hello welcome back so now let's talk about how we're going to use our cost curves to figure out the profit maximizing output how a monopolist is going to maximize profit so first let's look at what's changed with our demand curve okay so this is our demand curve it's now downward sloping like we've seen before and what you're seeing is we're going to draw a second downward sloping curve and that's the marginal revenue curve remember that marginal revenue is always below price so graphically that means the marginal revenue is always below the demand curve now it's actually fairly simple calculus if you understand calculus to say that to draw if you have a linear demand curve a demand curve that's a straight line like this then the marginal revenue is going to be the is also going to be down from sloping line that starts in the same place but has double the slope meaning it's twice as steep okay uh don't worry about that i'm not going to make you do that but i'm going to draw linear demand curves for you in these in your homework assignment and your exam et cetera and so always do it like this um and this is this is you know something that's easily provable calculus that if you have a downward sloping linear demand curve the marginal rapid curve should slope downward at twice as fast okay so i'm going to start with this picture um which is just because i want you to be able to reference it later and come back to this picture it's a little ugly and i admit it's a little hard to understand um and so after i show you this picture i'm going to go into an example where we're going to do the whole thing but what i want to show you is first here's my marginal cost curve here's my marginal revenue curve so we think about how many units a firm a monopolist is going to produce we start at zero and as long as the marginal revenue is above the marginal cost so again here's marginal revenue let me highlight them so here's marginal revenue here's marginal cost as long as marginal revenue is above marginal cost this firm is going to produce more and more and more units remember that's the whole story if this part hasn't clicked yet i mean we got to take a few steps back maybe back to the last chapter the idea is the marginal revenue is how much more you get for selling an item the marginal cost is how much it cost you so if you're bringing in more money the red line then it costs you the yellow line that's good you keep doing it you keep selling more and more you stop where they meet we stop where they meet because if you go any further the cost the yellow line is higher the revenue the red line meaning it's going to cost you more to make more pills or whatever this is then you're going to be able to sell them for so you lose money by doing it so you stop right there that is going to always tell you the quantity again that's so that's step one this is safe yeah step one where marginal revenue equals marginal cost that's going to tell you the quantity okay that actually does not tell you the price it is very tempting for people to go and look over here and say this is the price whatever the price is there is the price that's not what we're gonna do the reason is that's telling you how much how many units to sell to maximize your profit but the price you could sell well the demand curve is what tells you that the demand curve tells you how much people are willing to pay for that many units so we go up to the demand curve and that's step two that's going to tell us what price to charge lastly if we want to know the profit we just need to compare the price to the average total cost okay we didn't look at how this area this rectangle gives you average total cost in the last chapter but that's just another way to look at the things we talked about the way we typically do it is we we multiply the price by the quantity to get revenue we multiply the average total cost by the quantity to get cost and that difference is going to be the profit um but graphically yeah this green area of this rectangle is the profit okay so let's go through an example because i think this is gonna be nice to to to go back on to know where this slide is so you can look at it and help you go through the steps when you're doing your homework but let's go through a full blown example and see how that works and i just lost my cursor i hate when i do this to myself there it is okay consider the following market for epipen an epinephrine auto injector company operating a monopoly market so we're going to start with a b and c we're going to do d and e after a couple more slides a b and c what's the profit maximizing output for the monopolist what is the price charged by the monopolist and how much profit is obtained by the monopolist those are the three things we're going to look at okay i actually have a bigger version here it's going to make it easier for me to do this so again part a is going to be what is the quantity what's the profit maximizing output how many epipens are sold we're going to ask what price the seller sells them for and we're going to look at what the profit the seller has so step one to quantity we need to compare the marginal cost to the marginal revenue if the more sorry doing this with a kid home is not easy so compare the marginal revenue the markets will cost because if the marginal revenue is higher than the marginal cost sell more at depends if the marginal cost is higher than the medical stop selling epipens so that's why we stop right here at 175 epipens that's my answer again all i do is look for a marginal revenue equals marginal cost okay the next question is the price and like i said a lot of people are going to be tempted to put the answers 200 because that's they're looking at this point and think that must be a special point and it is it tells you the quantity but to get the price we need to look at 175 and follow it all the way up to the demand curve the demand curve tells us what people are willing to pay remember that whole thing about demand being the willingness to pay so the willingness to pay for 175 epipens is 600. okay so last thing we need to do is calculate the profit so remember there's two ways we can calculate profits when we have our cost curves the first way is to calculate the revenue and cost separately so 600 times 175 that gives me a revenue of 105 000 now the cost is we look at 175 epipens and we see it 175 epipens the average total cost curve hits at 400. 400 times 175 equals seventy thousand and so last of the profit is 105 minus seventy thousand which is equal to 35 000. that is the profit and remember there's another way to do this the other way to do this is just to compare the price with the average total cost that's this difference here 600 minus 400 that's 200 multiplied by 175 epipens that's another way we could have got to 35 000. and in the um in the that slide before when it shows that area that's what it's doing it's saying that this area here represents the profit because you remember the the formula from the area of a rectangle from you know high school or middle school whenever you took your first geometry course it's the base times the height so 175 times 200. so again that's just to show you what it meant by that that rectangle in the last slide um you don't have to do it that way okay so that's it really it's just those three steps and i hope those steps aren't that difficult for you okay so we're gonna have one more lecture um about efficiency but um this is this is the the meat this is the book this is what you're gonna have to do in the homework this is what you're gonna have to the exam everything else left is just me explaining what's going on and then our last look at efficiency