What is the relationship between marginal revenue and marginal cost for monopoly production?

Video transcript

Let's continue with our orange juice producing example In this situation I want to think about what a rational quantity of orange juice might be what would be a rational quantity of orange juice to produce given a market price So let's say that the market price right now is 50 cents a gallon and I'm going to assume that there are many producers here so we're going to have to be price takers and obviously we want to charge as much as we can per gallon but if we charge even a penny over 50 cents a gallon then people are going to buy all of their orange juice from other people so this is the price that we can charge 50 cents per gallon So, if we think about it in terms of marginal revenue per incremental gallon well that first incremental gallon we're going to get 50 cents the next incremental gallon we're going to get 50 cents for that one and the next one we're going to get 50 cents as well. for the first thousand gallons we're going to get 50 cents for each of those gallons for the first 10 thousand gallons we'll get 50 cents per gallon So, our marginal revenue curve will look something like this Our marginal revenue is a flat curve right at 50 cents a gallon so that is our marginal revenue at 50 cents at a market price of 50 cents per gallon now in this situation what's a reasonable quantity that we would want to produce? Now there's two dynamics here we want to produce as much as possible so that we can spread our fixed cost over those gallons that's one way of thinking about it or, another way of thinking about it is we have a certain amount of fixed cost we are spending $1000 no matter what so why don't we try to get as much revenue as possible to try to make up for those fixed costs or if we think about it in terms of average fixed cost the more quantity that we produce the component of the cost for that from the fixed cost goes down and down and down so we want to have as much as possible to spread our fixed costs now the one thing that we do need to think about is especially once we kind of get beyond the little dip in the marginal cost curve and as we produce more and more units the marginal cost is going up higher and higher and higher we don't want to produce so much that the cost of producing that incremental unit the marginal cost of that incremental unit is more than the marginal cost of that actual or the marginal cost of that incremental unit is not higher than the marginal revenue that we're getting on that incremental unit so, until marginal revenue is equal to marginal cost or another way to think about it you don't want marginal cost and this is after we go to this little dip here we're trying to do as much as possible marginal cost is going higher and higher and higher we don't want to produce this much right over here because here the cost for that extra gallon is higher than what we're going to get for that extra gallon looks like that cost for that extra gallon might be 53 cents while we're only gonna get 50 cents for that extra gallon so every extra gallon we produce over here we're going to be losing money so you don't want marginal cost to be greater than marginal revenue so when you look at the curves like this and make sense to just say when does marginal revenue equal marginal cost? and that's this point right over here and that is the rational amount to produce so that is 9000 units so we're going to be at this line over here we're gonna produce 9000 gallons of juice our revenue that we're going to get is going to be the rectangle of the area that is high as the price we're getting per unit times the number of units so this is gonna be the total revenue we get if we were to shade this in I'm not gonna shade this in because it's going to make my whole diagram messy and what's our total cost? well, we have our average total cost right here this is our average total cost at 48 cents that's the little green triangle here so it's 48 cents per unit times the total number of units our cost, the area in this rectangle so if I were to shade this in this little slightly smaller rectangle and so our profits are the difference between the two our total revenue is the area under the rectangle that has this marginal revenue line as its upper bound and our cost is the rectangle that has our average total cost this line right over here as its upper bound so our profits in this circumstance are going to be the area right over here the height is the difference between our marginal cost which is the same as our marginal revenue and our total cost so the heigh is going to be this two cents right over here we're taking the difference of 50 and 48 so it's gonna be 2 cents and then, the quantity produced is going to be 9000 units so 9000 we're making 2 cents per unit remember, our average cost our average total cost is 48 cents per unit we're selling that 50 cents per unit so we're making 2 cents per unit that's not 20 we're making 2 cents per unit 2 cents times 9000 units gives us that's 18000 cents, or 180 dollars of profit now what I want you to think about and we'll answer this in the next video is does it make sense to sell units at all and if so, how many units should we sell if, and here is the question if the market price is lower than your average total cost so does it make sense and how many units does it make sense to produce let's say if the market price were 45 cents per unit does it make sense for us to produce

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