welcome back so now we're going to go over how a firm in perfect competition maximizes profit by choosing their quantity so i'm going to show you two ways to do this and if you think back to our chapter on consumer choice chapter six we we looked at two different ways to think about maximizing utility the first one was by just looking at a total utility schedule if you remember that and then we used our margin utility method we said we're going to do with marginal utility because this reflects how actual decision making is made and so we're gonna do the same thing here we're gonna do it once by looking at just a table of total cost and figuring out where profits are maximized and then we're gonna show the margin utility method the margin sorry marginal cost method and then the marginal cost cost method is what we're going to be doing in our models in our homework our exam um so so that's that's coming later this first one is the total cost total revenue method and it's kind of just to show an overall picture of what we mean by maximizing profit okay so the following table shows how to find the profit maximizing output with a given price in the cost schedule so this is going to be a raspberry farmer so the cost for raspberry farmer are provided okay so here's the quantity of raspberries they can sell here's remember fixed cost variable cost total cost okay just this is why we did a last chapter to familiarize ourselves with it this stuff and now we're going to add the price of raspberries okay so the market price for a pack of raspberries is four dollars the table shows how to use this information to construct revenue profit so we're going to take this information the fact of the market price raspberry is four dollars and we're gonna come up with how many raspberries this farmer should sell so if your instinct is they should sell them all they should sell a hundred we'll remember what we learned last chapter about increasing marginal cost because of diminishing marginal returns you're increasing marginal cost which means the more and more raspberries you produce your marginal cost can go up so it might not actually make sense to produce as many as possible like imagine this farmer like eeking out every single raspberry in his plot of land by using more and more expensive fertilizer more and more labor hours to to pick and turn over to the point where it might not be profitable it may be producing a little bit less actually is the way to maximize the profit and that's what we're gonna see so this method is actually pretty pretty easy um because we know the price for a pack of raspberries is four dollars okay and we're given the quantity in this table so if you recall the revenue in in when you're selling your your good is just the price times the quantity so the price is four dollars here's the quantity so if you sell zero raspberries your revenue is zero dollars if you sell ten raspberries ten times four is forty dollars if you sell twenty raspberries twenty times four is eighty dollars and so on and so forth okay i'm going to just click ahead in my slides and have that table filled out now profit again pretty straightforward here is the total cost there's your answer i wanted to do a couple first like i did last one okay here we go here is your total cost here's your total revenue profit is just revenue minus cost cost revenue minus cost equals profit so if you're bringing in nothing because you're not selling your raspberries we have 62 dollars in fixed cost guess what you just lost 62. negative 62 is your is your profit or loss in this case if you are bringing in 40 in revenue and it cost you 90 to get that 40 bucks guess what you just lost 50 okay when we continue eventually get to the place where they're making money 160 in revenue minus 144 dollars in cost this is 16 with a profit and that's it now we can calculate the profit by just subtracting revenue from cost and there you go there's the table filled out and so if we want to know where profit is maximized we just look at where the number is the highest bam now in this example profit is maximized by producing either 70 or 80 packs of raspberries this is an example straight from the book um this is how the book questions are written if you remember in our maximizing utility champ chapter in chapter six we always all of our chapters are always set up in a way that the very last thing you purchased between the two goods was when the utility was equal that there's a there's a logic behind why books do this it's because they want to be consistent with um what the answer would be if you had a continuous quantity if it was the truth is the answer's somewhere between 70 and 80. so they do it like this in order to be consistent with what it looks like when you have a continuous quantity where you can produce 72 73 raspberries but to simplify in the table they kind of have to keep it this way so there's a reason why the book is always set up this way um we get to our examples in our um in that we're gonna do for homework we do for exams it's not gonna be like this there will be an actual answer and not this sort of prof is maximized when 70 or 80 raspberries are produced but still now you see the idea of profit maximization if you produce too few you don't make enough money if you bruise too much you make less money and again this is because of increasing marginal cost because of diminishing marginal product because eventually as you produce more and more raspberries becomes more and more expensive to produce more raspberries that's always going to be true in the short run according to the law of diminishing marginal returns okay and so because that's true in the short run in these short run profit maximizing stories the answer is not going to be produced as much as possible the answer is going to have a maximizing point somewhere okay if we look at this in a graph form this is just that table in a graph okay this is this curvy line is the total cost curve okay the total cost curve which has sort of that that that u shape okay the revenue is this straight line the reason revenue is always drawn as a straight line because it has a constant slope 10 times 4 20 times 4 30 times 4 40 times 4 50 times 4. so if you're like understand like how math works you understand that that um sorry if you understand math works you understand you have a constant slope if it's always x times a constant you end up with a straight line and so we look at the difference between these we're looking for the point where the gap between cost and revenue is the biggest because if you're over here the cost is higher in the revenue you're losing money if you're over here the cost is higher in the revenue you're losing money somewhere profit is the highest when the revenue is higher than the cost by the most amount if this graph is confusing you don't worry we don't use it i just i love these visuals personally that illustrate what's going on because i do think they help for understanding but they're not something we necessarily need to use to answer the questions okay all right so now let's do it instead of marginal revenue and marginal cost like i said this is going to be closer to the way you're actually going to do it after this we're going to have an example where we use the cost curve graphs developed in last chapter which is how you're actually going to do it but this is going to be the table version that informs we're about to see so the the the sort of the method the reason here is the idea that if you don't have at your disposal an entire picture of your cost curves it's practical to talk about small changes in your decision making remember back in chapter six there's a lot of similarity between chapter six and this remember in chapter six we always said what are you gonna do with your next ten dollars are you gonna purchase that next t-shirt or the next movie right and we did it step by step till we got the answer that's the idea here is are you going to produce another pack of raspberries or not if you are we know you're producing more if you're not that means you stop i'll show you what i mean as we go through this this example to do this we need to calculate what's called marginal revenue and marginal cost there's that marginal term again marginal revenue is the extra revenue that firms receive by producing another unit of the good so by producing another pack of raspberries how much more revenue will the farmer receive for perfect competition that is absolutely simple if the price of raspberries is four dollars and you're producing zero raspberries then you produce one pack and sell it for four dollars your revenue goes from zero to four so your marginal revenue is four dollars instead let's pretend you're producing 100 packs of raspberries and you produce one more pack that raises your revenue from 400 to 404 dollars so your marginal revenue is four dollars let's say you're producing 70 packs of raspberries you produce one more what are you gonna sell that one more pack for four dollars so your marginal revenue is four dollars what if you're selling 10 000 packs of raspberries and you sell one more pack what can you sell that one more pack for four dollars so your marginal revenue is four dollars in perfect competition because firms sell at the market price and we have the assumption of many buyers so you're always gonna be able to sell that next pack of raspberries the marginal revenue is always equal to the price again this is perfect competition we're gonna see it's not true in other market structures but in perfect competition you can always sell your raspberries at the market price so every time you sell another pack of raspberries that's four dollars more revenue the marginal revenue is fixed at four dollars whether that means your profit goes up or not depends on marginal cost but the rarjal revenue is fixed at four dollars the price of raspberries price is equal to marginal revenue as for marginal cost we learned how to calculate that last chapter it's the change in total cost divided by the change in quantity okay so here's an example just in case you forgot from last chapter if the total cost of producing 20 packs of raspberries and this is from the table is 110 and the total cost of producing 30 packs of raspberries 126 then the marginal cost is 16 divided by 10 which is the change in raspberries we say a dollar 60 is our answer sorry this is one sentence the change in cost is 16 divided by 10. the marginal cost is 16 divided by 10. okay so let's fill out this table again we did this last semester last semester last chapter chapter seven so hopefully you're familiar with how to do it to fill out the marginal cost we take the increase in cost 28 divide by the increase in quantity 10 2.80 cents increase in cost 20 divided by the increase in quantity 10 2 the increase in cost 16 increased in quantity 10 16 divided by 10 1.60 increase in cost hopefully you're seeing what's going on and remember it increases right so we get to the end increase in cost 80 divided by increase in quantity 10 so eight dollars it increases the end because the law of diminishing marginal utility says that marginal costs are going to skyrocket as it becomes more and more expensive to produce additional units filling out the marginal revenue column i just said that marginal revenue is equal to price so just got to come up with the price and pop it in there so how do you use marginal revenue and marginal cost to figure out where profits are maximized obviously we already know the answer we already did this one we know our profits are maximized but how can we use marginal revenue marginal cost to come up with that answer it's pretty straightforward look at it this way okay let me get my um tools out i'm gonna use here think about producing zero make that bigger think about producing zero raspberries and you want to know should i move up to 10 raspberries well the marginal cost of producing 10 raspberries is 2.80 cents that's how much it's gonna cost you to do that 2.80 per raspberry what's the benefit i lost my cursor again what's the benefit of doing that you get that's not the tool i'm using the benefit is you get four dollars worth of revenue so remember the one of the first things we learned in this course is decision making rational decision making is you do things when the benefit outweighs the cost the benefit of making more raspberries is four dollars the cost of making those 10 raspberries is 280. the benefit outweighs the cost you're going to add money to your pocket if you produce those raspberries so you do it you produce those raspberries you produce those first 10. should we go up higher the cost is two dollars the revenue is four dollars you should the revenue weighs the cost the benefit outweighs the the cost should we keep going a dollar sixty versus four yes we should keep going the beven if that weighs the cost should we keep going four out weighs a dollar eighty yes we should keep going should we keep going yes four out weighs 220 should we keep going yes 4 out weighs 260. should we keep going yes 4 out weighs 320. so every step along the way the benefit to the farmer by making more raspberries that marginal revenue that four dollars of extra revenue is higher than the extra cost when you do things that bring in more money then they make you spend you've raised your profit that's why profit keeps going up now let's go to this next one what we see here is if we keep going farther and we do this extra 10 the cost is the same as your revenue meaning you're indifferent it doesn't cost you profit it doesn't help your profit and remember that was our conclusion here is that we have this sort of two sided um answers where either one of these maximizes your profit should we go further by my color choice i think you know the answer but it's going to cost you six dollars and you're gonna bring in four dollars don't do it the revenue is less than the cost you're gonna bring in four dollars we're gonna spend six dollars to get that four dollars that's how you lose money by doing something that costs you more than you bring in and we look again in our at our profit column at the end you see exactly that story that if you go any further than 80 your profit starts to go down so that is the way we're going to do this is we are going to we're going to to do this and or we're going to do these questions in such a way that we're going to compare the marginal revenue the marginal cost and as soon as we see that it turns red as soon as you start to lose money you stop doing it and that tells us where profits are maximized profits are maximized if you keep making good decisions you make all the good decisions you maximize your profits okay graphically this is what it looks like remember our upward sloping marginal cost curve our upper sloping marginal cost curve looks like this this is what we developed in the last chapter and we're going to have a horizontal marginal revenue curve why is it horizontal because the marginal revenue is equal to the price the price is given by the market in this case it was four dollars whether you're selling zero 100 50 42 raspberries the marginal revenue is four dollars that's the price so everywhere down here sorry i'm lost my lost my drawing tools everywhere down here we see that the price four dollars is above the marginal cost so if you sell these raspberries you're selling them for a higher amount then you then you paid for them in other words you're making money so you keep selling raspberries as long as that's the case and then you hit a point where the marginal revenue is equal to the marginal cost and you stop because if you go any farther you're in the zone where the marginal cost is greater than the marginal revenue in other words it costs you more flow to produce those raspberries you can sell them for so you don't do it so this is what the continuous version of a question like this looks like notice that this answer looks like it's about 78 we couldn't see that in the table because the table just gave us these 10 20 30 40 50 60 so we weren't really sure what to do there when we do these examples for the homer for the exam we're going to be doing like this with the curves and because we're going to do them with the curves we're going to have a finite answer it's not going to be 70 or 80 or both perfect answers we're gonna say 78 or whatever this is and the table that you looked at if you're trying to think how did you get 78 from that table that table didn't have enough information it was an incomplete story the graphs are going to be complete stories we're a continuous level of raspberries okay so there you go we've reached our our magic formula our magic key our magic sentence to understand how you maximize profit in the world of perfect competition is you look where the marginal cost mc is equal to the price you find that point you find the point where the marginal cost is equal to the price when you find that place you know where profit is maximized burn that into your brains as much as you can for the rest of this chapter the marginal cost is equal to the price okay why is marginal cost is equal to the price because the price is equal to the marginal revenue okay so i'm gonna stop here then we're gonna do our first graphical example and that's gonna look like what you're gonna do for your homework okay