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# Review of revenue and cost graphs for a monopoly

AP.MICRO:
PRD‑3 (EU)
,
PRD‑3.B (LO)
,
PRD‑3.B.6 (EK)

## Video transcript

what I want to do in this video is review a little bit of what we've learned about monopolies and in the process get a better understanding for some of the graphical representations which we have talked about in the past but I want to put it all together in this video here so let's say that the industry that we are in the demand curve looks something like that so that is demand and I'm going to assume that it is a linear demand curve this axis right over here is dollars per unit in the context of demand that's price and this is quantity over here this little graph here we still have quantity in the horizontal axis but the vertical axis isn't just dollars per unit it's absolute level of dollars so over here we can actually plot we can actually plot total revenue as a function of quantity total revenue so obviously if we remember we're assuming we're the only producer here where we have a monopoly we have a monopoly in this market so if we pick a quantity if we pick if we don't produce anything we're not going to generate any revenue so our total revenue will be zero and if we produce a bunch but we don't charge anything for it and that's this point right over here our total revenue will also will also be zero and we've done this in other videos but then as we increase quantity from this point our total revenue will keep going up and up and up there'll be some maximum point and then it'll start going down again so our total revenue would look something like this total revenue would look something like that total revenue and from the total revenue we can think about what the marginal revenue would look like remember the marginal revenue just says if I increase my quantity by a little bit how much am i increasing my total revenue and so that's essentially the slope the slope of the total revenue curve at any given point or you could think of it as the slope of the tangent line and we've seen before when you start here you have a very high positive slope and we've seen in other videos it actually ends up being the exact same value is where the demand curve intersects the vertical axis right over there but then it keeps going lower the slope it becomes a little less deep less deep less steep is still positive less deep less deep and then becomes e go right over there and then it starts going negative so it becomes zero right at right at that quantity so it becomes the larger the slope of this keeps going down and down and down it's positive then it becomes zero and then it actually becomes negative and you see that here now it starts downward sloping even more steep even more steep and even more steep so that's the revenue side of things and let me label this this is our marginal that's our marginal revenue curve slope of the total revenue if we're going to maximize profit we need to think about what our costs look like so let me draw our total cost curve and I will do it in magenta so let's say our total costs look something like this total costs look something like that out here when we have very few units we have zero units all of our costs are fixed costs and then we as we had produce more and more units with the variable costs start piling on over there and even from this diagram you can actually start to visually see economic profit economic profit and when we talk about when we're talking about costs and profit in an economics class like this is kind of one I guess you remember you should view it in terms of economic profit when we're talking about total costs we're talking about opportunity costs so this is total total opportunity costs both the implicit the ones that you or both the explicit the ones that you're actually paying money for explicitly and the implicit opportunity cost total opportunity costs that's total opportunity cost and the difference between your total revenue so for a given quantity for a given quantity the distance the difference between your total revenue and your total opportunity costs that gives you your economic profit so for this quantity right over here your economic profit would be represented by the height of this little bar between these two curves but what we see what's going on is as we increase the quantity over here these curves are getting further and further apart that's because the green curve the total revenue has a its slope is larger than this purple curve which is total total opportunity cost or you could say total cost and so we could even go even further along this the distance between the two curves gets bigger Eggar looks like it maxes out right about right around here someplace and then the two things start getting closer and closer together now this purple curves slope is now larger than the orange curve slope so then they start getting closer and closer together and so if you were to just look at this graph whatever the maximum distance between these two things are it looks like it's about it looks like it's about there right over here that would be your maximum economic profit but we know we can also visualize it on this curve over here and we can do that by plotting our marginal cost and remember marginal cost just as marginal revenue is the slope of your total revenue curve marginal cost is the slope the instantaneous slope at any point of your total cost curve so I will do that let's do that in yellow so right over here you have a zero slope or pretty close to zero at least the way I drew it over there so your marginal cost is going to be pretty close to zero right over there and then we see that this slope keeps increasing and increasing and increasing and so our marginal cost will keep increasing increasing and increasing so it will look something like that that is our marginal cost curve so if if we pick a quantity and if we find that the marginal cost over here I don't know let's say it's five dollars per unit that literally means that the slope at that same quantity the slope of our total cost curve that the slope over there would have to be five that's what that is telling us this is plotting the slope of this curve right over here and if we want to maximize profit we already talked about how we would do it visually on this curve we can do it over here well right over here as we produce if we start from producing nothing to producing something for each incremental unit our mark the incremental revenue we get on that is much higher than the incremental cost so hey we should produce it because we're going to get profit there we could keep producing because we're going to get profit on each of these incremental units so we'll keep doing it we'll keep doing it we'll keep doing it until the marginal revenue is equal to the marginal cost at that point it doesn't make sense for us to produce any more if we produce an extra unit past that point on that unit our cost will be higher than our revenue so it will eat into our economic so this right over here is where we max the quantity at which we maximize profit and we see it we see it right over there the way I drew it luckily it looks like that is the maximum point between those two curves as well and it makes sense before at this point when marginal revenue is higher than marginal cost that means that the slope of the total revenue curve is larger than the slope of the total cost curve so they're getting further and further apart after this point F and right at that point their slopes are the same so the slopes are going to be the same right over there and then after that point the slope of the marginal cost curve or the marginal cost is higher which tells that the slope of the total cost curve is higher then the slope of the total return the total revenue curve and so they're going to get closer and closer together and this distance gets quenched apart so that is where you maximize profit and if you wanted to visualize the actual profit on this graph over here we cannot obviously visualize it here is the distance between these two curves if you want to visualize it over here we would have to find we would have to plot our average total cost curve and essentially what you're doing is just taking this total cost curve and you're not just taking the slope at any point that's the marginal cost instead you're just dividing it by the quantity so if you take this total cost curve if you take this value divide it by very very very low quantity you're going to get a very very very very large number you could imagine as you're spreading your fixed costs amongst a very small quantity so you can get a very large number then as you produce more and more and more your average total costs go down but then your variable costs start picking up and your average total cost might look something like that average total costs and so if you want to know your profit your that which you have maximized from this graph right over here say well this is the quantity that maximizes my profit marginal revenue is equal to marginal cost the price that I can get in the market for that quantity well then you go up to your demand curve and it gives you this is the price that you will get for that quantity and so that is on a on a per unit basis that is the revenue that you will get you could you can view price is equal to price is the same thing as revenue revenue per unit so on a per unit basis this is the revenue you're getting and on a per unit basis this is your average cost this is average total causes is taking all your costs and dividing it by units so on an average per unit basis this is going to be your economic profit on a on a per unit basis and if you wanted to find your actual economic profit you would have to multiply it by the total number of units so you would essentially have the area of this rectangle right over here this is your per unit average economic profit and show your total economic profit is going to be quantity times profit per unit and so this right over here is economic economic profit or maybe I should call total economic profit let me write it out total total economic economic profit and the area of that rectangle should be the same thing as the height as the height of this right over here and the only reason and we can maintain this is a sustainable scenario because we have a monopoly no one else can enter if this was not a monopoly if there were no barriers to entry then other people say hey there's economic profit there that means it's there's an incentive to for me to put those same resources together and try to compete because I'm going to get better returns than my then my opportunity costs would otherwise that then might then my alternatives is a good way to think about it