marginal revenue column, what quantity would result in the profit maximizing quantity if marginal cost were five? Well, where does marginal cost equal my marginal revenue? Right here at a quantity of 15. We then go up to the demand curve to set the price.

[00:27:10]But what is my demand curve from this demand schedule? It's just the combinations of price and quantity. So, they'd produce 15 units and set that price at seven. That wasn't part of the question, but it could have been. Okay, any questions on that idea before we keep moving?

[00:27:31]So, what's the second part? How do I know what the elasticity of demand is?

[00:27:36]If marginal revenue is positive, we said that that must mean as I lower the price, that percent change must be lower than the percentage increase I have in quantity. So if marginal revenue is positive, I know that consumers are very responsive or demand must be elastic.

[00:27:54]Might want to memorize that rule. Might ask you a question on the exam like this. If marginal revenue is positive, we know the demand is elastic.

[00:28:03]Now if I had a perfectly competitive market and let's say they had a marginal cost of three.

[00:28:10]So where would that perfectly competitive market end up at? Where supply is equal to got to know this perfectly competitive markets end up this is like back when we were talking about just market like module three where supply is equal to demand. Right? So my supply curve is nice and easy here because I gave you constant marginal cost of three. So where would that marginal cost or that supply curve of three hit demand?

[00:28:40]Right here at a quantity of 35.

[00:28:44]Now at that quantity of 35, if I was setting a single price, what is my marginal revenue?

[00:28:51]Negative. So the perfectly competitive market here ends up at a quantity where demand is inelastic. If marginal revenue is ever negative from setting a single price there, our demand curve must be inelastic.

[00:29:04]>> Now that doesn't always have to be the case. I think in the question in the game theory one, I gave you a similar setup, but I had a duopoly. It could be that where they end up when they break the agreement is this perfectly competitive point. It could still be where marginal revenue is positive. That that's that's possible. Okay, so this won't always be the case that the perfectly competitive firm ends up with inelastic demand, but that's how it would identify whether or not it was elastic or inelastic is based off that sign of the margin revenue curve.

[00:29:34]>> Now for a monopolist, this one would actually almost this would be really easy. If marginal cost is equal to marginal revenue, marginal costs have to be something above zero. So marginal revenue for a monopoulos would always be positive, which means they'll always be on the elastic portion of the demand curve.

[00:29:55]Okay.

[00:29:58]Any other questions on this one?

[00:30:04]Okay.

[00:30:06]Uh let me think if there's anything else I want to say here. Don't think so. Um, any other questions that people want to see where on a Yeah. So, I added this in for the last class. So, if I deleted this, this is going to be almost an identical problem that we just worked through. So if I have two firms now and they want to act together and they want to agree to collude and act like a single price monopolist, it's the exact same thing we just did, right? We know their marginal cost is constant at 11, right? We could then go through find what their marginal revenue is. Change in total revenue is 57 divided by a change in quantity of three should give us 19. change in total revenue of 51 divided by a change in quantity of three should give us 17. Now this is where I could keep go through and make these calculations but once I see that marginal revenue is falling by two I'm always going to give you examples where marginal revenue falls at a twice as steep rate. So once again price is going down by one marginal revenue must be going down by two.

[00:31:27]Right? So I do what? 15 13 11 9 7 5 3 1 - 1g -3 now I could go through and calculate these all by hand but test taking techniques once you see that marginal revenue falls by two you know it's always going to fall by two we have linear demand and marginal revenue curves so where would the single price monopolist set right if these two firms are working together they would set it where marginal cost is equal to margin marginal revenue that would be at a quantity in the market of 15 and they would set the price go up the demand curve and set the price at 15. They just happen to be the same values in this example. Now if this is duopolist they're setting the same price and it would be the same price that monopoulos would set. But if the total quantity of the market is 15, how much is each firm producing?

[00:32:23]Half of that. So the quantity of each firm I even kind of bolded right each firm would be 15 over two or seven and a half. Okay.

[00:32:36]So 7 and a half would be the quantity of each firm. They would both set that higher monopoly price of 15. Okay.

[00:32:44]Any questions on that one?

[00:32:48]So once again marginal revenue is positive. So they're on the elastic portion. What if they instead break the agreement? Right? So there's always this incentive to be the firm that breaks the agreement. Why? I was driving here today and saw a gas station gas was like $4.99 a gallon. Uh a half mile up the road it was $479. Where do you think everyone's going to go today? The gas station with a lower price, right? So there's always this incentive. Gas station set the price in the morning at the same time.

[00:33:18]There's always the incentive to lower the price. might be the one that sets a lower price because then I'm going to get a higher amount of demand, right?

[00:33:25]But each firm has this incentive. So, we both kind of start setting maybe if I can change the price. I see a person down the road, it's 20 cents cheaper. I call in to, you know, the main, you know, whoever's telling me to set this price. I say, you know, maybe we should lower the price. They tell me, sure enough, lower it so we can be competitive. So there's always this kind of I keep undercutting the other firm's price until we get down to the point where profits are zero or a perfectly competitive outcome. So if I'm thinking about if we both break this agreement, I want to set the price lower than the other firm and this continues until we end up at the perfectly competitive point which would be where marginal cost or that supply curve hits my demand curve. So I think in the next question I told you what if the marginal cost was instead nine where would that hit my demand curve at a price of nine right so there the quantity in the market would be 33 if this is a duopoly model then each firm would be producing half that or 16.5 okay and here it's negative so demand would be Marginal revenue is negative. So, demand is inelastic.

[00:34:42]Any questions over those two?

[00:34:47]Now, I think there's another problem on here, but since we're here, I'll just kind of give you an example of how this could look like. So, let's go back to the single price monopolist.

[00:34:54]Let's say these numbers ended up being 12 and 10. That's not what they are. But just for the sake of I want to show you something. If the marginal cost is 11 h don't have a marginal revenue that's 11 here. So if I give you something like this where there's jumps and you don't end up with a marginal cost that's exactly equal to marginal value. What you will do is you go through and it's the decision process which is I produce this unit if the marginal revenue is greater than or equal to the marginal cost. So if there isn't a point where they're equal, I will stop at the last quantity where marginal revenue is greater than. So here with a marginal cost of 11, do I produce the first three units? Yes. Next three. Yes. Yes. Yes.

[00:35:44]Yes. So I'm at 15. Will I produce go from 15 to 18? No. Right. And you know, you might be like, well, wouldn't I split the difference? I don't know.

[00:35:53]Maybe this is a product where like, you know, if I look at like a um pop, right? Maybe I'm producing these in 12 unit, right? A case of pop is usually 12 can. So maybe I can't produce half that, right? I'd have to set. So there I'm giving you these quantity jumps. I wouldn't produce 18. I'd stop at the quantity where the last quantity that I have the marginal revenue being greater than or equal to the one. In this case, the last quantity, the marginal revenue is still greater than. Excuse me.

[00:36:22]Okay.

[00:36:24]Is that clear? I know I kind of changed this one a little bit. So, any questions on that?

[00:36:33]Any other questions that people have they want to see work through here?

[00:36:42]So, I have one.

[00:36:45]Um, let me see. I think it's on this exam.

[00:36:51]No, I think it's on practice exam B since it's newer material.

[00:37:00]Oh, where is it?

[00:37:05]Maybe it was on A. Sorry.

[00:37:21]Well, I'll come up with it. I know it was somewhere, but now I'm forgetting exactly where it's at.

[00:37:28]Oh, here it is. Um, so 29, right? So let's assume that I see a firm experience an increase in demand. Okay, if they do and they didn't have to spend any money, right? It's just someone like used their product and they saw a demand increase. This could also happen. How does each firm in a monopolistically competitive market and I actually drew one out earlier. How do they see an increase in demand if other firms exit the market? Right? So I could ask you a question whether or not it's what happens if firms exit the market to quantity and price or what happens if firms maybe entered the market. So in this example I had where are these monopolists competitive markets going to start out.

[00:38:13]So I've got my demand curve, got my twice as steep marginal revenue.

[00:38:20]Here's my marginal cost curve.

[00:38:29]So they set the profit maximizing quantity where marginal cost is equal to marginal revenue. Sorry, this looks like a W.

[00:38:36]This is supposed to be a M. They go up to the demand curve to set the price. So I've kind of drawn one where the price is equal to average total cost. So my profits start out as zero. If they experience a demand increase, what's going to happen? So maybe firms exit this market. I don't know why they would do that if profits are zero. But let's the thought experiment. So if I've got now a higher demand curve and a higher marginal revenue curve, where is the new point where marginal cost is equal to marginal revenue? It's now going to be at a higher quantity.

[00:39:16]Now it looks like the point I'm at price is equal to average total cost. So why would profit still be zero? What did I not yet do? Once I find the quantity to set the price, I go up to my demand curve, right? Just like a monopouist would.

[00:39:36]So now I see that when a firm experiences a demand increase for their product, so whether or not this is like the celebrity endorsement example, or if firms exited the market, I know price and quantity are going to go up. So if I think about my profit equation, my average total cost curve hasn't changed.

[00:39:55]So if price and quantity go up, I definitely know my profits are going to go up as well. Okay. So I think if we look back at that question, it said which of the following is true?

[00:40:08]The price they charge will increase.

[00:40:10]That's true. Profits will increase.

[00:40:13]That's true. But what about the markup?

[00:40:15]Right. Well, we said and the way I drew it might look similar here. But if I'm It's because I didn't quite get this right, but if I look at the quantity as I produce more, so maybe I want to think about it this way.

[00:40:35]If I increase my production, what is always happening? So, if I had like a um here's kind of my kind of price that I would set and my marginal cost as I look at higher quantities, right?

[00:40:55]It's going to be that gap in between my price I can set and if that marginal cost shifts down, so I'm producing a higher quantity, that markup is always increasing. So if I have a demand increase and I'm looking at higher quantities, my markup is always going to be larger. So I could do that through a marginal cost shift or I could do that through um a demand shift as well. So kind of knowing that that markup is always going to increase. So seeing some confused looks. I did this with marginal cost. Let me do this with demand to kind of make the the the point here in terms of the markup. So let's say I have my marginal cost curve here.

[00:41:33]I'll draw this really extreme so you can see this here. So here was my original kind of quantity price and marginal cost. If demand increases something like this, right? Um, well, you're close to uh what'll always Well, I didn't draw these. Hold on.

[00:42:03]I need to get this to be parallel. So, let me look here.

[00:42:10]Okay, now my marginal revenue curve is parallel to the old one. What's happened now at that higher quantity? The gap in between demand and marginal revenue is increasing. So kind of what has happened to my markup? My markup has gotten larger, right? That has to be the case just because we have linear demand and a twice as marginal revenue curve. When we look at higher quantities, that gap is always going to grow >> for like this. I feel like bucks off.

[00:42:45]>> Um I mean I I don't uh I mean if I'm talking about price, quantity, and profits, we went through those. Um really the only other thing I could ask you about is the markup. So, you know, if it's hard to kind of draw these out and thinking about the markup, maybe think about it this way. Is a markup a good or a bad thing for the firm? Good. I'm setting the price. The amount of money I'm making is above the marginal cost.

[00:43:13]If I get a higher proportion of the overall demand, I have more market power. Is market power a good or a bad thing for firms? You want to be in Kelly should all say good, right? So, if it's a good thing, what do you think is going to happen to the firm's markup? it's going to get higher. Right? So, that would be the only other thing I could ask you about is markups. And there the graphs are kind of difficult because really the reason why I didn't draw this one correct is because technically I started demand not at the axis. So, I it looks a little bit and I would have to have these like parallel shifts. That's the only kind of shifts I would give you. Um because I just said there was an increase in demand, not a change in elasticity or anything like that. So if it helps with the markup kind of relying more on intuition that when I have a higher proportion of the overall demand curve I have more market power and my markup increases other questions on that before we keep moving.

[00:44:07]So another thing another type of problem if you're thinking about maybe how could I trip you up? Not trying to trip you up but something that you could kind of get confused on. Let's and I think this was question uh maybe it's not no there's not a question but I wrote the exam so maybe this is a good one to know so what if I had a monopolistically competitive firm I have demand I have marginal revenue okay so let's think about I'll start out what do I want to do here do a weird one here so let's say I've got marginal costs and I start out at a point.

[00:45:00]Here's my average total costs.

[00:45:03]So, I set that quantity where marginal revenue is equal to marginal cost. I go up to the demand curve and what I see here is the price I'm setting is just barely above my average total cost. Right? So yes, my profits are positive.

[00:45:21]They're pretty small. Okay.

[00:45:24]Now, what if instead I don't have a shift in demand, but maybe I don't know, the government makes something illegal.

[00:45:32]I don't know maybe they start sending out the labor force I was relying on out of the country right my marginal cost of production might increase right so if my cost curve increases what's going to happen so here's my new marginal cost well if my marginal costs are higher so would my at well sorry I'm drawing without looking at what I'm doing why was that wrong cuz marginal cost has to average total cost at its minimum point, right?

[00:46:07]So, here's my new cost curve. Well, I haven't changed demand. Where is my marginal cost now going to hit my marginal revenue? So, it looks like now it's over here, right? So, when my costs increase, intuitively, I end up producing less.

[00:46:27]Now, this is kind of a counterintuitive result, but maybe the price I can set in this example actually goes up. The problem is even though my price went up, what also went up?

[00:46:43]My average total costs. And so now what is true about price relative to my average total cost? It's less than. So I went from small positive profits to now my profits are going to be negative prices below average total costs.

[00:47:01]So when I have shifts in my cost curve, I can also go through and think about what happens to this monopoly competitive firm. they'll produce less, potentially sell at a higher price, but because their average total cost increased, I'm going to end up seeing that those profits that I had before are now lower. Okay. Um, and the kind of reason behind why we didn't really dive into this, but if you wanted some support, because it's kind of counterintuitive, you might be like, well, yeah, but what if the price increased enough so it was above average? What if that? Well, we know that won't be the case because we're on the elastic portion of the demand curve.

[00:47:38]We didn't push it that far, but if you were thinking through this and you're like, Professor L, why would this happen? That's that's why. But we didn't dive into that, right? All we're thinking about here is we could draw these changes in the cost curves. And once again, I think the intuitive result is if my costs go up, I will produce less than before. And if my profit started out, maybe this is the way to think about it. If my profits started out at zero, demand hasn't changed, but my costs go up, what's going to happen to profits? They go down, right? So maybe instead of getting lost in kind of drawing this out, I think the intuition here in terms of quantity and profits is easier to think about when I have these cost curve shifts. And I might ask you the same thing, but if I lowered my costs, in which case everything gets kind of reversed. Can they shift the average cost per directly vertical >> like a parallel shift >> or like because like if you if it were to be like lower down it's still higher first average cost like this.

[00:48:36]>> So if my marginal costs go up because average total costs are calculated using those I would she see all we've done in this is use linear marginal cost. So I would have kind of this parallel shift in the two curves.

[00:48:49]I guess I didn't draw them quite parallel. This should kind of like taper off a little bit more.

[00:48:54]Okay.

[00:48:56]Now, what I won't do, and I think there was a question like this on the practice problems from module 13. I won't give you like a simultaneous change. So, I would either ask you about a demand change, what that would do, or I would ask you about a cost change and what that would do. I won't kind of combine the two. There were kind of we could work through it if you wanted me to. Um, you know, I could ask you that question.

[00:49:16]And I'm not going to, but there it's pushing price in opposite directions.

[00:49:20]Maybe we don't know what happens to to profits or price, but I'm not going to combine those two. Just know how to answer questions about a demand increase or decrease and just answer questions if the costs increase or decrease. Okay?

[00:49:33]And that's what you see on those practice exams. Okay?

[00:49:37]This is where feeding everything into AI might give you questions that are even more difficult and that might not pop pop up because some of those practice problems I gave you week to week were a little bit more difficult than maybe the ones I I show you on the practice fun.

[00:49:50]Okay.

[00:49:53]Any other questions that people want to see worked through here?

[00:50:04]>> Yeah. So, I'll draw this out.

[00:50:07]for us here.

[00:50:09]>> So, I've got firm one. It's the decision tree one, right? Yeah. So, let's say they have this choice to kind of set two quantities. They can set a higher quantity or a lower quantity.

[00:50:24]Now, this is an example where we have firms making sequential decisions. So firm one sets its quantity first and then in response to that firm two gets to choose its quantity. So it gets to go second. It's not simultaneous.

[00:50:40]So I think the resulting payoffs here were 250 250 400 300 300 400 350 350. Okay. So the way I'll go through and solve these is with what we called backward induction. Okay? So whoever is going second, we figure out what their best response is to person one's choices. So I would even do this if I had the exam in front of it. If firm one sets a low quantity, what should firm two do? The way I'll always write the payoffs, and I put this in words on the exams, but it's just the way we would think, right? One comes before two. So the the payoffs on the left are for the person one or firm one.

[00:51:28]Payoffs on the right are the person going second or firm two. So if firm one sets this low quantity, what is it better for firm two to do?

[00:51:39]Is 400 greater than or less than 350?

[00:51:45]Greater. Right? This yikes, right? We got to be able to answer that question.

[00:51:50]Right? So if 400 is greater than 350, they choose to produce a higher quantity. So we know firm two is not going to choose to do this.

[00:52:00]Now if instead firm one set a high quantity, what would firm 2 do? Is 250 or 300 greater?

[00:52:07]300. So they would set a low quantity.

[00:52:10]We know they won't choose to do this.

[00:52:13]Now knowing that we now say, okay, firm one can see these payoffs. They know what incentives exist to firm two. So if I produce a high quantity, I know firm two will always choose a low quantity.

[00:52:26]My payoff is 400. If I choose a low quantity, firm two will always set a higher quantity and my payoff will be 300. So what is better?

[00:52:36]400. So our Nash equilibrium where we have two circles now on like the same branch, right? That would be our Nash equilibrium. Okay.

[00:52:48]Any questions on this idea?

[00:52:53]Um, what if So, would this be an example of a prisoner's dilemma?

[00:53:03]So, what's the definition of a prisoner's dilemma? It could be applied to extensive or these normal form matrix schemes. It has to be a Nash equilibrium where both people would be better off if there was a different combination of strategy choices. If we were over here, both people are actually worse off. If we were here, well, one of them is better off, but the other isn't. So, no.

[00:53:26]Over here, one of them is better off, but the other isn't. So, no. We don't have any other combinations of strategies where both would be better off. Okay. Now, an example of a prisoner's dilemma would be, and I'll set these up so we'd end up with the same Nash equilibrium. So, what do I want here? I want uh so here I'll do actually no, sorry. In the games that we're doing, I only ever give you two and two. So, here we would never have we won't have this prisoners dilemma. In these extensive form games, there's like kind of no change I can make in these payoffs, at least keeping both of them consistent, where we would ever kind of see this prisoner's dilemma. Okay. Now, in a normal form game, we can have these. In fact, we see them a lot, right? There's a couple examples on the practice exams.

[00:54:23]Any other questions on this question before we kind of keep moving?

[00:54:30]Any other problems people want to see work through?

[00:54:37]Yeah.

[00:54:43]>> So, we've simplified since the last exam. Every model we've looked at, right? We're just thinking about these kind of constant marginal costs. I think there's one question where I gave you a depiction where you can see that portion, but it doesn't ever play into our decision-m. Yep. In terms of these markets and these firms, Yeah. So, the first question here should be something that hopefully when I look at the exam, everybody gets right. So if I'm thinking about perfectly competitive markets in the long run, what should always be true about my profits?

[00:55:32]They're zero. I mean hopefully I mean if I ask this as a standalone question, hopefully everybody answers C or D here.

[00:55:39]So this is where test taking techniques, you know, I'm not sure on one, but I know the other. I can at least limit my options down to two here. Now, if I'm thinking about what's going to be my average variable costs, okay, so I've got this price of 70.

[00:55:57]Why do I know the market above is in the short run?

[00:56:06]I have some fixed costs. Average total and average variable costs aren't the same thing. So, if I look at that price of 70, right? Um, was that what I was looking at? No. Yeah. Price of 70.

[00:56:19]If the price is 70, right?

[00:56:24]I might look at this and think, okay, here's going to be the quantity. I go down, look at the value of average variable cost. But in the long run, that price can't be 70. Why?

[00:56:36]If the price was 70, that hits marginal cost at a price or a point where that's above my average total cost. So profits are actually positive. So what will firms do?

[00:56:49]Profits are positive. Firms are going to enter the market. We said in the market that increases our supply curve which pushes the price down. As that price goes lower and lower, we look at this earlier. We end up at that minimum point of our average total cost curve in the long run. at that minimum point that is where marginal cost hits the average total sorry marginal cost hits my average total cost that's going to be the point where profits are zero.

[00:57:19]So what's going to be true in the long run? I end up with that minimum point with my average total cost. But in the long run, average total costs are my I've eliminated fixed cost. So my only costs are variable. So my average total cost and average variable cost will be the exact same thing. So I would look at these average total costs. When I know profits are zero, that's the minimum point of my average total cost curve for a perfectly competitive firm. That would have to be at a price of 60 which we said like in the long run everything's equal to marginal revenue equal marginal cost equal average total equal average variable. So in the long run my average variable costs are the same as my average total. I know I end up at that minimum point. So my average variable cost would be 60 there.

[00:58:08]So in the long run, we always end up with a perfectly competitive market at that minimum point of my average total cost curve. And my average total costs in the long run are the exact same thing as my average variable costs. Okay.

[00:58:26]Any other questions people want to see work through here?

[00:58:36]>> Yes. If I'm trying to set a regulator, that's this one, right? Yeah. If I'm trying to set a regulatory price here.

[00:58:43]So, I'm thinking about where does the single price monopolist end up? Well, they set the quantity where marginal revenue is equal to marginal cost. So, that's a quantity of 18. They go up to the demand curve to set the price price of 60. Price is above my average total cost. So, their profits are positive.

[00:59:01]This isn't as answering the question, but just to kind of as we got through.

[00:59:05]So I end up with this price of 60. If this was a perfectly competitive market, let's just assume that for a second.

[00:59:12]Ideally, that price would be where marginal cost or supply is equal to the demand curve. So that would be all the way down here at a price of 20. So this is a unique example where the market can't be perfectly competitive because if I lowered the price down to that 20 that value of 20 that I would see a perfectly competitive market end up at what's true about profits there well price would be a below if I extended that out below average total cost so profits would be negative what will firms do I can't hemorrhage money forever ex the market so if there is a monopouist and and I lower the price to 20. I would make their profits negative. If they leave, who's left?

[01:00:00]I had one firm. They leave, I have zero firms. What did I lose? The entire market. If I lowered the price down to 20 here, I wouldn't minimize dead weight loss. I'd actually maximize. I lost everything. So, what's the lowest possible profit I could get the monopolist to where they're indifferent about staying or leaving? Zero.

[01:00:23]So if I they have this kind of higher price of 60, I want to use a price ceiling to lower the price. Price is right here, still above average total cost until I get to that point on the demand curve where the price I've set is exactly equal to average total cost.

[01:00:41]That's the lowest possible price I could regulate this market to. Okay. So if I had wanted to originally my dead weight loss would have been the area in between supply and demand marginal cost representing supply. So it would have been like all of this huge triangle. If I lower the price to the point where profits are zero now dead weight loss comparing to that perfectly competitive point is this like small triangle. So, I've gotten dead weight loss to be lower, but I can't push to be any lower because if I lower the price anymore, profits are negative, the firm leaves, dead weight loss.

[01:01:18]So, maybe if it helps, the lowest possible price I can set is where my average total cost hits that demand for quote. Now, you'll notice here I sometimes get questions. Well, actually, couldn't it hit demand at two points?

[01:01:33]Yes, but it's always going to be the lower of those. Why?

[01:01:38]Monopolists always set a price that is what relative to a perfectly competitive market higher. So what am I trying to do to move to that perfectly competitive point? Lower the price. So that regulatory price is always going to be lower. It'll be that lower price where average total cost hits the main.

[01:01:59]Any questions on that idea before?

[01:02:06]Yeah.

[01:02:10]So there's a lot of local markets, right? Um like electric companies because if their fixed costs are huge, uh as soon as there's a second firm and we split demand, nobody can make profits because the costs are astronomical. If we both put up our own power lines, right? I mean, it's cra. So unless there's only one firm, nobody can make positive profits. The second firm leaves and then we're always just left with one. So usually it's examples where we have huge um like upfront costs or huge fixed costs. Right?

[01:02:44]Any other questions?

[01:02:49]So I've got one question that I want to work through. I don't I think it's on an old practice problem. Let me make sure.

[01:02:58]Don't think it's on practice exam. Yeah, actually never mind. It's right here.

[01:03:01]Okay.

[01:03:02]So, I probably wouldn't give you one that This is a little bit tricky. I was just trying to kind of use some some old pictures I had. I would give you one that has more grid lines, right? So, I'm going to draw this out just to make the point and then we'll kind of return to this. So, there's a couple questions and I saw some confusion on this as people were asking questions studying for module 13.

[01:03:26]So, let's say I've got an example where I'm looking at monopolistically competitive markets.

[01:03:34]I've got my marginal costs.

[01:03:39]Draw this kind of extreme. So, I've got my demand.

[01:03:44]I've got my marginal revenue.

[01:03:55]and I have my average total cost curve.

[01:03:58]So if I'm thinking about this monopolistically competitive market, they're going to set that quantity where marginal revenue is equal to marginal costs, right? They go up to the demand curve to then set the price. So I started out with a scenario here. Why would I think about this is in the long run? Because price is equal to average total cost. I know that the profits are going to be zero, right? Our profit equation was the quantity we're selling times the difference between price and average total cost. If these two are the same thing, my profits are zero.

[01:04:38]Now, if I wanted to calculate dead weight loss, right? What I would do is think about where would the perfectly competitive market end up at?

[01:04:49]Well, supply is representing mar or mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar mar marginal cost represents supply of the firm. So if this was a perfectly competitive firm, we'd end up at that point where marginal cost or supply hits demand. So if I was calculating dead weight loss, I'm thinking about comparing it to that perfectly competitive point. What is total surplus in the market? It's the difference between the marginal benefits and marginal cost. What represents marginal benefits in the market? My demand curve. So this monopolistically competitive market ends up at a lower quantity. So I miss out for every one of these units not produced. I miss out on that difference between my supply and demand curve. So if I gave you values this, you could calculate dead weight loss.

[01:05:34]Now we mentioned something earlier. I could also ask you about what's the markup. That's going to be my difference between price and marginal costs. And then we said if I was looking at a perfectly competitive firm um price ends up being exactly equal to marginal cost. So their markup was zero.

[01:05:57]Now when I'm calculating excess capacity, we will not compare this to where a perfectly competitive firm would be facing this demand curve. We didn't really dive into the reason why this exists, right? I'll I'll explain to you kind of that there is a difference and I'll try to give you a reason second, but we don't need to focus on the reason for the sake of this example. So excess capacity is going to actually be the difference and some of the depictions I gave you the perfectly competitive point ended up being the same as what we call the efficient scale production. That's not necessarily always the case. So our excess capacity refers to the quantity that this monopolistically competitive firm chooses compared to the efficient scale of production. The efficient scale of production isn't necessarily in these models where total surplus is maximized.

[01:06:54]The efficient scale refers to the point where average total cost is at its minimum or our per unit costs are as low as possible. So in this example that efficient scale of production that quantity is actually different than where the perfectly competitive firm would end up. Now in our perfectly competitive models we said well no we always end up at that efficient scale but that was because in a perfectly competitive market we didn't face this demand curve. We actually faced a horizontal demand. There's a little bit of difference there. We didn't kind of dive into that what that change in elasticity necessarily would do here.

[01:07:33]We're just thinking about if the perving competitive market did face this demand, which it doesn't, but that's the hypothetical. If it did, we'd end up at this quantity. So the dead weight loss created by the marginal, sorry, the monopoly competitive market would be this area here. But when we're calculating excess capacity, it's what how much how many more units would this monopoly competitive firm have to produce to get to that minimum per unit cost. So for us, just to put some hypothetical values to this, if this was 10, this was 20, and this was 25, our excess capacity is not 10 units, it would actually be 15. We're comparing it to that efficient scale of production or that quantity that would put us on that minimum point of the average total cost.

[01:08:23]>> Exploring how that applies to 45.

[01:08:25]>> Yeah. So if we're thinking about this here different values, but where is the monopolistically competitive quantity?

[01:08:34]Right here. So at 3.5, where would the perfectly competitive firm choose where marginal cost hits my demand curve? So if I'm calculating dead weight loss, it would be this area right here. Okay? So I could do what? 17 - 4 times 1 and a half. Now, if I wanted excess capacity, it's not one and a half units because I don't compare to that point where marginal cost hits demand. I compare to the quantity where my average total cost is at its lowest point. That would actually be what? I know it's this point because where does marginal cost hit average total cost at its minimum point? Now once again on the exam I give you more grid lines here so it's very clear like it's not 5.9. Now I didn't give you any numbers that would like be confusing there but like if I go down here it's right at six. So my excess capacity would be 6 minus 3.5 giving me that 2.5 out. So, I wanted to make sure I made that distinction because I know what's on the hand that you're not comparing it to where that perfectly competitive firm would end up. You're comparing it to the minimum point of the average or the efficient scale of production. That's the quantity you're comparing to. Okay.

[01:09:57]Any questions about that idea?

[01:10:01]Okay.

[01:10:03]Any other kind of one more question here?

[01:10:11]No other questions.

[01:10:15]Okay. Um, so I've got a couple more things I'll mention here in the next five minutes. Um, you'll notice these practice finals, you're getting about similar number of questions from each module, right? I think if you look across the two, there's a lot of similarities in the types of questions. So, I really would focus on these when you're studying for the exam. Okay? Now, some of the things I add in or talked about today or in that video that I posted that replaced Tuesday's class, I'd make sure I watch that, right? And kind of take notes like you would in class along the way as I'm working through those questions. So if you haven't done that, that is something I would strongly suggest is to excuse me, go back through that, watch that video because even though I'm working through practice exam questions like today, I might kind of expound or you know, expand upon or whatever, I might go further into depth and add some things in that probably did it for a reason, right? Could show up on that final, right? Um, now before I let you get out of here, I mentioned this and I think I have this set to be due a little bit after 10:50. So, I'm going to publish this here. I've got an additional in-class quiz. I've got it set to be do at 10:53, which is after class. Should give you plenty of time to get on and do this. I am not going to look at these results for one student. I don't I don't care. Well, I shouldn't say I don't care. I don't care what any one of you did. I'm not going to like look into, you know, exactly what your responses are. I care about kind of the total class's response. So, I'm always trying to get better. I'm trying to think about how to cater this class in a world that's constantly changing. So, I have seven questions here. There's no right or wrong answers, right? This is just me asking you about your use of AI.

[01:12:06]also for you to maybe do some self-reflection and think about did the use of AI not just impact whether or not I got a higher grade more of the quiz questions right or whatever it was getting the Canvas discussions out of the way easily but thinking about how did it actually impact your learning do you think the use of AI in these you know assignments leading up to or the quizzes leading up to exams did you rely on it too much did it improve your learning were you using it to better understand the concepts or were you kind using it to just kind of get things done. Um, so and then there's what did you use it for? Some other questions. If you could try to think, you know, I know you want to get these answered and get out of here, but just take the next couple minutes, try to put a little bit of thought into answering these. I'm going to look at the overall kind of responses across my two sections. Probably start to cater things. I really want to get an idea and kind of get some self-reflection on on how you're using it, whether you think you're using it effectively, and maybe ways that I can kind of hopefully incorporate into the class of how to teach you to use it more effectively and hopefully what some of your other professors are going to be doing as well. Okay? So, make sure you're getting on getting all of those answer to get the full credit. Basically, what this will do is instead of dropping your four lowest, if you did this today, I'll drop your five lowest. All right? So it kind of like replaces one of the right drops another lowest view. If people aren't here and they didn't do it, I still kind of drop the same number. It shouldn't hurt or help them or help hurt or help.

[01:13:30]It won't hurt or help them, but if you do it today, it'll help you. Okay. Um other than that, good luck studying those extra CL sessions tonight. My office hours on Monday, I will see you guys on Wednesday.