hi everybody having covered both short-run and long-run costs let's dive straight into revenue revenue is just the money made from sales by business and therefore we can look at these core equations and understand them very clearly total revenue is just the price that the business is charging multiplied by the quantity they are selling at that price it is P times Q average revenue is just total revenue divided by quantity but if we pay that through we get to P times Q over Q can't allow the Q's were left with just price so average revenue is just the price a great trick for you their marginal revenue marginal just means extra so in this case the extra revenue generated when we sell more output so therefore the equation is the change in total revenue divided by the change in quantity what will our revenue curves look like well it depends on the level of competition there can only be two groups of competition perfect competition the most intense in the same competition or imperfect competition like a monopoly we're going to look at perfect competition first and see what our revenue curves look like there well we need to understand what the characteristics are of a perfectly competitive market first in this kind of market there'll be many buyers and sellers if I mean precise infinite buyers and sellers this is a very theoretical extreme market structure insane intense competition all these firms are selling homogeneous goods and services meaning identical goods and services and that means that these firms are price takers they have no ability to set their price they have to take the price in the market and charge that price there are no barriers to entry and exit and there is perfect information of market conditions no barrier to entry and exit means free movement in and out of the market ok so we get the basic idea insane competition what does that mean in terms of revenue that's what we're looking for well it means this firm is a price taker crucially so regardless of the number of units they're selling they're always going to be selling them at the same price so let's say the price is a pound and here the units that are selling let's work out TR MRNA are using our equations above TR is P times Q so we're going to get 1 2 3 4 & 5 so we say this is in pounds or dollars whatever marginal revenue is the change in TR divided by the change in Q the change in Q is always once we're just looking at the change in TR which in each case is 1 easy stuff and average revenue you look at the trick is just price so that's gonna be one as well okay that's great so if we see the numbers here it's very easy now to draw our revenue curves let's start by drawing average revenue and marginal revenue we've gotta have price and revenue on the axis because we're joining any are here but we can see that both AR and M are are the same and they are constant over a range of quantity so AR and M are in perfect competition will just look like that but I'm not going to stop my labeling there I'm also gonna say AR equals M R which equals demand and at the end of this video I'll explain why average revenue is equal to demand that will come later but there we go that is very simple and if I had to put a figure here that figure would be one pound there what about total revenue we can see that total revenue is increasing but always increasing by one so therefore if we're drawing our total revenue curve it's gonna be a linear upward sloping line showing a constant gradient always increasing by one so very simple revenue curves in perfect competition easy as you like what about when there is imperfect competition how do our revenue curves change there well in perfect competition is the exact reverse of perfect competition let's look at the characteristics so now there are a few buyers and sellers they're all selling differentiated goods and services making them price makers now so they can set their own prices there are high barriers to entry and exit and there is imperfect information of market conditions everything in Reverse here the key thing is that firms are price makers and we can see now that we've got different prices being charged by the firm but crucially they are going to be govern these firms by the law of demand so at high prices quantity sold is going to be low and a low prices quantity sold is going to be higher right but we want to focus on revenue that's what we're here for so let's calculate TR MRNA are given these figures here TR is just P times Q so we're going to get 10 18 24 28 30 30 28 24 18 and 10 very simple P times Q in each case let's do marginal revenue which is the change in TR over the change in Q the change in Q is always 1 so that makes a very easy we just have to look at the change in TR so we have ten then we go to eight two six two four two two two zero and then mr can go negative and it does here to minus 2 to minus 4 minus 6 and then minus 8 to finish average revenue is just the price that's our little trick lovely trick so just have 10 9 8 7 6 5 4 3 2 & 1 really simple stuff using these numbers we could plot the curves I'm not going to plot I'm gonna use these numbers to give us a general shape of the curves what I want to draw first is our average revenue curve and we can see that average revenue starts high and then it falls doesn't it remember average revenue is just a demand curve and if we draw it it looks exactly like a demand curve than we are used to okay great what about marginal revenue marginal revenue starts at the same point and also decreases it's also downward sloping but you can see at a much faster rate than average revenue and it can go negative so marginal revenue is going to look like that precisely marginal revenue is twice as steep as average revenue there are two ways to understand that one is with the mathematical proof if you click on this link here guys I have done that proof in a different video you can watch that it's very interesting I probably the best way to understand it mathematically but intuitively look at it this way when a firm drops its price it's not just dropping its price for the next unit sold it's dropping its price on all the units that it's selling even the units that it saw beforehand are now being sold at a lower price and that means that marginal revenue is going to drop twice as steep as average revenue it's going to drop faster than average revenue but you don't need to know the the detail logic there at orders make sure you draw it roughly twice as steep as average revenue okay while we're here why is a verage revenue equal to demand this is important here all right let's look at demand demand is just a downward sloping linear line and all linear lines take this form from maths if you remember y equals MX plus C that's the basic equation in the linear line okay where C is the y-intercept M is the gradient it's the coefficient of x so M is just the gradient right the slope of the line okay fine our demand curve is downward-sloping it's a linear line but let's apply it now to this form so why is price when we draw a demand curve isn't it so we could say price equals let's take our y-intercept first and let's call it a so a is our y-intercept and it's a negative gradient so it's going to be not a positive number but a negative number minus let's call that coefficient that gradient let's call it B and on the x-axis it's not gonna be X its quantity so P equals a minus B Q that is our demand curve just apply it to the basic form of y equals MX plus C now we've just said that average revenue is equal to the price so average revenue is equal to price and if I saying price is equal to this and this is our demand curve it must follow that average revenue is equal to demand there is no way you need to know that at all in that way all you need to be able to do is to write down here that average revenue equals demand but something of interest for you know that you're asking that question beforehand okay great what about total revenue now well you can see total revenue is rising rising rising better a slower rate each time because marginal revenue is falling it hits its peak and then it starts to decrease okay how do we draw that when we have to draw it precisely total revenue will hit its peak where marginal revenue is zero so it's going to be rising but at a slower rate it's going to hit its peak when marginal revenue is zero and then it's going to fall there's our total revenue curve and we can write that on the side that total revenue is maximized when marginal revenue is equal to zero why is that well when marginal revenue is a negative total revenue is going to be decreasing all of these extra units are being generated with negative extra revenue and therefore total revenue is going to come down and we see that very clearly here when marginal revenue is negative total revenue decreases okay fine so any point to the right of where Mr is zero cannot be maximizing TR any point in the left can't be either because any point to the left marginal revenue is always positive and therefore producing one more unit will always give you more revenue and therefore total revenue will keep rising their rate at which it rises will be falling because marginal revenues decreasing but TR will always rise as long as marginal revenue is positive so the only point where TR is maximized is when there is no more extra revenue to be gained and that occurs wet M are a zero so that's everything you need to know guys that covers revenue curves in both imperfect competition and imperfect competition you can see that an imperfect competition that curves them very different to have they looked in perfect competition you've got the calculations you've got the equations you've got everything you need to smash this topic area really hope you get it now stay tuned for the next video we're going to dive into profit now putting costs and revenues together I'll see you all in that video can't wait for it guys [Music]