1

concept

## Revenue in Perfect Competition

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Alright, now, let's discuss revenue in perfect competition. And define average revenue and marginal revenue. So, we've talked about revenue before, and not too much is changing here revenue, right? That's the money coming in to the firm. So we're gonna say that our total revenue is gonna be equal to the price times the quantity, right? Whatever price we sell at times the quantity that we sell. That's all the money that we're gonna bring in. So we talk about revenues. These are the benefits to the firm, right? So when we think about benefits, right? Remember we're talking about marginal benefits and marginal costs. These would be the benefits to the firm. So, a marginal benefit to the firm would be, how much more revenue can we get when we sell one more unit? Right, So we're gonna talk about that in a second. So let's let's dive into this average revenue and marginal revenue, right? These are gonna be important concepts throughout all of these chapters. Uh So let's go ahead and see how it relates in perfect competition. So, average revenue, we're always gonna just label it A are for average revenue and marginal revenue. M. R. Right? M. R. For marginal revenue. Let's start here on the left with average revenue. So, average revenue, right? Whenever we take an average right, average, that means divide by Q. Right. That means to divide by the quantity. Okay. Um So that's exactly what we're gonna do. We're gonna take our revenue our total revenue and then we're gonna divide it by quantity. Right? So total revenue divided by quantity. That's average revenue. But we can rewrite total revenue, right? We have our formula up here? Price times quantity. So total revenue is really just price times quantity, right? That's total revenue. We're dividing by quantity. So what happens here? The quantity on the numerator and the quantity in the denominator? They can cancel out, right, we can cancel this and this and we're gonna be left with p average revenue equals P. Alright, this is just what it is, right. We took our formula and divided by quantity and left us with p the price, right? Average revenue is always going to equal the price and that's gonna be our demand curve. So when we see our demand curve, that is our average revenue curve. Okay. And this is true for all market structures, I'm gonna scroll down just a little bit true for all market structures. Okay. Not just perfect competition. So every market structure, average revenue is gonna equal price, and it's also gonna be the demand curve. All right, now, let's talk about marginal revenue a bit. It's this right behind right behind me here, this marginal revenue equals the change in total revenue over the change in quantity. Right? When we're talking about margin, the marginal right? That's what happens when we add one more right, one more. So if we sell one more unit, how much more revenue are we gonna get? Right? So our our formula here change in total revenue over change in quantity. Uh This denominator change in quantity. It's usually one right? Like what happens if we sell one more unit? Um So let's go ahead and see what the implication is here. In perfect competition. I'm gonna get out of the way here. Um And let's see what happens, right? So what happens to our total revenue when we sell one more unit? Right. Well in perfect competition, remember that the price is fixed to the firm, right? The market sets the price and then the firm has to sell all its product at that price. And the firm can sell as much as it wants and it will always sell at this price. So knowing that if the firm decides to increase its quantity by one, if it decides to sell one more unit. Well what's it gonna sell that unit at? It's gonna sell it at the price, right? The market price. The price isn't gonna change because the firm increased its production. So it's gonna sell one more unit for p and this should be a little different than what you're used to, right? Because what we're used to is when you want to sell more quantity, you're gonna have to lower the price, right? You don't get to keep the same price to sell more quantity. Now this is a special case because we have that flat demand curve, right? The perfectly elastic demand curve the firm faces and they can sell any quantity they want at that price, right? Because their their influence on the entire market is so minimal because there's so many sellers so they can produce as much as they want and they will sell it at P. So what happens? They sold one more unit for P. How much more total revenue did they get? Well, the change in total revenue is P. Right? They got p more money in whatever the price was. So, what's our conclusion here? The marginal revenue is going to be equal to the price as well, imperfect competition. Right? If you want to sell one more unit, well, you're gonna bring in one more price, right? You're gonna bring in one more price. Worth of revenue. So, whatever the price is, that's what you sold that extra unit for and every unit you can do it at that price. Now, I just want to make a note that this is true only for perfect competition. Okay, every other one we are not gonna see that the marginal revenue equals price. Okay, So this is a special case here that we're dealing with imperfect competition. And we can make this conclusion, right? Because the marginal revenue equals price, the average revenue equals price. So we can say that the average revenue equals the marginal revenue equals price. They're all equal to each other. All right? And this is gonna be true. Just this is just true here in perfect competition. Okay? And we're gonna go ahead and do a numerical example below. So, you can kind of see what what this means. And but this is a very special case, and it leads to special things happening in this market. All right. So, we're gonna start discussing all of those. So, let's go ahead and understand how this marginal revenue stays constant at price. Okay. And let's do that in this next video with a numerical example. Alright, let's do it now.

2

example

## Calculating Profit from a Table

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Alright, so let's dive into this numerical example. Now, generally when we deal with uh perfect competition or any of these structures, we don't usually do these types of boxes like we've seen in the past, we're gonna be dealing with the graphs or something like that. But this is a good way to just kind of introduce you to this, this concept of marginal revenue and how it stays constant. Okay, so let's go ahead and dive in here. What we've got is a market for wheat and the market price was $4 for a bushel. I don't know if that's a good price or not, but we're just keeping our example pretty simple here. Alright, so we got $4 a bushel and that's gonna stay constant, no matter how much we sell, right, there's not gonna be an increasing quantity, decreasing price, none of that. So the price is gonna stay constant. So let's think about this in our in our little table here, we've got, you know, quantities were given to us and the cost to produce those quantities. So let's go ahead and fill in this revenue our total revenue, right? That's our price, times quantity, right? Just like we're used to well when we sell zero, we're not gonna make any revenue, right? Our revenue 00, times 40. Now let's move on down. What about when we sell one unit, one unit for $4 we're gonna bring in $4 right? About two units, two times four. Well then we bring in $8 right, three times four is $12. 4 times 4 16, 5 times the $4 price. 20. And finally six times the $4 price of 24. Alright, pretty simple. Just doing our multiplication table right there. Then we've got our cost given to us. And how about profit? Remember that profit is gonna be that total revenue minus the total cost, right? Whatever is left over, that's profit. We brought in so much money, it costs us so much to get that money. What's left over? So let's see it when we sell zero units, we've still got a cost of $2.50. These could be some sort of fixed cost, right? No matter if we sell units or not, we're gonna have this cost. So we've got zero minus the $2.50. That gives us a negative profit. Right? We're losing $2.50 because we didn't bring anything in. How about the next one? What we brought in $4 but it costs us 4 50 so we're still losing money but we're losing less money, negative 50 cents. How about the next one? Eight and seven? Well now we've got positive profit, right? We finally brought in a dollar and then with three units we bring in 12 but it cost us 10. So that's 2 12 minus 10 is 2 16 minus 13 50. That's $2.50. And then 20 minus 18 $2. And then finally 24 minus 24 is zero. Right? So now let's dive into marginal revenue and marginal cost. So marginal revenue. Right? That's how our revenue changes as we increase output. So let's think about this in the first case. Right? So 10. We can't do it. But what about when we add one unit? We had the first unit? Well, we had zero profit before. And now we've brought our excuse me, zero revenue before. And now we brought our our revenue up to four. Right? So our revenue increased from 0 to 4. Our marginal revenue is four. How about the next one? Our revenue was already for we are we added one more unit and it brought our revenue up to eight. So we started at four. Then we got to eight are marginal revenue is four again. Right? Notice this constant marginal revenue and this is because we're selling one more unit at that price. The next one. Right? We were at eight already. We sell one more unit for the price and it brings us up to 12. Right? Are marginal revenues for again, say same thing. All the way down 12 to 16, marginal revenue of 4. 16 to 20 again, four. And the last 14 as well. Right? Are marginal revenue is constant. It's constant four. And that is equal to the price, right? Marginal revenue equal to average revenue equal to price, Right? That's gonna stay constant in perfect competition. How about our marginal cost? We've talked about this before, but let's go ahead and do it just to see our change in profit. Well, marginal cost. Right? That's how much does our cost change as we increase production? So here we started at 2 50 it went up to 4 50 right? It increased by $2 right? Our marginal cost increased by $2 there. And then the next one we were at 4 50 it went up to seven, right? Seven minus 4 50. Well, that's 2 50 right to 50 is gonna be the marginal cost there and notice that these are not constant, Right? This is kind of what we expect from When we discuss marginal cost, that marginal cost would generally increase as as we get diminishing returns. Right? So how about the next one? We were at seven and cost went up to 10. Well 10 minus seven. That's a marginal cost of three for the next unit. If we want to produce one more. Well, we're already spending 10 and we're gonna increase to 13 50. So that's an extra 3 50 in cost. How about the next one from 18? We go all the way up to 18 from 13 50. Well the difference, they're 18 minus 13 50 is $4.50. And finally 24. Uh we go up from 18 in cost to 24. That's a marginal cost of six, right? So last but not least. Let's fill in this column change in profit. Right? So we can calculate the change in profit um by taking the difference between what our profit was and what our new prophet is. Right? So we could say, well we started at negative 2 50 in profit and we went up to negative 50 right? We're still losing money but it did increase. Um So in that case are changing profit was to. Now another way you can do it is you can just subtract your marginal revenue and your marginal cost, marginal revenue minus marginal cost. Well, that's gonna be our change in profit, right? The marginal revenue was, how much extra money do we bring in from selling one more unit? And the marginal cost is how much will that extra unit cost us? So the difference is gonna be how much extra profit we get. Okay, so um just going down, we already saw that. We could do it either way, right? We could calculate the difference between the profit and just do it the easy way and just subtract marginal revenue from marginal cost. And you can just double check that this fits uh with the other method as well. Right, So four minus 2 50 that means our profit increased by a dollar 50 there. Four minus 314 minus 3 50 that's 50 cents there. Four minus 4 50. Now our profit started decreasing again. Right? It's negative change in profit and then four minus six. That's a negative to write our profit decreased by two when we added that last unit. And that's kind of what you see happening with the profit. Right. So what's the idea here? Where would we want to produce when we look at this table? It's kind of easy, right? Because we want to maximize our profit. So we want to be where the profit is the most. So where would that be? It's pretty easy. We look on our profit column and we see $2.50, that's the most profit we can get. So we're gonna want to produce a quantity of four. Now, like I said, we're not usually gonna be dealing with tables like this and filling in a table to find the max profit. We're gonna be looking on a graph. Okay, so this this kind of just shows you how that marginal revenue is constant, the marginal cost increases and then we find a point where we're gonna maximize our profit. Okay, so now let's go ahead and take all this information onto a graph and see how we're usually gonna be solving these types of problems. Alright, let's take it to the graph. Now