Greetings. In our last video, we looked at how to individual firm would optimize. This is a graph of that individual firm. We've got a lowercase q, so we know it's an individual firm, and that firm would maximize profits by finding the output where marginal revenue exactly equals marginal cost. Okay, and we'll call this output q star, and we're going to put a zero here just to associate that that's the output associated with price P zero because that would give you that marginal revenue curve. That was our optimum, that was the output that would maximize profit. But one of l the things we haven't talked about here is up here in the corner, what is the level of profit associated with that? Well, in this picture you can't be sure, okay? It could be that the firm's making lots of profit. It could be the firm's losing money. It could be the firm is just breaking even. In order for us to do that, we need to think more about what the other cost curves are involved. So I'm going to take this picture and I'm going to replicate it several times. So we're going to take this picture and we're going to add information to it. Graphs that will allow us to figure out what is the size of profits, and we know how to do that. We've done it before. We add average cost curves, and in particular, we add average variable cost curve because that's also important for us to know about something that we call the shutdown condition. So I'm going to go to a new page, and I'm going to draw myself an axis system here. On this vertical axis I'll put dollars and cents and on the horizontal axis I'll put quantity. We'll have some original price. We'll call that P_0. Where's that come from? Well, it comes from the market and we're trying to figure out where that it came from, but we know there's some price that's going to come there. Given that's the price, the firm will treat that, see it's a little bit. Given that the price, the firm will treat that, it's not coming out very well here. We've got one last try. Given that's the price, the firm will treat that as the marginal revenue, okay. So this marginal revenue curve looks like this, and then, of course, profit maximization requires you to put marginal revenue equals marginal cost. So we'll put a marginal cost curve on here that looks like this, and we know this firm will produce at q_star_0. What does the profits associated with that? Well, we need to put on an average total cost curve. Remember we solved earlier that profits were equal to total revenue minus total cost, which can be rewritten as price times quantity minus average total cost times quantity. Which I can just factor the q out and say profits are just output times this bracketed term price minus average total cost. This bracketed term is really per unit markup. If you're getting $4 for a jar of mayonnaise and the cost was only 350 to make it, you're making ¢50 mark-up on each jar mayonnaise. Multiply that times the number of jars of mayonnaise you sell, there's your profit okay. So if we could figure out average total cost, we could do this, and of course, we did this many times. So you know how to do it. So I'm going to put an average total cost in her. Where's it? Well, it is, I know it has general, it's shape is it's U-shaped, and I know its minimum lies on the marginal cost curve. We can prove that, okay. Its minimum lies on the marginal cost curve. In this particular situation, the firm's making a lot of money, okay. So this gap, this vertical gap would be equal to price minus average total cost, right? Recall this. This is the size of price. Price is this high that's here. This is the size of average total cost, that's like here. So this gap is price minus average total cost, and then I would want to multiply that times the number of units produced. If I multiplied this horizontal line times this vertical line, area of a rectangle is base times height. This whole rectangle would be my positive profits. That's positive economic profits. That's a good deal. Okay. But sometimes, and so we know in a situation like that that's okay, but sometimes, we have situations where, in fact, it's not so rosy. So I'm just going to take this picture and I'm going to say suppose I told you that the average total cost was actually up here. Average total cost was up here. I know you're going to get tired of me saying this, but remember, if I the real cost curve, a functional form, I know exactly where it is. I don't know that, but I do know that in general they're U-shaped, and I know for certain that the minimum of the average total cost curve lies on the marginal cost curve, so I have satisfied that here. In this situation, the firm is in fact going to be losing money here. Price minus average total cost is actually less than zero because price is less than average total cost. Over the number of units produced, which would be this distance. So if I've multiplied base times height on this this rectangle, this rectangle would be negative profits. What's the firm going to do in the short run? It's losing money. In the long run, it wants out. But in the short run, it's losing money. Now, we know that in the short run, it will continue to produce. In the short run will produce q_star_ 0 if price is at least as great as average variable costs. Well, I don't have average variable cost on this picture. So I have to add average variable costs on a picture. Suppose I put average variable cost that looks something like this. Again, average variable cost has its minimum along the marginal cost curve. That's a legitimate average variable cost. In this case, the price which is not a good price for the firm, they're losing money, but the price is in excess of average variable costs, which means they can't get out from underneath their fixed costs in the short run. They've got this fixed cost set in the corner of the room, and if they locked their doors, they're just going to eat the entire fixed cost. But in this situation, they can have workers come in. This shows us that the amount of money they would make and revenue off of the output the workers made that day, would exceed what they actually had to pay the workers. So that they have some residual left to at least take away part of the pain of that fixed cost. Well, now we're ready to think about what our main goal was, which was to create a market supply curve. The way we're going to do this is to think about, I'm going to draw a new graph, a little bit cleaner. I got to put my axes system on here, and I'm going to have a price, I'm not going put a price on there yet. Yeah, that's going to be even more interesting. I'm going to put the cost curve graphs on here. So I got a marginal cost curve looks like this. I got an average total cost curve which is U-shaped, and has its minimum along this curve, average total cost, and I have an average variable cost which is also a U-shaped, and has its minimum along the marginal cost curve. Remember these two: curves, average variable cost, and average total cost, asymptotically hit close to each other, because for large outputs, average fixed cost is varnishing. So these things are going get closer as we go forward. Now, given this situation, what is the individual firm supply curve? I'm going to write it out because it's important. I'm going to say question: What is the individual firm's supply curve? Well, you say let's see Larry. We back when we first talked about supply curve. The definition of a supply curve was, how much will a firm provide for different possible prices? So let's try different possible prices. We've got the pen, we can just try different possible prices here. Suppose I pick a price like this. Let's just pick a price and let us put these prices here in a balloon blue. P_0 at a price of [inaudible] write zero so you can tell it. P_0, well, that price would be then a marginal revenue, all right. Because we know that the price is treated as a signal. They're price takers, and they would go to where marginal revenue equals marginal cost, or they want to produce there? Yeah, they got positive progress, they are happy. But all we care about is that, this is an output point that shows me for one possible price, how much they'll produce. Now let's try different price. How about this price? Well, at that price, they're going to want to go there. How about this price, P_2? I should label this just so that they make it a little bit more sense. At P_2, that marginal revenue curve hits the marginal cost curve here. Life is not good. That price is below average total cost. You see? Price is below, let's took up, the firm's losing money. But is this a short run equilibrium for them? The answer is yes, because the price is in excess of average variable cost, so they're not going to shut down in the short run. So let's make sure that you have this on your notes. We're looking here at a short run equilibrium. Just know that's what we're doing, but I want to make sure you've got on your notes. So I can try another price. How about this price? At this price, marginal revenue equals marginal cost, would be there. Not so much that price is lower than average variable cost. Which would mean that if the firm actually tried to go here, they'd be losing money not only on their fixed cost, but they'd be losing money on their variable cost too. So they're going to put a padlock on the gate of the factory, and stare at the phone waiting for the broker to call and say, "I found a buyer for your brick-and-mortar. So you can get out of this industry, and go move to someplace else and see if you can make a better life for yourself." Well, what this means is, back to what I started this little page about. I said, we want to find the individual firm supply curve. So over here. So all we have to do is call on a bunch of prices, and as you can see, I'm going to do a few here, just a couple more, just to humor myself. This price P_5 symbols here, this price P_6, marginal revenue goes out like this, marginal revenue 6, this was marginal revenue 5. Now you begin to see that the individual firm supply curve is that portion of the marginal cost curve at or above minimum average variable cost. Any price you want to charge, I'm going to use my laser pen now, any price you pick, check this price, boom, you go right here, try this price, boom, you go right here, try this price, boom, you go right there. Any price you pick, the firm will optimize by jumping out to where its marginal cost curve is at that particular price. That means that for us, the answer to this question is that, the individual firm supply curve is the marginal cost curve at or above average variable cost. Now we have an individual firm supply curve. How do we go from that to real supply curve? Well, it's pretty. We have one last picture, and then we'll have accomplished this. We think about the fact that there is an individual firm for firm 1. We'll call this firm 1. Firm 1 has got its own little marginal cost curve, and that will be it's own supply curve. Okay? So it's the supply curve for firm 1. Then there's another firm which we'll call firm 2, and that firm also has its own little marginal cost curve, which is the supply curve for that firm. Any price you quote, this firm will want to go here, this firm will want to go here. We could do this so on and so forth. But what we want to do is, we just want to add up dot dot dot all the way out to firm N. Firm N will also have its own little marginal cost curve. We'll call this marginal cost 2, this is a marginal cost N. They'll have their own little marginal cost curve which has their own little supply curve. As we just proved from these previous picture, the marginal cost curve added above the average variable cost curve is that firm's individuals supply curve. How many firms are there? There are N firms. If we add all those up, we end up with something that looks like this. I think I'm going to take up back to, I told you just going to be last picture. I'd said I want one more grand pictured in this. We have our axes system, and now we have market output here. The supply curve is equal to the sum for i equals 1 to N of the marginal cost for each firm, firm i. In fact we want to make sure you understand it's the marginal cost at or above average variable cost. So that's really good information for us. Now we know that the supply curve is really just the sum of the marginal cost curves of all the players in the industry. That's going to mean, it's going to be great for us to figure out equilibrium. It's also going to be great for us to think about efficiency properties in this industry. Now that we know how much each firm's marginal costs are, their incremental cost of operation is all captured in this supply curve. If I'm a researcher, I could be a researcher in a statistical department for a firm in the industry, or I could be a researcher at an academic unit, or I could be a researcher at a regulatory agency like the Federal Trade Commission, and I want to know something about what the supply curve looks like, I can go out, and make these estimates of that and I can be confident that estimated supply curve really just represent a proxy for us of the sum of the marginal cost for all the players in the industry. Thanks.
