Let's do one more of these which is the more stable conformational ring isomer. So here we've got this one two three Trimethylcyclohexane And you can see they're all pointed towards us. Okay, so they're all pointed up so the first thing again you want to do is draw the actual cyclohexane ring and Then show the ring flip structure Like I always say get good at this prior to the exam because They're not the easiest thing to do as you can see even mine This one's not as good looking as that one and that's what it tends to be. Well, I'm right handed But anyways remember what we said so Label your carbons one two three and you can start that labeling wherever I like to start with one at the top. That's just my personal preference and Ups, I'll just like to put as axial on this this one. So I guess we should label in here too. So one two three four five Six Okay, so we got the axial there Two is Up right, but down would be axial here. So up must be equatorial and then three up Remember when that's pointed up it's going the up is going to be axial when it's pointed down the downs This one's pointed up. So up is axial. Okay, so let's go ahead and label our ring over here. So we've got one two three four five six Remember it's just like an envelope. You're pushing that side down Okay, so if it's axial over here, then it's equatorial over here. So one two Equatorial over here. So it's axial over here You don't even need to know that because this one's pointing The point is pointed up. So the axiom is up and then Here of course Okay, so here we've got how many axioms how many equatorial so two axioms one equatorial Here we've got one axiom two equatorials So this one's more stable Because remember equatorials are more stable than axioms. So So hopefully you can do these do a few of these problems in your book Find them in the back your buck. I'm sure they have some okay


So what do you want to tell me now? I says, what are you still doing here?  I thought he cracked the pool. I wish I was big. Just you once.  What do you mean I'm funny? You know, it was a good story. You're just funny. The way I talk, what? It's just, you know, the way how you tell a story. You're just a funny guy. Funny how? What's funny about it? Donny, you got it wrong. No, Anthony.  That's what I said. Funny how? Just, you know, you're funny. And let me see if I understand this. No, maybe I'm a little messed up, but funny how? Funny like a clown. I amuse you. I make you laugh. I'm here to amuse you. What do you mean funny? What's funny? You know, how you tell a story? No, I don't know. You said it. You said I'm funny.  Tell me, what's funny?  I can't.   Was he taken prisoner? I wonder about you sometimes, Henry. You might fold under questioning.


All right, folks. So we are going to do a deep dive. It's been a while since we've looked at one of CNN's voter panels with Alison Camarota and usually, you know, if anything, these are entertaining, but sometimes they're genuinely insightful Other times they make me lose faith in humanity But this one it got my interest because it consists of six people three of them Former Trump supporters the other three current Trump supporters now They're not asked generally about why they support Donald Trump These questions are all about whether or not they support Donald Trump's handling of COVID-19 And even if you're supporting Donald Trump for some policy reason, like you want the wall If you genuinely think that he's doing a good job handling COVID-19, then I question your sanity So with that being said, let's go ahead and watch. I haven't seen all of this. I've seen some of it I've skimmed it. Um, and this one is uh, it's something so Take it take it away, Alison Show of hands, how many of you voted for president Trump in 2016? Okay, all of you voted for president Trump show of hands, how many of you plan to vote for him again in november? Okay, three hands went up got a posit right there. Okay After there have been 150,000 americans who have died because of COVID-19 an eviction crisis coming And this president is focused on statues like To still support him you have to be in a cult like you've drank in the Kool-Aid And you just believe that he can do no wrong. I mean, there's no other way To rationalize this. Um, but nonetheless, I'm not gonna get too much here into the uh, overanalyzation of this because uh, I think this is gonna get spicy Daniel tell us your thoughts. I believe that his handling the pandemic has been horrendous I think his lack of accountability and Um, an old political term he waffles on everything. He he did say this. He didn't say that and and He meant this but he didn't mean that He's totally unpredictable. I don't think any okay I'm glad that you have come to your senses, but is that really a new phenomenon with donald trump? I mean, wasn't he contradicting himself like every five minutes in 2016 and 2015 like For you now to have this revelation. I mean You can argue that it's good that he changed his mind and I can kind of give you a pass if you evolved politically But I mean donald trump has always been the same person He's always been a bumbling buffoon and an imbecile who's narcissistic So, you know, it's weird that you'd point this out now.  I know leaving a colt might be a little bit scary But you've done it. You made a huge step and I I applaud you for it Anyone could have handled it any better listen to health experts when donald trump says something about ingesting lisa Don't take it. Obviously. That's an absurd statement.  They don't want to believe that daddy trump can do anything wrong It's just ridiculous He should not be speaking on health matters Then why do you support him? He's the president wasn't taking it as seriously as he should but the entire No, no, no, no, you just said That it couldn't have been handled any better by anyone else And then you say he's not taking it seriously like there's just no consistency And uh, she said let me go back a little bit that the entire government has failed Yes, of course, but I mean leadership Is important during this crisis So if you're admitting that downaltrum has failed in some areas then overall How could you with the straight face say oh well nobody else could have really done a better job than him? I mean if they just had basic common sense, they probably could have based on your own reasoning Wasn't taking it as seriously as he should but the entire government failed us. They were focused on impeachment as COVID was spreading What? Impeachment was over in January. Was it not like am I am I missing up messing up the timeline in my head? Like what are you talking about? That's what they were focused on they were So smug show of hands have any of you had a friend or loved one or know someone who got very sick with COVID and or died It's funny how the two people uh, two of the three people who abandoned Donald Trump They Have people who or they know people who have COVID-19 interesting Okay, so okay never mind. I guess three three of the three people I don't know why that took her so long three of you know people who got sick Tommy tell us what you think about president trump's response to coronavirus Well, um, they didn't get extremely sick and died But I had a nephew and several friends that have tested positive for COVID I will say this I am a business owner my wife and I own a fitness a 24 seven fitness center We had to close our gym for 84 days. We've had the business for seven years Uh, and I just want to point out again that this half this all happened While Donald Trump has been president Yeah, um, and Like I feel like it shouldn't have to take you knowing someone who's been affected to actually take this seriously It's extremely serious like my friend One of my best friends has had COVID-19 now for like three months.  Um, I think that she caught herself. She was going to say pandemic probably Uh, she's a Trumpy person uh, chud So I'm guessing that she's a little bit of conspiratorial Let's let her carry on who I do know who have tested positive for COVID my in-laws Okay, one she had to wear the mask because she's got allergies I think the breathing of her own breath and having to you know, deal with allergies. I think that got her sick What?   What are you talking about?   She goes home had fever for two days. She's fine now Good that doesn't mean that it's not serious.  She's older I guess i'm confused about your point. I mean, do you think that people are not done? Call her a jackass. Alison do it call her a dipshit What i'm trying to say and make a point to is it 382 million americans 4 million of tested positive and 145 thousand have died. Yeah, so you're going to live with those numbers. Those numbers are okay for you During the math, no No number of death is okay. If you do the math is a 99.9 survival rate What if you do the math, it's a 99.9 survival rate What math are we talking about like what numbers are you plugging in because that's not what i've seen like the rate of death for covid-19 is like Two or three percent And i'm gonna pull it up because i'm curious because i don't know what she's doing To get this number 99.9 percent like that would be That would be a different story like it's still be serious like you're still sick.  So look at these countries who are affected. So the united states mortality rate right here Just under four percent and it rose to uh, almost six percent in may So i don't know where she's getting this number from um Wow in italy it was like It is actually as of july 28th uh 14 percent that's insane. So no this isn't This isn't something where 99.9 of the people are okay And even if we assumed that it wasn't as fatal as she's saying it is There's still long-term health issues that covid-19 Causes I mean scar tissue in your lungs that give you lifelong breathing issues blood clots in younger people.   I'm not going to give them heart disease This is a contagious virus What's not to understand Also three times more deaths of accidents and car accidents, but we didn't shut down the interstates and take people's cars away Like our car accidents contagious like do they spread? I mean it's it's contained to an area Like you could see a pile up, but I mean like this isn't the same thing That's a false equivalence and I love how like she's clearly glancing at her numbers Because she's like she's she's bringing the facts.    What breathing problem asthma like what are we talking about here?      I don't know what to tell you.  Um, you probably she she probably does not believe in it Like you know at the beginning when she said it's a pandemic.    You fence that are take a stance I also do believe that uh here in america We have a lot of serious problems that need to be taken care of that honestly have been allowed to fester for far too long I don't think there's anything trump. That was a very like milk toast centrist answer Dad that would make his supporters at our dug in not vote for him Yeah, because it's a cult say it's a cult in my opinion It's a cult say then they would then they would be thinking like me right now I'm hearing a repeat of 2016 the anti trumpers the people who are like, oh, I can't vote for him It's not fair to call someone like me and never trump her because I voted for the man in 2016 Correct. Thank you. Yeah Yeah, you all did. I mean you all did it's um what i'm saying is a rhetoric It's a rhetoric of the never trump movement. I didn't say you It's a 2016 Okay, I am genuinely worried that this lady is like going to get a show on fox news or OAN Like she she has all the talking points down like she has her numbers from info wars Uh, she she's got it down. She has her talking point.   We gave him the opportunity. We gave him The chance it's what he's done in office not What he didn't shouldn't have though That's not a good thing on his twitter feed or his personal life or private life prior to becoming president I think we need someone with the temperament of donald trump even though sometimes he is unpredictable I think we need the temperament of donald trump because he is someone who is willing to call out Well, other people are will refuse to call out and I think that's something that we really need right what The temperament of donald trump so the temperament of like A six-year-old who's throwing a tantrum in the grocery store The temperament of donald trump Like out of all the qualities in donald trump you could say look, I like that.  I think it's funny.  I saw an interview with donald trump with the guy from barstool sports the other night And something that donald trump said hit me It pretty ironically he said, you know that the preceding years prior to me announcing running for president were the best of my life I was I can't remember his exact quote But he was fabulously wealthy and had this great life And I would just like to remind him that barack obama was president during the best times of his life So if donald trump loses we will get through it Not last comment because it's like The thing that irritates me is they go from like being a magica to like a full-on like a democratic party sick of fat um when you know barack obama's years That wasn't good for most normal people like rich people were doing fine But obama was bombing seven different countries. He ramped up the drone war that george w bush started I mean look If you're leaving the maga cult and you're going, you know to Uh the democratic party's sycophancy side. I don't know whatever, right?     Why aren't they dropping dead?  I swear to god if I see this lady on like fox news or oan or on youtube For whatever reason and she starts to like become famous I'm gonna lose my shit Because this is the exact person who would like make it in right wing media Who like the billionaires would fund because she's bombastic and like she's she's confident Okay, yeah, we're done here. Uh, nothing left to see folks. Yeah I


It's already ready, so we can announce it's Plotomiro Caffolla from Durham University, and his talk is dissipation and lubrication of solid-liquid nanointerfaces, complex balance of substrate topography, molecular diffusion, and environmental conditions. So it's a long title, yeah? Yeah, it is. So it's always yours. So thank you very much to the organizers for the invitation. It's a real great pleasure and honor to be here. And as the title and so was suggesting, and above all, as we have seen over the last couple of days, lubrication and dissipation are really complex problems. So today I would really like to focus on the importance of molecular ordering on lubrication, by our defects in the fluids, in the surface, and microface separation impact the molecular ordering and hence lubrication. And finally, a very, very quick look at the potential smart pathway to control ordering and lubrication. So before actually going to the core of the presentation, a little bit about myself. I'm a postdoc at Durham University. My main research interests are in the area of nanoscale interfaces, particularly solid-liquid interfaces and transition metal oxide interfaces, and also some interest in developing new technique biomedical studies. So going to solid-liquid interfaces and lubricated friction, we all know the crucial importance of lubrication in a wide range of systems, our joints, engines, electromechanical systems. And we also know that this is a very complex problem. So for example, if we zoom in in one of these contact, and we consider just one molecule, looking at a perfectly flat surface, then we can relatively well understand the system. The problems arise when we go actually to the real case scenario, when the surface is not perfect, there may be contaminants in the fluid, and so we have to worry about solid-liquid interactions, liquid-liquid, potential jumping, geometrical effects. So to tackle this problem, I used a combined approach, mini-experimental, based on imaging the liquid-lubricant solid surface with atomic resolution. This is combined with nanorealogy, with highly localized shear measurements. And what possible, I did also some molecular dynamic simulations so as to get our better insight into the dynamical evolution of the lubricant molecules. Looking at the details of the experimental techniques, they are both based on atomic force microscopy, AFM. Imaging is done in amplitude modulation, so we oscillate the cantilever with a constant oscillation, sort of probing the interface like the stick of a blind person would do, basically. This is complemented with using the AFM also as a nanoscopic shear rheometer. So what I do in this case is that I laterally oscillate the sample and I record the induced torsion of the tip. And the magnitude of this torsion gives us information about the magnitude of the lubricated friction force. And the phase lag between this torsion and the oscillation of the sample gives us information about the viscoelastic properties of the sample, with a phase of zero for a perfectly elastic coupling, conservative system, and a phase of 90 for a perfectly dissipable viscous coupling. So let's see how we can use this combined approach to study the ordering of the lubricant molecules. And the first case study is based on axial solutions confined between the AFM tip and mica. Yeah, we have a pictorial representation of the lattice. And if we have just pure water due to the nano confinement, epitaxial effects, the water molecules get well-ordered in a nice, ice-like structure. But as soon as we introduce point effects in our fluids, in this case ions, because of the electrostatic interactions, they tend to disrupt the hydrogen bond network of the water molecules. And what we observe is different absorption profiles depending on the charge density of the ions. And they have a huge impact on the dynamic response of the system. So it's very clear the response of the system just in pure water. And when we add ions, so when we add ions, the system is more disordered. It's less able to resist when applied load. We see the decrease in the shear force. And we see that the shear phase suggests a much more liquid-like behavior. Still, the linearity of the friction force with respect to the applied load allows us to extract an effective friction coefficient mu, which we can model as a function of the charge density of the ions rho, and an empirical parameter lambda, which captures the thermally-activated motion of the ions. They need to overcome an activation barrier per unit charge, Ea over Q, with the thermal fluctuation over the megalattis favoring the jumps of the ions between adjacent sides. And both Pietro and Nicola gave really nice talks about Prant-Tomlinson model. So to a certain extent, this is an adapted version of the model. The FM tip provides energy to the ions, and they need to overcome an energy barrier represented by the interactions with the surrounding fluid molecules and with the surface. So take a message from these first case studies that point defects in the fluid that disrupt the order and hence reduce the friction force. Let's look at another type of defects. In this case, defects in the surface. And in this case, we look at a system that is quite relevant for industrial application, since our fluid molecules are made of squalene, commonly found in lubricants. And the surface is graphite, and we know that carbon-based surfaces are quite common in contacting parts. And the type of surface defects that are considered were step edges. So here we have a classical step edge. And if we are cold enough, what we see is that the molecules tend to self-assembly in sort of lamellar structure, very similar to what Roland was saying on Monday. And this is very clear. In particular, if we take the derivative of the topographical image, something that we call the amplitude channel, it's very sensitive, emphasizes the local variation. And we see that when we adopt the system, then the order progressively vanishes, except in a region in close proximity of the step edge. And then when we further ramp up the temperature, then the order progressively vanishes. And finding disorder at the top and the bottom of the step edge seems a bit counter-intuitive if you think that the order persist in particular close proximity of the step edge. So you would expect actually the geometrical singularity to disrupt the order, not to promote it. Molecular dynamic simulations run both on the top and the bottom of the step edge, seem to suggest that there is a loss of mobility in proximity of the surface defect. So this is why there is an increase in order. So this is a completely different scenario from the case when the ions were actually disrupting the order. So what happens here is that in proximity of the step edge, the molecules have less configurations to stably absorbed, and so there is a reduction in entropy. And this, of course, comes with a cost. So if we take our nanorealogical measurements in close proximity of the step edge, we see that the friction force is much higher and the system behaves much more like a solid-like way. The molecules are stuck. So being really the relaxation dynamics of the lubricant molecules dictating the lubricated friction force response, what we can do is to examine the evolution of the system when we change the shear velocity and the temperature. And what we find is that increasing the shear velocity, the molecules have less time to explore available configurations. So they are stuck in their position and explore a greater friction force, something very similar to happens when we decrease the temperature. And actually, I use all this data taken on different shear velocity and temperature to develop a quantitative model to describe the dynamical response of the shear lubricant. And overall, the response of the shear force curves is this. So we have an initial ramp-up corresponding to an effective yield stress than a plateau-like region. The yield stress presenting a number of irregular features I actually focused on the linear region for the fitting. And in this linear model, the intercept correspond to a yield stress and the gradient to an effective dynamical friction coefficient. And what I found is that it's really the yield stress that depends on the velocity and the temperature. When it comes to the velocity, the dependence is a power law. With an exponent that is classical for a system where the thermal fluctuation are lower than the activation energy, but still able to promote some molecular motion. And what is really interesting is that in this firmly activated motion, the activation energy, EA, is basically just four times smaller than the latent heat of vaporization of squalene in the bulk. So at the interface, of course, the molecules have fewer neighbors, but still this EA is very much the energy needed to break the intermolecular bonds and get a molecule free from the cage of his neighbors. So it's a penalty cost that we have to pay, but once we have paid that, we are on a free ride, and so the friction coefficient does no longer depend on the velocity and temperature. And take on messages from the second scenario is completely different from the point defects in the fluid. Surface defects here actually promote order, and they also provide us with a complementary framework to better understand the usual roughness increase of friction that we often experience in contacting parts. So far, what I have been examining are relatively ideal case scenarios, but as Rob was mentioning on Monday often, we have in our system an amount of undesired particles, not just point-like defects, and for example, water molecules. They are undesired in many car engines' applications. So what I have here is an hydrophilic alumina silicate, MICA, very common in engines, no MICA, but alumina silicate, and on MICA what you have in ambient conditions is that there is a nanoscopic film film of water absorbed on it, and then I use the hexadegan as a model lubricant, and what we see if we track the evolution of the interface with temperature is that when we ramp up the temperature, the water nucleates forming these water nanodroplets, they increase in size and number with temperature and they coalesce when we cool down the system. And these nanodroplets have a huge impact on the friction force. So if we compare the friction force on one of these nanodroplets and on an homogeneous area of the interface, well, there is a twofold increase in the friction force. So this is very much related to a penalty cost that we have to pay because what we are trying to do on the water nanodroplet is that we are trying to mix two separated phases. And of course, this anomalous temperature behavior can be well rationalized because here the temperature effectively shifts the probability of water nanodroplets nucleating. So the higher the probability, of course, the greater the number of water nanodroplets that you find on your surface, and the greater the friction that we experience. But we can shift the equilibrium of the system also playing with the water content of the system. So we can sort of dry out the atmosphere, decreasing the probability of the water nanodroplets to nucleate even at a high temperature and get a relatively low friction force at all the temperatures. Or we can actually saturate the atmosphere with water. We increase the probability of water nanodroplets to nucleate and we increase the friction force. And what we have seen experimentally can be rationalized with a simple thermodynamic model with water and hexadegon. Of course, we know they don't like each other, but they have a similar work of adhesion when it comes to the mega-surface. So they compete against each other for the substrate. And once the water nanodroplets get the size that we have seen experimentally, then they are thermodynamically favored in their spherical shape as they also minimize the interactions with hexadegon. So this is very much a liquid-liquid problem. So what we can do is that we can add a surfactant model. Now, if I work in the UK, I'm still very much Italian, so I use oleic acid, the main component of olive oil. And basically what we do is that with this surfactant molecule we reduce the interfacial energy between hexadegon and water. So we decrease the probability of the water nanodroplets to nucleate and we decrease, hence, the friction force at any temperature. So take on messages from these free-case studies is that the ordering of the lubricant plays a very important role in lubrication. And we have seen two different types of response when it comes to very localized defects. So defects in the fluid ions, they disrupt the long-range order of the water molecules and reduce the friction force. Whereas in the case of surface defects, they result in reduction in entropy and then increase in the friction force. And finally, we have seen how the microface separation affects also lubrication and an effective way to help with this is to use surfactant molecule. So what is really cool to me is this controlling of the lubricant ordering. And we have seen that temperature and humidity can do that, but probably they are not the tools that we would like to use. So something that I have started recently doing is to investigate how we can control the order of the lubricant using, for example, magnetic field. And so here I have used... These are preliminary experiments where I used a magnetic ionic liquid. Here there is a steel interface with some iron oxide particles deposited on it. And when the magnetic field is off, well, the magnetic... And we see that there is basically no magnetic signal. The friction force is pretty much homogeneous with the magnetic ionic liquid helping also with the roughness of the iron oxide particles. But as we switch on the field, well, in this case, this ionic liquid can perform these domains, microface separation, Nicola published a paper a few years ago about this ionic liquid, not this one, but generally speaking that they can give rise to microface separation. And hence we have again an increase in the friction force because probably what is happening here is very similar to the hexadec and water case, when we try to mix two differently separated phases. This is pretty much stuff. Hopefully maybe if there will be again this conference next year within two years I'll be able to show you more data on this. I would like just to finish off highlighting this conference in Durham that I'm organizing. So thank you very much already to a number of invited speakers who have confirmed their presence. So I hope I'll see you many of you there. If you'd like to come just drop me an email. And thank you very much again for your attention. When I was talking, there's already very nice work. I'm wondering about for the squalane on the graphite was the surface. What was the tip material? The tip material was made of DLC, diamond like carbon. I really expect some interactions, significant ones I think between those molecules in the tip too. And so I'm wondering if you've thought about, I think this is a hard question to answer without simulations, but could there be some organization and influence of the tip, organization of molecules interacting with the tip? And the reason I'm asking is, is the shearing, I'm wondering if the shearing is between the tip and the molecule, or is the shearing you're measuring between molecule adhered to tip and the molecule adhered to surface, both of which are interesting. Yeah, so definitely that is a very much a possibility. What I'm trying to do is to replicate also those experiments using different tips. But at the moment I don't have any definite results, but it's a very nice idea and thanks. Yeah, yeah, yeah. Basically, I don't have a definite answer, because I don't have yet the complete data set for that. And above all, as Rob has you were suggesting, there will be any dose for some mega-dynamic simulations, and I have some limited experience with that. I was curious about the nanodroplet experiments that you showed, because one imagines that if the contact angle of the nanodroplet is sufficiently low, they actually should act as an additional lubricant, so as if you had a liquid-infused surface. So I was wondering whether you can tune the contact angle of such droplets, because in the end, not always they should act as defects, but on the other hand, they could be. Yeah, so we, in the experiments that I run, I couldn't control the angle the nanodroplets were at. Also remember that when we run our experiments, they run completely with the tip immersing the fluid. So basically, imagine that there is this huge drop of hexadegon, which is the dominant liquid, because we were talking about 200 microliters of hexadegon with the tip completely immersed, and then this nanoscopic film is like two nanometers. And so what you are doing is that basically you go, this is what I have in my mind, is that you go on one of these droplets, and that doesn't just act as a pinning point, but there is also, you are trying basically to remix the water with the hexadegon while you shear it. So definitely anyway, the point of contact angle is a good one. Try to do some more experimental, the macro scale for the paper. That was more related to work out, to the work of addition. Yeah, controlling the contact angle is definitely something to explore. Thanks. We have to proceed, so thank you again for a nice talk.


here today on an adventure in the south of Israel right behind me here is what's called Mahtesh Ramon.  You can see there's some a little few rock formations down there but not a whole lot besides Ibex's Ghazals and some other forms of wildlife. It's 40 kilometers however all the way down and two to ten kilometers across just outside of Mitsperamon which is one of the southernmost communities in Israel literally right in the middle of the desert. I was reading last night on Wikipedia that when this was built or formed this community in the 1950s so relatively soon after the foundation of the state the foundation of the state in 40 to 48 this was considered a very very tough place to live. There was a supply truck that would literally stop by the settlement once every two weeks so it was really a labor of love to live here in a very very difficult life I can imagine for those who were here.


It's never the same. Anytime you take a cut of cold out of your going someplace, man has never been before. Each day you go into the mine, your workplace is changing. No two days is the same. And so you can't let your guard down. You've got to be aware. As safe as coal mines are, they are a safe place to work and yet it's still a dangerous occupation. Last year nearly 70% of the underground coal miners that were killed in coal mines were due to roof and rip fall. That's the highest percentage of underground fatalities that roof and rip has had since we've been keeping records. The percentage of underground fatals climbed due to roof and rip falls near 70%. And we've got to do something to turn that around. We began putting out information on serious accidents that were happening in an effort to get these roof and rip fatalities back down on the downswing. Here's two coal miners, two separate incidents, a miner operator and a roof boulder operator who seemed to be doing everything right. They'd examined their workplace. They were well under supported roof. Others had been in the area and examined the workplace and still they got hurt. It can happen to you. We turned the slider to get the miner in. It kept both sides here. And as I was loading this car, it was just about loaded as he's sitting in here and I'm standing in this area right here. Okay, there's pins in by me all the way through, pins back behind me, pins around here. None of them been cut out, nothing. But standing right here in this area, I'd look back. Everything was going fine. Look back at him about that time when it caught me out of this corner and from what I could see, it came from this way out. Enough to get me on my left side, more or less knocking me down enough that my minimum of my own weight took me into the unbolded area. As it had me down, I could see the car driver with his light on and mine had been knocked and my head had been busted and knocked off. So here I am in the dark and I see his light coming to me. He said, soon as I saw you go down with no light, he said I knew something was wrong. I got off the car and then I ran over to Louie. He was having a hard time breathing. I mean, he couldn't hardly breathe getting, you know, to catch a full breath. As he gets to me, he said, you're all right. All I could get out was, I think so. And I said, I need a breath. I need to get it off of me. The piece that was on me was ever been probably eight foot, eight by five, something like that. So here he is. He tried to lift it enough for me and him together with my right arm called under it, pushed up, so I got a breath of air. After that rock fell on me, I couldn't get it off of him. I felt, I felt bad, you know, I felt like I should have been the one to get the rock off of him, you know, but I couldn't, I couldn't do nothing about it. I had to leave, I had to leave the Louie land there until I had to go get some more help. And when they came back, they started to come up and I told them by this time, I said, just take your time and look around. Well, all the pins were still tight. And after they looked, they said, that is odd. And my left leg, it had broke the smaller bone in the left leg and just a crushing blow to the heel on the left leg. Six ribs broken total and the sternum was fractured. Well, he had his remote station in front of him, holding his remote station, and when the rock fell, sort of assuming it hit him, struck him on the head, came down, hit the remote station and kind of made him pitch forward. First thing I asked him was, you wouldn't have them under pins? Well, he said no. He said I was, he said I didn't look up. He said I knew it wasn't past the last bolt. And he said it just all of a sudden come in and got him. I didn't think the breathe like that would fall, you know, after it has been pinned up. But after I've seen that it can fall out in between the pins and everything, it makes me, you know, it makes me kind of scared a little bit. It can happen to you. The accident happened. It occurred about 4.30 in the morning. I was waiting on my buddy to come back from dinner. They just got through blowing a crosscut through, went around to blow another one through. Me and my manager topped for a little bit. My buddy came back from dinner. I bolted the corner to the left. We moved the roof bolt or imposition in the crosscut. Start our first roll, the bolt to blow through. We bolted our wing bolts or center bolts. So I moved my boom over. I set it down, went back there, changed a bit. There's a lot of that top. It's limestone after a foot or two. And went back there to get a roof bolt and a plate. And whenever it fell, it pushed me towards the boulder. And the blunt of the impact of the rock hit my lower back. And whenever it hit my lower back, that's what crushed the pelvis on each side, broke my tailbone and messed up four vertebrae, the wings that hold the muscle. If it would have came directly on top of me, it'd have killed me. And when you start to react, it's already on top of you.  I think I was kind of stunned. I never did lose consciousness, no. All during this here. And I never felt any pain till it moved me. I knew I was scared. I knew I was hurt bad. I mean, he was in a lot of pain, especially when he moved his leg with that ankle or his foot actually just about turned all the way back around the other way. And like I say, they got him stabilized, got him on the backboard and got him on the man trip and took him out. All the pre-shift examinations had shown that everything was okay as far as the roof conditions go in the area that they were working in. As a matter of fact, from what I was told from Gary, that he and the mine manager had just been in that area just a short while before that and carried on a conversation concerning the conditions of the mine and the mine roof and different things that were going on in the area. After this happened, we went to each shift, we went to each crew and re-emphasized the importance of checking areas. I've thought about it and I've thought about it and I've laid in bed and thought about it. I laid in the hospital and thought about it. I think I did everything that I could with the experience and the knowledge that I had in the mining industry. And if I'd go back into the mines today and I'd seen the same thing, I would probably say it's okay. It can happen to you. I think no matter what job you do in the mine, especially if it involves in the face area and roof control, I think you've got to be extra cautious at all times.  Sometimes there's some loose slate up there or something that you might not be able to see, but your buddy can see it from his standpoint. It's important to communicate and especially about roof hazards. You have to be able to communicate those things to each other and let them know what the top's like and let them know what kind of conditions you've got. And certainly if you've got conditions that need to be corrected, correct those. I see more and more where IMFSA is taking education and training role, I think, to a higher level. Trying to talk with the miners, to try to get them to be aware, work safely, and to always follow the roof control plan, to know the roof control plan, to provide them with some information to impact them. You know, like the Preventive Roof Rib Outreach Program. Prop was one step in trying to reach out to miners. When we go underground and give safety talks, we have these best practices cards. Our inspectors take those out and provide those. And these are things that have been offered by coal miners themselves. I mean, if you want to know how a roof-bowling machine operates, talk to that roof-bowler operator that operates with it every day. You want to know how the roof's acting? You go talk to your roof-bowler operator. They're our best source. We've got to make an impact, no matter how we can do it. I mean, if it's training, if it's talking more to the miners, if it's getting to the miners themselves or their families, we've got to make an impact. And roof and rib fatalities is one thing, but we've got to impact also miners that are being injured. Those serious injuries and accidents that are occurring are potential fatalities. Being in a serious injury like this and almost losing your life, I look back at it now and I think I would be a lot more cautious in the mines and where I walk and when I walk, I look. When I go back to work, I want to try to find a little bit further place to be that I can still see what's going on and still do my job without exposing myself to any more than I've got to. To all the miner operators, at least try to stay at least two bolts, maybe two or three bolts behind the last row of bolts. Mine to mine, you could be a roof-bowler in one mine for 10 years and move 30 miles away. The strata conditions is different. The top conditions is different.  And the message brought forth there is that the bad top you're always looking at, you're always checking, you're double checking. And if you get in a good top, a lot of times you let your guard down. You need to make your own examination, scale down any loose top that you see, any fractures in the roof, make sure that you support those properly. If you've got different conditions, if you've got heads in the top, or if your top starts getting a little grummy, pay more attention to it. It just pays to watch everything. The ribs in the area, a lot of times they'll be loose. We always teach them to pry those down as well. You can never be too careful in a coal miner. We want coal miners to be able to go to their job, work safely at their job. We want to be able to go home to their families. It can happen to you. Don't think it can. Some IMSA best practices include make thorough examinations of your work area, correct hazardous conditions, communicate to co-workers about roof conditions, know and follow your roof control plan, stay at least two roof bolts back from unsupported roof, always be aware of your surroundings and watch for changing conditions. And do not go under unsupported roof. Remember, you cannot outrun a roof bolt. For more information, contact your local IMSA office or visit us at our web page at www.msha.gov.


So, welcome to the third session of Managerial Economics, we are on the first model of managerial economics which deals with the introduction and fundamentals to the managerial economics. So, if you remember in the last class, we just started our discussion about the marginal analysis. So, in today's class, we will talk about the marginal and incremental analysis first. Then we talked about a model of any typical economy, how it works, what are the different sectors, how the flows works between two different sectors. And then we will focus on the basic tools of economic analysis and optimization techniques. So, coming to the marginal analysis, as we discussed in the last class, marginal is always a unit change in any of this variable, whether the variable is cost, whether the variable is revenue, whether the variable is utility. Whenever there is a change in the output, what is the corresponding change in the cost, what is the corresponding change in the revenue or what is the corresponding change in the utility? That is the marginal cost, marginal revenue and marginal utility. So, marginal cost is the change in the total cost because there is a change in the output. Marginal revenue is the change in the total revenue because there is a change in the the output, output leads to revenue and marginal utility is the change in the utility because the consumer consumes one more unit of the output or one more unit of the product. So, marginal cost or marginal revenue or marginal utility is the total cost utility revenue of the last unit of output. Whatever the total cost, whatever the total utility or whatever the total revenue of the last unit of output, that is the marginal cost, marginal revenue and marginal utility of the corresponding unit. So, if you consider, if you need to identify what is the marginal cost of any unit, then it is the total cost of any unit minus total cost of n minus 1 minute, where n is the number of unit of output. So, this marginal cost of any unit is nothing but the total cost, whatever comes in the last unit of the last unit of the output. So, we know that profit is the difference between the revenue and the cost. Whenever there is a change in the total revenue due to unit change in the output, that we get as the marginal revenue. So, mathematically we can find this by taking the first order derivative of total revenue function with respect to Q, that is output and geometrically this is the slope of the total revenue curve. Similarly, change in the total cost coming from the unit change in the output that gives us the marginal cost and mathematically we find marginal cost by change in the total cost with respect to change in the Q or that is output. So, similarly the geometrically the slope of the total cost curves gives us the marginal cost curve. We will take an example to understand all this concept particularly with respect to marginal analysis. So, if you look at in the table this is a hypothetical table. So, this is not a information relevant to the real world. So, there are six units of output 1, 2, 3, 4, 5, 6. The second columns gives us the total revenue, the third columns gives us the marginal revenue, the fourth column gives us the total cost, the fifth column gives us the marginal cost and the last column gives us the profit. As we know the total revenue is equal to sorry total profit is equal to total revenue minus total cost. So, if you look at if there is when there is one unit of output the total revenue is 20,000 and total cost is 4000. So, the profit comes as 16,000. Since there is only one unit there is no marginal revenue associated with this unit of output. When there are two units of output the total revenue is 34,000, marginal revenue is 14,000. Now, how this marginal revenue comes? This marginal revenue is the difference between the second unit and the first unit. Similarly, what is the total cost? Total cost is 8,000. Here the cost is fixed because for one unit if it is 4000 and for the second unit it is 2 units it is 8,000 then the cost remain constant. So, if you look at we will get a constant marginal cost because the per unit cost is remain constant. So, in this case total cost is 8,000 for two units and marginal cost is 4000. Now, how we get this marginal cost is 4000? That is the difference between the second unit of output the cost associated with the second unit of output and cost associated with the first unit of output. So, this is 8,000 minus 4000. So, marginal cost comes to 4000. In this case how we will find out the profit? The profit is total revenue is 34,000 and total cost is 8,000. So, 34,000 minus 8,000 that gives us 26,000 as the profit for second unit or the two units of the output. Similarly, for the third unit of output total revenue is 42,000, marginal revenue is 8,000. How we get the marginal revenue here? The difference between the third unit of the total revenue and second unit of the total revenue. So, 42,000 minus 34,000 that gives us 8,000 as the marginal revenue for the third unit of the output or the for three units of the output. Now, what is the cost over here? Considering unit cost remain constant for three units it should be 12,000. So, if it is for one unit it is 4000 for the third unit it is 12,000 where there are three units of output. Marginal cost again it is same because it is the difference between the third unit of the total cost and second unit of the total cost. So, 12,000 minus 8,000 that gives us 4000. Now, what is the profit over here? Total revenue minus total cost so that comes to 30,000 that is 42,000 minus 12,000 that is 30,000 as the desired activity level. I will talk about the desired activity level bit later once we understand the table. Now, for the fourth unit total revenue is 46,000. How we will find out what is the marginal revenue associated with the fourth unit? That is the difference between the total revenue of fourth unit and the third unit. So, total revenue of fourth unit is 46,000, total revenue of third unit is 42,000. So, 46,000 minus 42,000 that gives us 4000 which is the marginal revenue associated with the fourth unit of output. Total cost it is 16,000 for one unit is 4000. Considering this as a fixed cost for the fourth unit this is 16,000. Marginal cost 4000 the difference between the cost associated with the fourth unit and the third unit. So, marginal cost is 4000, marginal revenue is 4000. Coming to fifth unit total revenue is 42,000, total cost is 20,000. For fifth unit for one unit is 4000, so 5 units total cost is 20,000. Now, what is the marginal revenue and marginal cost? Marginal revenue is the difference between the fifth unit of total revenue and fourth unit of total revenue. So, this is 48,000 minus 46,000 so that comes to 2000. And what is the marginal cost? It is constant, the difference between the cost associated with the fifth unit of output and fourth unit of output. So, marginal cost comes to 4000 for fifth unit. Then it comes to sixth unit, sixth unit the total revenue is 49,000. How to find out the marginal revenue? Again the difference between the sixth unit and the fifth unit. So, in that case if you look at there is a difference of 1000 over here as the marginal revenue. Cost is 24,000 given 4000 as the per unit cost when it were using 6 units. So, this becomes 24,000. So, the marginal cost is the difference between the cost associated with the sixth unit and fifth unit. So, that comes to 4000. Now, what is the profit in the case of fifth unit and sixth unit? For profit is 28,000 in case of fifth unit that is 48,000 minus 20,000. And for sixth unit this is the difference between the total revenue 49,000 and the total cost 24,000 where the profit is 25,000. So, this is a hypothetical scenario where we are getting whatever the number of unit of output we are getting total revenue, we are getting total cost, we are getting marginal revenue, we are getting marginal cost. From the difference between the total revenue and total cost we are getting the profit. Now, for any producer what should be the desired activity level and what should be the absolute activity level? Now, what is the difference between the desired activity level and absolute activity level that on the basis of the profit and on the basis of the what is the value of marginal revenue and marginal cost. So, if you look at the cost remain constant, marginal cost remain constant, marginal revenue is going on decreasing. It started in started with 14000 and it reached to 1000 and marginal cost remain constant because the per unit total cost is remain constant that is at 4000. So, in the first case the producer is getting profit as 16000, second case it is 26000, third case it is 30000, fourth case it is 30000. Now, between third unit and fourth unit, one is desired activity level and second one is the absolute activity level. Now, why this is a desired activity level? If you look at in the third unit, still the marginal revenue is greater than the marginal cost. It means the per unit revenue by the third unit is more than the per unit cost associated with the third unit. So, still it is profitable for the producer to go further because by producing one more unit, he is getting a profit same level of profit, but the marginal revenue is still greater than the marginal cost. So, when he is operating in the fourth unit, the marginal revenue is 4000 and marginal cost is also 4000. So, this is the point the marginal revenue equal to marginal cost. If the producer is going beyond fourth unit, then the revenue is decreasing cost remain constant. So, the marginal revenue is less than the marginal cost. What does it imply? It implies that whatever the last unit revenue by producing one more unit of output, whatever the revenue generated at the last unit that becomes less as compared to the whatever the cost incurred by the last unit. So, marginal revenue is less than marginal cost. Now, what happens in case of second unit or third unit? In case of second unit and third unit, the marginal revenue is greater than the marginal cost. It means still there is a scope for the producer to produce more because the per unit revenue generated in the last unit is more than the per unit cost associated with the last unit. So, unit 4 is the point where the marginal cost is equal to marginal revenue. Any unit above this, the marginal revenue is greater than marginal cost. Any unit below this, the marginal cost is greater than marginal revenue. So, the choice between the producer is to operate whether in the third unit or whether it in the fourth unit. So, using marginalist principle, we will see which one is the ideal level, whether it is third unit or whether it is the fourth unit. So, to maximize the profit, output should be increased up to the point where marginal revenue is equal to marginal cost. So, if you are going by this policy or this rule, this marginal revenue equal to marginal cost that is at the fourth unit where the marginal revenue is equal to 4000 and the marginal cost is equal to 4000. So, at this point, marginal revenue is equal to marginal cost. So, even if the profit remains same between unit 3 and unit 4, the revenue is more in case of fourth unit and going by the marginalist principle, we have to maximize the profit. The output should be increased up to the point where marginal revenue is equal to marginal cost. So, in this case, fourth unit is that level of output what the producer should produce to maximize the profit. So, one possibility when marginal revenue is equal to marginal cost, there are two other possibilities where we are getting that at some point or at any level of output, either marginal revenue is greater than marginal cost and the marginal or the marginal cost is greater than the marginal revenue. Now, we will check when we are encountering the position or we are encountering the possibility where marginal revenue is greater than m c and when the marginal revenue is less than m c. What does it imply when marginal revenue is greater than m c? It means the last unit of output increased revenue more than the increased cost. So, this is profitable for the producer to produce more because the last unit of output is generating more revenue than the cost. Now, what is the other possibility? Marginal revenue is less than marginal cost. It means the last unit of the output increased cost more than its increased revenue. So, the cost incur in the last unit is more than the revenue generated. So, it is not profit, it may not be the profitable for the producer to go beyond this or produce at this level because they are not generating extra revenue rather they are generating extra cost and whatever the extra revenue they are generating that is less than the extra cost. So, marginalist principle is always marginal revenue is equal to marginal cost and this is the profit maximization principle. And this we are going to follow in case of our managerial economics that in order to maximize the profit there should be equality between the marginal revenue and the marginal cost. So, in the last few minutes we are discussing about the marginal analysis. So, what is the basic understanding about the marginal analysis? What is the change in the revenue? What is the change in the cost or what is the change in the utility? It is total revenue, total cost and total unit when there is a per unit change in the output. So, basically marginal analysis deals with per unit change in the variable. When you take this to a real life example maybe we get some situation we get some examples where per unit change is not possible. The change is not per unit the change is chunk. If it is a per unit change sometimes there is a difficulty in evaluating sometimes difficulty in estimating. So, the particularly in those time period the change is not per unit change is in a chunk. So, in reality variable may not be subject to unit change always and specifically at those situations we need the incremental concept in order to analyze whatever the change and how it affects the other variable due to this change. So, incremental concept is applied when change is not necessarily in term of single unit, but in a bulk unit. So, marginally specifically per unit change and when there is no per unit change in this case we use the term incremental concept for the change in bulk not change in the single unit. Now, it estimate the impact of decision alternatives sometimes some decisions that may not lead to per unit change the change is in term of bulk. So, in that respect incremental analysis estimate the impact of the decision alternatives. Now, we will check what is incremental cost and what is incremental revenue. Incremental cost is the change in the total cost as a result of change in the level of output or investment whatever may be the variable. What is incremental revenue? This is the change in the total revenue resulting from a change in the level of output or the price. So, when there is a change in the level of output when there is a change in the level of price what What is the change in the revenue that is incremental revenue and what is incremental cost when there is a change in the total cost as a result of change in the level of output or the investment. And how the manager decides like marginalist principle, the profit maximizer rule is marginal cost is equal to marginal revenue. Similarly, in case of incremental analysis, how the manager decides whether the decision is profitable or whether the decision is not profitable, managers always decides determines the worth of a decision on the basis of the criteria that is incremental revenue is incremental cost. So, whatever the decision taken the outcome should be that incremental revenue should be greater than the incremental cost because of this typical decision or because of this typical change. So, if you look at marginal also deals with change, incremental also deals with change, marginal analysis deals with change for one unit and incremental analysis deals with change in the in unit change in the bulk not the single unit. So, we will take an example in order to understand the incremental analysis. Suppose, the firms decides that they will go for online selling, they feel that or they adopt a strategy that if they are going for online selling, it will be profitable for their firm. So, this is one kind of decision taken by the firm that they are going for online selling in order to increase the revenue or in order to increase the sales which will increase the revenue. So, after going for online selling, there is an increase in the sales of the firms. Now, what is incremental revenue here?暈 revenue is that there is a increase in the sales of firm due to introduction of online selling. Online selling is the decision due to online selling, there is a increase in the sales of firm that leads to increase in the revenue. So, increase in the total revenue due to increase in the sales of firm that is incremental revenue. Now, what is cost here? Cost of launching the online selling mechanism. And they have taken a decision for introduction of online selling, it involves some amount of cost that increases the total cost of product. So, cost of launching the online selling mechanism is the incremental cost. Increase in the revenue due to sales of firm due to increase in the sales of firm is the incremental revenue. So, if incremental revenue is greater than incremental cost, decision of introducing online mechanism is right. Now, manager on what basis he will take a call that whether he should go with the whether he should continue with the online marketing, online selling or he should stop it. For him the decision criteria is that till the time the incremental revenue is greater than incremental cost, the decision of introducing online mechanism is right and the manager will continue with this decision. If it is not, then if the incremental revenue is not greater than incremental cost, then the decision is not bringing any profit to the firm and the manager will discontinue this online selling. So, incremental analysis the decision rule is incremental revenue should be greater than incremental cost in order to bring the whatever the decision taken by the firm to be profitable. So, as we discussed if you compare between the marginal versus incremental analysis always the marginal analysis is it relates to one unit of output and incremental analysis relates to one managerial decision it may involve multiple unit of output. So, marginally strictly deals with one unit of output and incremental is always deals with the decision which involves more than one unit of output. Then we will come to take a typical model of an economy and we will see what are the different factors. So, what are the different sectors here and how it works or what is the money flow, what is the real flow for each sectors and how generally typical economy works here. So, if you look at in a typical economy there are four sector, one is factor market, second is product market, third is household and fourth one is business firm and fifth one is government sector. So, if you look at if you are not considering market as the sector there are typically three sector one is household, second one is government and third one is business firm. So, household sector is basically deals with providing manpower to the business firm and in return of that they get a goods and services produced by the firm what they purchase. Government sector does a transfer payment to both the household sector and the business firm and in return of that they get a tax and fee from the both the household firm and the business firm. So, let us first analyze the flows between two sector household and the government sector. Now, household provide manpower to the government sector and in return of it they gets the wages and the salaries. Now, what the government sector gets out of it? The government sector gets taxes and fees what is the revenue of the government sector what they gets from the household sector. Now, the third sector is business firm. Now, what is the relationship between the government sector and the business firm? They get a business firm gives a transfer payment to the government and governments pay for their purchases of their goods and services produced by the business firm. And also the business firm gives tax and fees to the government sector which is their revenue. Now, what is the relationship between the households, household sector and the business firm? Households provide the input in term of manpower to the business firm to produce the goods and services. In return of that they get the wages and salary and what is the outcome of the business firm or what is the output of the business firm? They produce goods and services they sell it in the open market and they get a payments for their purchases from the household sector and from the government sector. So, if you simplify it household sector and business sector how they are related? If you are considering it is a two economy there is only household sector and the business sector in case of household sector they provide the manpower to produce goods and services by the business sector. In return of that they get the wages and salaries from them. Business sector use the manpower from the household sector. They utilize that for the production of goods and services what they sell it to the household sector and in return of that they get a payment for their purchases of the goods and services. How household sector and government sector they are dependent? Household sector again provide manpower to the government sector in return of that they get the wages and the salaries. They pay tax and fees to the government which is revenue of the government and government sector provides transfer payment to the household in term of the pension and different type of payments benefit. Now, in order to facilitate this payments of the in order to facilitate the sales of goods and services of business firm to the household and the government sector there is product market. So, business firm after producing the product they send it to the product market in order to sell those goods and services. So, there is a product flow from the business firm to the product market. Product market determines the product price which is consumed by the household. So, household buys the product from the product market there is a product flow of goods and services from the product market to the household. In term of that household gives the payment to the product market which goes finally to the business firm who are the producer of the goods and services. Now, in order to facilitate the input market like in order to produce the product the business firm needs certain factor of production or certain inputs that he gets through the factor market rather than getting directly from the household. So, household provides labour and capital to the factor market which gets used by the business firm in order to produce the product. Now, the factor market determines the factor price since household is providing a factors to the business firm they are getting a factor income which is in term of wage and interest. So, wage is the payment for labour and interest is the payment for the capital. Now, after using the factors labour and capital the business firm gives back the wage and interest to the factor market which finally goes to the household as the factor income. So, how factor market and business firm they are related factor market is facilitating the factor requirement for the business firm getting it from the household and providing it to the business firm. The business firm using the factor provided by the household produce the product give it to the product market and product market is sending this to household what the household buys from the product market and get a payment for it what is finally goes to the business firm. So, if you look at apart from the government sector there are two major factors one is household and second one is business firm. Household provides the factor input to the business firm business firm produce the product and the household again buys it from the product market and gives back the price of the product as the income of the business firm. Similarly, what is the income of the household? The income of the household is that whatever the factor they are providing to the business firm the payment made for that if they providing labour it is wage and if it is providing capital then this is interest. So, if you look at the income of the household become expenses of the business firm and the income of the business firm becomes the expenses of the household. So, all the sector they are interrelated with each other when it comes to the economic activity of the economy. Government sector is there and it is interlinked with both the household sector and the business firm. They provide transfer payment to household sector get the transfer payment from the business firm. They do the purchases from the business firm and make a payment for it. They take the help of the manpower to operate the government sector and in term of that they pay the wages and salaries to the household. And what is the revenue of the government sector? Whatever the tax and fees they get from the household sector and the business firm that becomes the income of the government sector. So, basically there are three sector one is household sector second one is the business firm sector and third one is the government sector and all the three firms are related with each other. There are two market one is factor market it is deals with sales and purchase of the input and the second market is product market it deals with sales and purchase of the goods and services. So, business firm sell their product through the product market and get their factors through the factor market. How soon sell their factors through the factor market and buy their product from the product market. Now, there are two kind of flows here one is real flows that is the real transfer of goods and services from product market to household and the real transfer of labour and capital from as a factor flow from the factor market to business firm. And second kind of flows is money flows it is the income the real transfer of income from factor market to household in term of factor income and real transfer of income from product market to business firm that is for the from the payment of the product that is made by the household sector. So, there is inter linkages between all these three sectors and there are two markets which facilitates the transaction one is factor market and second one is product market. So, whatever we discussed in the last class and this marginal analysis few opportunity cost few other concept and this marginal and incremental analysis these are the session references. And then we will move to our next topic that is basic tools of economic analysis and optimization technique. Now, what is the learning objectives or session outlines of this topic? We will first look at what are the functional relationship between the economic variables. Then we will discuss some important economic function then we will see slope and it is used in the economic analysis derivative of various function optimization technique and finally, how we do a optimization with a constraint ok. So, coming to the relationship between the economic variable now what we consider as an economic variable any economic quantity value or rate that varies on its own or due to change in its determinant is an economic variable. Any economic quantity or value or the rate the variables rate any variable when its value whether its rate that changes due to its own or due to change in the determinants of each and economic variable. So, when the variable changes the value due to its own value or due to some other factors those are considered as the economic variable. We can take the example that demand for a product whether it is 10 units whether 12 units and 13 units every time it is changing a value the demand is not constant. So, this is a economic variable price of the product wage rate advertising expenditure these are few examples what we consider as the economic variable where the value get changes either due to own factor or due to change in the determinants the factor separating the demand for the product. Suppose, you take the example why there is a change in the product price or why the price of goods increases when the cost of production increases. Suppose, you take the case of this marker the cost of production is 10 rupees. So, price is on the basis of 10 rupees when you add a normal profit and attacks with this that becomes the market price for this marker and suppose the market price of this marker is 13 rupees out of this cost of production is 10. So, what is the determinant of this price of this marker the cost of production. Now, on what basis there will be increase in the market price of this marker when there will be increase in the cost of production. Suppose, the increase in the cost of production has become from 10 rupees to 11 rupees. So, the market price given all other factors the value of all other factors remain constant the market price of this marker will go up by 1 rupees. So, it will go up to it will go till now if it is 13 rupees to 13 rupees now it is 14 rupees. So, product price in this case the product price is changing due to change in the value of its determinant. So, this is one example of the economic variable. Now, all these economic variables are interrelated and interdependent all the economic variables they are not independent they are interdependent and they are interrelated. This implies that a change in one variable causes change in the value of other related variables if they are interrelated and interdependent when value of one variable changes generally that leads to change in the other variable. Suppose, we take the example of price and quantity of a product. If you take the same example price of marker earlier the price of marker was 13 rupees due to change in the cost of production the price of marker is 15 rupees. Now, price and quantity of the product they are interrelated. If price is more now if it is from 13 to 15 rupees few customer who cannot effort to pay 15 rupees for that they will not buy this product. So, this increase in price affecting also the quantity of the product what is getting sold in the market. So, price increases that leads to decrease in the some quantity of product that getting sold in the market. So, if you look at price and quantity of product they are interrelated because of that when there is a change in the price or when there is a change in the value of one variable that leads to change in the value of the other variable. In this case typically the price and price of marker gets change that leads to change in the quantity of the products getting sold in the market. Similarly, income and consumption expenditure. If your income is more you consume more you spend more. If income is less you spend less. So, if you look at income and consumption expenditure they are interrelated. So, value of one get changes due to change in the value of the others. Similarly, interest rate and demand for fund if the interest rate is less more people they go for loan. If the interest rate is high there is at least decrease in the demand for a loans because the interest rates are on a higher side. So, economic variables are interrelated they are interdependent. When there is a change in the value of one variable that leads to change in the value of the other variables because both of them they are interdependent and interrelated. Now, what are the kinds of economic variable? Variables are classified on the basis of economic variable. So, the first category is dependent and independent variable. The value of this variable depends on the value of other variable in case of dependent variable and independent variable the value of this variable changes on their own or due to some exogenous factor. So, dependent variable is one where the value of this variable is always dependent on the value of the other variable and independent value is the value of this variable changes due to their own or may be some exogenous factor, but not due to change in some other variable. So, if you take the example of computer price and demand for computer. Here demand for computer is dependent, computer price is independent because demand for computers is dependent on the computer price. When there is an increase in the computer price that leads to decrease in the demand for computers, when there is a decrease in the computer price that leads to increase in the demand for computers. So, in this typical case the computer price is the independent variable and demand for computer is the dependent variable. Similarly, there is an increase in the petrol price. If you look at nowadays there is an increase in the price. Why there is an increase in the petrol price? Because there is a hike in the import oil price. So, in this case which one is dependent and which one is independent? Petrol price is a dependent variable because petrol price is related with the value of the import oil price. Whenever there is a change in the import oil price, either increase or decrease in the import oil price that leads to change in the value of petrol price. So, if there is an increase in the import oil price that leads to increase in the petrol price. If there is a decrease in the import oil price that leads to decrease in the petrol price. So, in this case petrol price is dependent, import oil price is independent variable. So, dependent variable is one where the value of that variable is dependent on the other variables and import oil price also and sorry the independent variable is one where it is not dependent on any other variable for its value, rather the value changes due to own or the exogenous factor. The second kind of economy variable is endogenous and exogenous variable. Now, what is endogenous variable? Endogenous variable is the value of this, the value of this variable is determined within the framework of the analysis model. So, if there is a model between price and quantity, the endogenous variable is one where the value of price or value of quantity has to be determined within this specific framework or specific model. And exogenous variable is what? The value of this variable are determined outside the framework of the analysis model. So, any exogenous factor or any external factor will decide what is the value of this exogenous variable. Now, we will take the example of the endogenous and exogenous variable. If you are going to the same petrol price example, domestic oil price is endogenous and international oil price is exogenous variable. So, domestic oil price is dependent on the import oil price. So, in this case the value of the domestic oil price is decided within the framework from the import oil price. However, exogenous variable is international oil price. International oil price is not strictly on the basis on the import oil price. It has some other factor and the value of the other factor also decide whatever the international oil price. So, in this case domestic oil price is the endogenous variable whose value is determined within the framework and international oil price is the exogenous variable which value is decided on the basis of the external factors. Now, when we analyze the relationship between the variables, we can analyze this or we can present the relationship between this variable through three methods. One is tabular method, second one is functional method and third one is graphical method. So, if you are taking the example of price, demand and supply, suppose there are three variables. This relationship between this price, demand and supply, we can present through a graphical analysis, through a supply curve, through a demand curve, taking quantity in the right axis and price in the left axis. We can do a tabular where we can find out what is the demand and supply when the price is 1 rupees, when the price is 2 rupees, when the price is 3 rupees and when the price is 4 rupees. So, this is the tabular representation of the relationship between the variable. This is the graphical relationship between the relationship between this variable and third one is functional which deals with the cause and effect relationship which we analyze or which we present through a functional form. So, in this typical example, when we are deciding the relationship between demand and price, it will take a functional form which is equal to q d which equals to a minus b p where a and b are constant and p is the price of the product and q is the quantity demanded for this product. So, relationship between three variable can be presented through graphical method, through tabular method or through the functional method. So, tabular and graphical form is useful when number of variables and observations are small. If it is a two or three variables, then tabular and graphical form can be used, but if it is the number of variables are more specifically in case of economic analysis, if you look at all the economic variables are interrelated and interdependent. So, the number of variables and the number of observations are more. So, in this case, it always good to use the functional form in order to represent the relationship between this variable. So, most economic problems are complex. It involves a large number of variables because they are interrelated and interdependent. And in such cases, economists use a mathematical tool known as function to express the relationship between the economic variable. So, the tool is functional and we generally called it a functional representation of relationship between this relationship between the economic variable. For economic analysis, it is more useful because there are large number of variables. Next we will see what is a function because function is used to represent the relationship between different economic variables. So, it is a mathematical tool used for expressing the relationship between economic variable that have a cause and effect relationship. When they are interrelated if one is cause and other is effect and it is a relationship between different economic variable, it is a mathematical tool. Function is a mathematical tool used for expressing the relationship between the economic variables. There are two types of functions. One is bivariable function and second one is the multivariable function. Bivariable function involves only two variables and multivariable function one dependent and more than one independent variable. In case of bivariable function it has only two variables one is dependent another is independent. In case of multivariable function there is only one dependent and more than one independent variables. Now, we will take an example to understand this bivariate function and multivariate function. If the value of variable x depends on value of variable y then the relationship between two each y is a function of x where y is the dependent variable and x is the independent variable. So, this is a typical function which express the relationship between y and x where y is the dependent variable and x is the independent variable and y is a function of x. Now, taking the example of a demand function if you consider p is the price of the product and dp is the demand for the product the demand for the product is always dependent on the price for the product. So, in case of a bivariate demand function when we are assume when we are taking that there is only one dependent variable and one independent variable. In this case we use this function dp is a function of p and this is a bivariate demand function where the demand for the product is dependent only on price. Now, suppose we assume that demand for the product is not only dependent on the price, it is also dependent on the income which is represented through Y, dependent on A that is advertising expenditure and also depend on the taste and preference of the consumer. So, in this case, how we represent the relationship between the variable price demand for the product, income, advertising expenditure, taste and preference of the consumer through a function. We know that demand for a product is dependent on price for the product, income for the product, advertising for the product and taste and preference for the product. So, demand for the product is a function of price, income, advertising expenditure and taste and preference. So, this is the example of a multivariate demand function where there are four independent variable and one dependent variable. Here, the dependent variable is D P and it is dependent on four independent variable that is P, Y that is P is price of the product, Y is the income of the product, A is the advertising expenditure associated to the product and T is the taste and preference of the consumer for the product. So, there are two types of functions, one is bivariate, another is multivariate. Bivariate essentially deals with two variables and multivariate deals with one dependent variable and number of independent variables. Now, how do we specify a function on the basis of the nature of the relationship, how both of them are related, whether they are positively related, whether they are negatively related and second is on the basis of the quantitative measure of the relationship or the degree of relationship. If they are positive, they are negative up to what extent, what is the, how we can quantify the degree of relationship that is on that basis we can specify a function. Generally, we use a regression technique for specification and quantification. Now, look at this example, suppose we take a demand function which is 500 minus 5 P. What are the different implication of this demand function or how we can analyze this demand function? When the price is 0, demand is equal to 500 units because the intercept value is 500. So, the first implication is at 0 price, demand is equal to 500 units. There is a negative 5 P. So, negative source, there is a inverse relationship between the price and demand. This is the nature of relationship between price and demand is inverse and the value 5 implies that for each 1 rupees change in the price demand change by 5 units. So, 1 rupees change in the price leads to 5 unit change in the demand. So, this is the degree of relationship between the price and quantity demanded. So, at 0 price demand is equal to 500 units. So, when you get the product at free, the price the demand is 500 units. What is the significance of this minus that shows the nature of relationship between two variables and the nature of relationship is inverse. There is a inverse relationship between the price and the demand and 5 implies that for each 1 rupees change in the price demand change by 5 units. So, if you look at there is a 5 time change in the, if you have quantity demanded, when there is a 1 time change in the price, this is the quantification of the relationship or the degree of the relationship. Now, what is the general form of a demand function? The general form of a demand function is q x is equal to a minus p p x, where q x is the quantity of x, p is the price of x and a and b are the constant. So, constant in a function are called the parameters of the function and what is the role of this parameters? The parameters of the function specify the extent of relationship between the demand and between the dependent and independent variable. So, this a and b they will specify what is the extent of relationship between the dependent and independent variable. They will talk about the nature of the relationship and the degree of relationship between dependent and independent variable. So, taking this demand function q x is equal to a minus b p x, here constant a gives the limit of q x when p x is equal to 0 and b is the coefficient of variable p x which measures the change in the q x as a result of change in the p x. So, this is basically the change in the q x which is equal to minus b and the change in the p x. So, in the previous example if you remember d was equal to 500 minus 5 p. So, 500 was the value of a which gives the limit of q x when p x is equal to 0. So, when price was equal to 0 500 was the quantity demanded and b is the coefficient of the variable p x. So, in the if you look at in the previous example 5 p. So, 5 p is the value of b which is the coefficient of variable p x which measures the change in the q x as a result of change in the p x which was 5 times because the change in the q x was 5 which we can get through the value of b and change in the p x is 1. So, when the in the previous example when there is a 1 time change in the price that leads to 5 times change in the quantity demanded. So, there are few other function like demand function and other thing like production function cost function that we will discuss in the next session. And for this specific part like basic optimization technique and basic economic analysis followed this managerial economics d and d by d of 7th addition. Thank you.


What's up everyone, Takedown here. Welcome back to the channel. Today is going to be an unboxing video. I'm super excited because I'm going to be unboxing Geek Fuel EXP Volume 1 It is a big box. I'm super excited. Let's get right into it So even though volume 2 just came out the reason I'm getting volume 1 is a I didn't get it yet I didn't get it whenever it first came out months ago and 2 I just had to pay shipping for it I think it is only $15 shipping and there is a lot in it like I showed you it's a pretty big box So to me it's well worth it $15 you're guaranteed a shirt and the shirts usually $15 to $20 So even if everything else in this box is garbage, I know I'm going to get a pretty good shirt out of it So that's why I went ahead and bought it. Okay, so let's open this up and see what is inside So the first thing we have I like these enamel pins Planet of the apes these are the planet of the apes pins and there is one that is rare. Let me see which ones I have I have dr. Cornelius and dr. Zeiss The rare one there's only 500 and it's george taylor but in a spacesuit So that would have been a pretty cool one to get but I'm a huge fan of planet of the apes I don't have anything in my collection Two pretty good pins and you got the ansa might be mispronouncing that Basically nasa that is in the movies Get a pin for that too, which nobody usually mentions mentions that pin. So pretty good. I do like that Next up. I'm assuming Bob's burgers burger of the day Let's see what this is I'm honestly not a fan of the show. I don't watch the show but Uh, we are going to see what this is Okay, so we got an apron with all of the characters from the show on it. Honestly, that's pretty cool It is a higher quality one. I thought it was going to be cheap stuff in this but This is Pretty good quality. I'm not going to lie. It's pretty heavy Um, it's probably not something I'm going to use myself Uh, just because I don't use aprons, but that is a pretty cool item and it is pretty good quality So to me, I think that's pretty good for it being in the box next up is this merch This might be the shirt. Yes. This is the shirt Okay, this shirt looks amazing Deadpool you show the print there for you guys That looks amazing.  Can't really see it, but Honestly, that looks pretty good again high quality. I don't know why but their shirts are so high quality Let's just go and try this on see and make sure it fits. Okay. So that is the shirt that fits amazing It's such good quality. It's very snug and it is gray. I know it looks black on the camera here But it is gray normally when if you get shirts from subscription boxes from what I see anyways Most of the time they are black. So the fact that this is gray It just makes it so much more better for me brady bunch Deadpool shirt Definitely a win definitely worth the 15 box even if this was the only thing I got in it This was well worth it. So next up we have a game of thrones figure I believe this one here. Everybody got the same one. I know it shows them on the back here But I think everybody got the same one. I think it's a special edition now a trigger warning I'm not a fan of the show, but let's check it out and see what is inside Okay, so it's in this bag here. I was not expecting it to be in a bag that looks glow in the dark I'm not exactly sure what it is. Like I said, I don't follow the show I don't watch the show comment down below what it is just so I know but It is pretty cool. It looks like it's high quality. There is a lot of detail on it The eyes are painted. It's all painted, but it does look low in the dark I will let you guys know but to me it looks low in the dark Game of thrones on the bottom. That's pretty cool. It's a small figure as you can see But that is pretty cool. Even though I don't follow game of thrones. I do like that figure Okay, so next up is a marvel item This looks like it's going to be amazing. It looks like wolverine on the cover of the box Now I know that probably doesn't mean it's going to be wolverine, but let's just see what it is I am so happy because I have been looking for stuff like this for so long It is a canvas print. I have been looking for canvas print for so long This is a pretty cool one wolverine. I think this is the first comic book of him So cool. I do love that Definitely going to be hanging that up in my room I'm going to be just setting it up on display But that is amazing. That is high quality as well That is definitely worth it. Definitely going to be putting this in my room and adding this to my collection That is amazing. I'm just so happy. I got that so freaking cool Next up looks like it could possibly be a knockoff item It says kawabunga pizza cutter and it's in the fonts of teenage mutant ninja turtles So I don't think it's an actual teenage mutant ninja turtles item I think it's just going to be a knockoff, but let's see what it is The cool thing is the box looks just like a slice of pizza and let's see when we open it up in here Wow, that looks pretty cool Look at that pizza cutter Now I don't know if this is something that you can actually use. I'm going to check it out here Okay, so it is a big blade. It does look like you can use it Something tells me these at times with your pizza are going to get in a way So I'm not a huge fan of that the grip is pretty nice I thought it was going to be all hard plastic, but it is actually spongy the grip part That is pretty cool. I don't know if I'm going to use this kitchen gadget or not I don't think it's going to work properly and the last item that is in today's box is a lego star wars book That is pretty good. I wasn't expecting a thick book like that At least with my knowledge. I think this is a rare lego, which I don't have any rare lego So I'm not sure exactly if I'm going to keep this book or if I'm going to gift it to somebody that likes lego star wars Maybe one of my nieces or nephews, but Pretty good book pretty cool I'm not sure what it is is if it just tells you about everything Which looks like it looks like it tells you everything about lego star wars So it is a pretty interesting book like I said I might just put this on my shelf or I might gift it to somebody that likes lego star wars So out of everything I got in geek fuel exp volume one. I would say these shirts would be my favorite I just love getting these shirts. I'm a huge fan of deadpool. I like how it's a brady bunch concept I do love that. I also love my pins. I've been collecting them a little bit. I don't have a big collection, but I do love them I'm going to keep them in the packaging So to me the fact that it could have got a rare one to me is so unique and that makes this so much more special Love plan of the apes and this is a great item to get and the canvas print is so cool and unique I didn't know they actually had canvas prints in subscription boxes Something I've been looking for for quite a while not necessarily a wolverine one But it is a good one to put in my room and put in my collection So I'm really happy for that for the rest of the items even though they are cool and unique They're not necessarily for me the figure. I just don't watch game of thrones The pizza cutter is a cool kitchen gadget, but I'm not sure I'm going to use it and the apron I'm not a fan of the show so I'm probably not going to wear it But since I just paid shipping for this box only $15 to me I definitely got a lot of stuff for what I paid for it. So I'm extremely happy. Thank you geek fuel So hopefully now that volume two has released Hopefully I will get it whenever volume three comes out because they'll probably have the same deal where you just have to pay Shipping for it. I know you guys probably seen people unbox this box whenever it first came out about four months ago I know I'm extremely late, but I did buy it. I did want to unbox it on my channel And I hope you guys do enjoy watching them as well But this is all I have for today's video. I hope you guys did enjoy and I'll see you guys in the next video Please take care. Peace


I got a feeling that today's gonna be a good day. But today's gonna be a good day. But today's gonna be a good day. Bala Baga