so let's go ahead and get started um in terms of announcements I do have office hours tomorrow from 3:30 to 5:30 if you have questions or need help with something we are in chapter two as we mentioned last time um core syllabus skeleton notes are online if you're not using the skeleton notes I highly recommend it they're highly useful um it was a few years ago we actually put them all together and so we update them every year as we need to um but it's to help you follow along so you don't have to scribble everything down on the slides um in terms of events we do have lab Thursday and Friday this week um lab report number one is due at the beginning of your lab so if you do have lab tomorrow remember that one's due you you guys got it a day early um and so we'll collect those if you miss lab please I don't have the labs today if you need one email me and then we do have tutoring starting today at 3:00 in waters Annex 104 just show up there's no sign up sheets and um we have it tomorrow from 5:00 to 6:30 and you can join via Zoom um and double check the zoom links online okay questions and no class on Monday if you come on Monday you can sit here and pretend we're in class I will not be here so if you're super excited for next Wednesday come Monday work off some of that excitement okay next Monday's Labor Day University's closed so none of your professors will show up that day so just FYI So today we're going to continue our exploration of production economics and look at different concepts to describe the production process in essence we want to enhance our story okay of how we look at production and we need to do this before we actually ask questions about production in terms of profitability costs and stuff like that and so this is always the foundation of understanding how we look at those processes in a firm so remember we characterize production with a production function so the production process is represented by this production function that relates output to the factors of production or inputs okay and that remember this is land labor Capital Management okay this can be represented with a function so we looked at a linear function looking at output and water and so mathematically this is the most complete description but it's not always the most useful if you're trying to present it to people or explain it um an easier way is a production schedule or a table showing input use and output produced or a graph showing something similar while we have linear production functions that may only exist for a certain range of input use likely your production function is nonlinear takes this hill shape where you have increasing production you hit a maximum and then that declines was maximizing output the equivalent of maximizing profit no we're likely to produce in which side of this the right or the left left side right why cost inputs yeah inputs cost money that means when you produce output you need Revenue to cover those costs as you get toward the top of that production function you're probably not earning enough Revenue to cover those costs so it may not be profitable the only time that top is for sure the most profitable point is if all your inputs are free but there's no free lunch okay so today we want to further describe this concept and so we're going to look at three different concepts and I want to present them up front here and then we'll look at them more in detail the first one is what we call Total Physical product TPP and as you've learned there's a lot of acronyms this will get used this will help you get used to working a government job or working on a government contract and so Total Physical product in essence this is output but a specific type so this is the relationship between output and one input okay set it holding every all the other inputs constant an example of this was the corn production function we looked at with water okay and we're going to look at that also in our lab we also have AP which is average physical product this is the average productivity of each unit of variable input used so it's a measure of efficiency of your production process physical efficiency and it's simply the average output produced per unit of input it's your total output divided by the level of input use so y divided X I should make my skeleton notes and have it transfer all the letters so you connect the dots that'd be horrible but it'd be really funny to see people try to do it I'd probably throw it away and take my own notes the last one we're going to look at today is marginal physical product that's MPP it's probably the most important concept here mppp is a measure of productivity it tells us how productive the next unit of input will be how much output will we get on the margin from the next unit of input it is notice MPP is the change in output from one level to another over the change in X okay and so this is is the formula we've seen it already of a slope and so I mentioned we'll have these marginal Concepts which in essence are slopes MPP is the slope of the production function and so notice this is the same formula as the slope for a linear line and in en even for a nonlinear the difference for a nonlinear function is you have to recalculate it at every point but it is this slope okay and those slopes are what we're really interested in later on what we're going to find out it's those slopes that drive us to figure out where profit maximization points are for a linear production function MPP is constant but for a nonlinear production function function that changes as you move that productivity changes as you move along the production function and so as you add more and more input your productivity does change in Ence so what I want to do is to teach you these Concepts I want to look at an example okay so we're going to look at TPP then a then we RSV MPP so we can get over to the op to the USPS and then we'll talk to the CEO if you got all that more power to you I got lost somewhere and just started making up acronyms or adding ones I knew okay so I wish I someday I'll actually write one down that I figured out and then I'll tell people interpret what I just said but for now maybe I'll maybe next time so I want to look at an example of a winery if you don't think wineries are economics they are be light Vineyards big a industry in California and other places in Oregon in other places around the country um we have even some wineries here um so Acme wines is a new winery in southern Oregon that specializes in making exotic wines such as chocolate Blackberry chardonay yum not really chocolate wine gross I've had it not this exact wine but um chocolate wines so but you can find these there's blueberry wine you it seems like you can make wine out of anything that has sweetness I've not seen carrot wine but I think you could make it so hey more power to if you want to make carrot one I I haven't seen it on the market yet so um carrot juice is sweet so you possibly could so we're going to look at this one it is a real wine I don't know if you can still buy it was when I made up the example we're going to look at the filling Factory here for here for this wine the primary production input in the filling Factory where wine barrels are filled prior to shipment is labor okay the table on the next slide will show you the production function for this filling facility so we're looking at the filling facility with one input labor and so we're our output is barrels okay and so this is our production scheduled first two columns and so what we had is as we add a number of employees on the production line in the filling Factory this tells you how many barrels per day can be filled and they're using ladles imagine if that was your job one Ladle that's a barrel oh my gosh right I I would hope I wouldn't pick it um so this is your output and barrels per day based on the number of employees what we want to look at first is MPP which is going to tell us about the productivity of each additional employee on that production line okay and so we're going to look at MPP here in a minute I do so if we take that production schedule and graph the production function we get something that looks like this all I did was all this program does is graph the points and connect the dots okay this is a well beh example but notice we have our typical shape of a production function that we get this increasing productivity of Labor and we get that we as we add more employees we get more and more output but that does start to fall as we hit the top and as you hit the top and you add that last employe production starts to fall okay and so we get less output with the 10th employee total production Falls at that point so remember MPP is the slope of the production function for the linear corn production function we looked at with water we got the following production function y = 160 + 4 * W where W is the amount of water applied what is MPP here it's the slope which is four it's constant this is a linear production function so it's four it never changes no matter with the first acre inch the 10th acre inch the 100 Acre inch the millionth acre inch I get four more bushels of corn with every acre inch which is also the reason we thought it was a bit unrealistic and so for each acre inch I get four Bush breaker notice this is constant because this is a linear production function okay but we're dealing and so in linear and we'll talk about what this means here in a little bit but for nonlinear like in our one example that MPP changes as you add employees so let's look at that in the table so MPP is the change in output over the change in input moving from one level to the next okay notice I don't have a zero labor if I have zero laborers how much barrels can I fill zero okay if you had trouble answering that one go into a room try to make a paper airplane say hey there's no one here put a piece of paper on the desk leave wait five minutes come back and see how many planes were made it'll put it in the concrete example okay so the MVP [Music] is zero so there's implicitly a z0 here but we should know that no input no output but that's our starting point in these graphs right so if we calculate the first MPP it's the change in each of those from row to row for output and input and so notice it's the change in output it's 10 minus the row prior zero over the change in input which is one minus zero so it's 10 over one or 10 that means the first laborer gives me 10 Barrels in one he can do 10 barrels what about the second laborer how many barrels can I get so what's MPP at 22 barrels or two laborers or what's my really the way to ask it is what's my MPP for the second labor because it's on the margin it's what it's 11 right that's well not 11 that's average it's 12 it's the change in output over the change in input the change in output is 22 minus 10 which is 12 / changeing input 2 minus one right so 12 ID 1 is 12 what's the denominator always here one I caution you that is not always the case sometimes inputs will jump in increments and so that denominator can be non one it can be another number it's just the difference okay what about for the third laborer what's my MPP yeah it's 15 it's 37 - 22 over 1 take about a minute work on the rest of the table here if you need to ask your partner for help if you're confused ask your neighbor for help and ask them hey what's going on or raise your hand we'll come around you want to know what's worse than chocolate wine chocolate beer that to that was a CHR AER a little good conference to so what did you get for the fourth yeah you got 20 and so on so notice what happens to productivity so notice as I had employees initially in the production process productivity is going up right but then what happens remember that curve starts to Plateau you get less and less output for each unit of input that we see that here it's starting to Plateau we're getting less and less output there okay notice eventually it falls that means that 10th employee likely what's going on nine employees is probably enough on the line a 10 there's just too many people in the room it actually causes inefficiencies reduces total output actually would it be cheap so like at n you can have a day but at four since you're paying less people most outut be most and that we're going to talk about that here in a little bit you're on the right track but in essence at the ninth I talked about why at the top it's can be not profitable if I only make 10 or say $80 on this barrel and I pay my labor $100 I'm losing money on that additional barrel and so that's where those costs come in and we're going to get into that so we can graph this notice the graph is different from the production function how that y AIS is no longer output just pure output it's output per unit of input it's because we're looking at productivity so it's still wi but it's barrels per employee and then all this is is plotting and then connecting the dots and so then I have Labor number of employees on the bottom axis so the MPP this is the curve this is our MPP curve and the MPP curve tells me if I go to a level of employees how much additional output I'll get for that employee okay and so this is this is the slope function for the production function and it's not constant so why we get a function if it was constant it' be a straight line a linear and so some of the terms we want to look at is we can now talk a little bit more about the production proc process and start describing it using the MPP and that's what we want to do here and using the graph so here I brought the MPP graph and the production function together notice that the mppp doesn't exist at zero why not it never hits the x axis why not I think someone said it well you well you could I don't know but there's a more basic reason than that what oh it's not negative that's true it won't go negative but actually never hit zero why not if remember what's the formula change in y over change in X do you have zero in the denominator no you can't divide by zero it doesn't exist mathema Al that point does not exist it'll never hit that axis it actually starts right after it and if you want to look at fractions of an input but there are inputs you can look at fractions of people probably not and it's probably not there's an ethical question there too if you're presenting that but we would in general we will consider like two and a half if laborers because then you can look at that over like a week period with that on but in our case it starts at one and we get our function okay so notice the production function here is directly related to the MPP it's derived from it right we did that in the table and so there's a connection between these two and that's what we want to look at for a linear function just reminding you the MPP is constant it exhibits what we call constant returns to scale or constant returns all all that means is the slope is the same number never changes no matter the level of output in word in more plain English that says for every unit of input I add to the production process I always get the same amount of output and if you have constant resurs scale it means you have a linear production function it is a property of that kind so this is something in economics we look at a lot there's nice properties to have this in production processes but a lot of the time it's not constant but it makes things easier to examine so for nonlinear production functions we look at different areas of the graph the first area is this Orange Box so this is the area where the MPP curve is increasing it's going up climbing up the mountain here this is where the production function is increasing what we say at an increasing rate the slope is growing it's positive and it's getting bigger and bigger in essence this is the area where productivity is growing for your inputs we're getting more and more output for every labor we add to this production process okay so this begs the question is your profit maximization point in this area well not initially a lot of times reduction process is you're losing money right at the beginning you're starting you're turning it somewhere in here it likely turns around but are you maximizing profit in this box yeah usually unless your production function is flat but for our for all intense purposes yeah or let me put it another way would you ever stop producing in this box instead of adding laborers no because for think about it this way I add a labor right the price of your labor is constant at least for us right now okay so I'm paying $100 a day per se for each labor I add I'm getting more and more output if my output price is constant that means I'm making more Revenue off every laborer which means what more profit your bottom line is growing across this entire box so so you're earning your profits are starting to stack up here you you should in essence what does that mean don't stop production here if your inputs are this productive keep going you need to get out of this box actually and keep moving what's interesting is in least developed countries one of the reasons small farmers have a really hard time economically is they're never able to get out of this box and they're literally at the point where they're on the brink of profitability but they may not achieve it because they can't get the gains and productivity they need because of labor Credit and other constraints and access to resources after increasing resources you get to the next Orange Box next to it and that's this the next part of the production function and this is where it goes from it's increasing output is increasing but now a decreasing rate it's starting to Plateau we call this the area of decreasing returns this is where the MPP curve is falling we're on the downward slope here but it's still positive meaning total output's growing we know maximizing profit is not the same as maximizing output notice this box ends at the top of theu ruction function and so at the end of this box you're maximizing output we know you shouldn't go you shouldn't stop producing here because of productivity gains in your production process and so somewhere in here is likely where you're going to maximize profit that's all we know so far we will learn more we need to bring in costs and prices to be able to answer specifically where because if cost and prices change that point changes it's not fixed and so we need to bring in more information from the market and we'll do that in the next couple weeks but in this case we're somewhere in this box we'll maximize our profits so we want to get to the point where we have decreasing returns where you don't want to go is to the next box this is the area of negative returns this is as you add more input total output or PPP is now falling your slope is negative you're on this point of the MPP curve that is below zero this is a double whammy if you've never seen that game no whammy no whammy no whammy you got a double whammy here okay the first whammy is you're paying for that input the second whammy is your revenues have just Fallen you've taken a double economic impact there's one way to put it but you it's kind of that double whammy you you're incurring the costs and then you've just lost Revenue if you're operating at this point I tell people think of this as the pink slip Zone what's a pink slip nope is not the title to your vehicle much worse than that if you get a pink slip on your job what does it mean you're getting laid off or fired this is the Zone in which management goes H if people hit this Zone all the time what you want to do is get out of it if you notice this is happening go backwards right you need to get back over here because here you're losing money and it gets worse and worse the farther you go down in that box those losses grow exponentially or they can't and so you don't want to be there okay questions so far so we have constant returns which means your a linear production function productivity is static it never changes it's the same level and then for nonlinear we have three types increasing where productivity is going up MPP curve is on its upward slope decreasing where it's dropping but outputs still going up this the mppp is falling but still above zero and then negative where productivity actually starts causing drops in total output and so your MPP is negative it's kind of a neat way to remember this one if you have a negative slope you're a negative returns okay so what does this all mean in economics well we've seen that as you add more of an input that is used the less output we get out of each additional input Setter Paris we like that phrase I would star that phrase and know what it means but this property so we've done a lot of economic studies we've seen this nature and process and production processes increasing to decreasing the negative returns so much so we come up with our first law in economics unlike physics our laws are not unbreakable we always have exceptions to our laws but it's so pervasive it tends to hold for almost most situations we call this the law of diminishing marginal return and what it says as as we add additional units of an input and as they're combined with the fixed amount of other inut puts a point is always reached at which the additional output produced from the last unit out of input will decline more simply put in every production process we will hit a point of decreasing returns we will always hit a point where productivity Falls as you add more input you can go back to the example we did with studying in your exam grade as can you think of if you keep studying hour after hour after hour so at the eighth hour if you put eight hours in good for you say it's still positive do you think you're it's productive in gaining information and learning it at the 16th hour what about at the 24th hour no especially if it's all in one day if you've had to stay awake with Mountain Dew nojos coffee and there's a lot of others so as Red Bull or the any other energy drinks you're probably not doing well at the 24th hour you probably hit an area of diminishing returns and information you're ging gaining at the 24th you might even be in negative returns you're actually losing information so stuff you did at the beginning now you're losing because you're getting tired your brain's tired and it can't compete anymore and so this example applies to a lot of situations and so do we see this in crop and livestock production yeah if you keep feeding cattle grain continuously and never stop what happens what they get obese right what happens your gain goes up what happens to your quality though and the output of that meat actually and what you earn it crashes you don't want big steers they don't sell as well okay and so the law of diminishing returns is something that we see again and again in a lot of different situations at some point as you keep adding input or keep doing something it becomes less and less productive the other concept we want to look at that's related is average physical product or AP and it doesn't mean it's not app but ABP is your average kind of productivity of your inputs it's a measure of efficiency how well am I using those inputs on average at a given point of production where the marginal asks about the next unit AP is actually describing the production process from the beginning to where you're at and it's saying how well have I used those inputs AP is also and I forgot to say this on the other one MPP sometimes is abbreviated just as marginal product drop the physical because it's really long word or sometimes we had an input name at the end and we call it marginal product of for labor would be of Labor and we say the name of the input AP is similar it's also referred to as average product and sometimes like average product of a given input average product of labor okay they're all synonymous and so if you see those terms so AP is your total output divided by your total input what I want you to do is you have to actually do this talk to the person next to you if you're on the outside and the person next to you turns the other way tap them on the shoulder and say hey talk to me and then nicely go I haven't met you my name is and then they'll face you go my hey nice to meet you my name is right and so introduce yourself if you don't know each other but please work with your neighbor next to you introduce yourself so you get to know people and calculate AP in this table e e e e e e so let's go ahead and come back so AP is total output divided by total input so it's just this column divided by this column just make sure I'm pointing to the right one right and so what's my AP for the fir when I have one unit of Labor 10 what's my AP when I have two units it's 11 11 what barrels per person so this is the average barrels per person notice this is different than MPP I get 12 barrels for the second but on average it raises that average what about three employees yep 12 and a third if you want to be exact you'd write a third or point3 33 forever what about four yeah and so on check your answers so this is graded I need you to rip your I'm just kidding quiz not graded don't worry right so check your answers oh you're fine this is the most productive right so he's asking that number with four would that fourth employee be the or that level be the most efficient well they're getting the most productive that fourth employee is the most productive of all of them so productivity is going up but notice that may not be the most efficient point if your average the average is still going up I'm still adding quite a bit here but notice and so it still pulls it up a bit um and we're going to look at that relationship here in a minute usually a big question is so this measures product activity of your inputs as you add each unit or hire a person this is your average that you're getting out per person which do you think is more important so if you're going to use this for managing your production line which one should you use MPP or AP most people use so if you go into management and I've seen this a lot they use AP they talk about averages in reality though and it's not bad to look at that because you can look at averages and see Finding efficiencies and why it's doing that but more importantly actually is mppp this is the one that drives profits this has related to that but it can lead you down a wrong path a little bit potentially it may pay to be a little inefficient and so maximizing efficiency and using that people do twoo objectives plant managers very common and we see this in Productions maximize output maximize efficiency the problem is efficiency gains may not be that profit maximizing point you could do better by being a little inefficient okay and so it's MPP is really what you want to be looking at and it's not that you ignore a though and so if we can graph the AP curve on the same graph we put the NPP curve the units are the same they're both barrels per employee so notice we have the MPP curve here I just graph the AP by just plot the points connect the dots these two curves are directly related in actuality the AP curve is driven by productivity or the MPP curve so your efficiency is driven by productivity and so the relationship between these curves kind of is as follows when MPP is above the average the AP curve it's pulling it up in essence you're adding enough to Output that you're pulling that efficiency that average up whereas when it falls below the a curve the average is falling so you're not adding enough output fast enough to keep the average high it starts falling and it's because productivity is falling so notice where these curves intersect so what's true when they intersect efficiency is maximized but what we learned and I don't cover deeply in this class but it is in your book if you're interested this point is where you start actually looking for the profit maximizing Point decreasing returns actually starts here you can actually ignore this part to this point the profit Max will actually be from that intersection to where you start hitting negative returns and so notice that's on a point where your efficiency is dropping and so you want to hit Max efficiency but you actually want to go beyond it you don't want to become utterly inefficient though that means you might be a negative return Zone that's the pink slip Zone that's where management goes byebye you've been here too long if you've been in the if you've been in the negative return Zone okay that's the end zone you don't want to hit it would be like playing football and making touchdowns in the other team's End Zone every time that would be bad you're likely not GNA even be benched you might not be on the team okay so that's where kind of This falls in so remember your laps are do when beginning of your lab otherwise have an awesome afternoon we have tutoring we'll see you tomorrow