Greetings last time we introduced new character to our to our series of videos, and that character is called the benevolent dictator. The benevolent dictator is just here to help us think about how to measure efficiency because the benevolent dictator's goal is to maximize efficiency, okay? To maximize the size of the pie, what are the net benefits to all the parties in the market? And right now, we still don't have government involved with all the parties are just consumers and producers. Let's see if we can figure out how to model, how we can draw a graph to explain this. I'll show you a supply curve and I'll show you a demand curve. And the supply curve, Of course, is the sum of the marginal cost of production for all of the N firms. That's this N, all of the N firms in the industry. And the demand curve is essentially our marginal, Willingness, To pay. And last time, in the previous video, we understood that for any given output point, which we introduced something called Alpha. For any given output point, The social gain, I'll write this back up here. Social gain is the sum of the gains to consumers, that's consumer surplus, plus the gains to producers, producers surplus. Those are the only two players in the game at this point in our in our video construction. This particular unit alpha the net of consumer value above price plus producer value price minus cost is the total vertical gap here, okay? The total vertical gap would be that amount. Now, the benevolent dictator says, okay, I know output alpha that's exactly the social game, but I don't like output alpha as the outcomes that we strive. Because if I could just force you guys to do beta instead, we'd also get this. And in fact if I can get you all the way out to here. We'll call this Gamma. At the point gamma I know I don't want to stop short of gamma because if I were to somehow stop anything short of gamma as a benevolent dictator, I would know that there's a there is some value for that. But also by just going a little bit more to that just by going a little bit more in that direction, I'm going to get more gain, more gain, more gain, more gain. Every time let's step this through, okay? Let's save this? I'm going to go back because I'm going to really mess this picture up now. I'm going to say that every time we add another unit I get gain in excess of social cost of that amount. So keep going to the right each time I'm getting gaining excess, each time we can gain an excess, each time, I'm getting gain and excess. I don't want to stop short of gamma, because if I stopped going to short of gamma like say this value. That's good, but I still have some gain in here. You see this little spot? There's this little spot here where there's still some gain and we can get. So if the benevolent dictator wants to do is to push all the way out to that particular value. Ask yourself the question was a benevolent dictator want to go pass gamma? And the answer is now by going past gamma cost to society are greater than value, marginal willingness to pay of consumers the cost of resources burned up. That's this one, is greater than what the value is to society. So what's happening to the size of the pie if we go past gamma? Well, the size of the pie is getting smaller because every units that we go past gamma is costing society more than what society values it, that's a net negative amount, the pie is shrinking. The benevolent dictator said no, no, no, grow the pie. So for every, just to keep pounding on this, it's good I did save an extra picture. For every unit that we keep producing more we're getting extra gains and the pie is growing, growing, growing, growing as we keep stepping to the right output, output, output, output. We're getting you another slice, another slice, another slice, all these things are making the pie larger until you get the gamma. Once you get to gamma you've maximized the size of the pie. So for us this gamma is basically what we'll call the socially, I don't write it all out, socially optimal output. The benevolent dictator would not have output less than that because if the benevolent dictator picked some output less than that, let's think about this by drawing one of my little balloons. My little thump balloon would say look, If I were to have a situation like this, And this was my, This is my demand curve and this is my supply curve, that if I were to stop here at this output point, the size of the pie would not be as large as it could be. The benevolent dictator is a wait, wait, wait, don't do that, that allocation is wrong. Given what I know because I'm the benevolent dictator, what I know about people's willingness to pay and that's this. And I know about people's cost of operation, the marginal cost, which of course, is all contained in this supply curve, the selling the marginal cost for the end players. I know that stopping at this point would be wrong. What you need to know is go all the way out here, and that will make the pie as large as possible. That's what the benevolent dictator wants, stopping a smaller pie is not efficient. It is an allegation, the benevolent dictator, good, he or she would be wrong. But it could say let's just do Q sub wrong and that's enough call it a day and go home. [LAUGH] That's not good enough for the benevolent dictator. The benevolent dictator wants to make sure the pie for society is as large as possible, and that happens by going out to this point, which we'll call Q socially optimal, okay? Well, now, let's go back and think about what we know about a market. If this was back in our videos about perfect competition. What would they be the perfectly competitive output? Well, you say, well, it's easy. And this would be the price and this would be the output. Now, at that output in price, what do consumers get? I know that Larry, give me the pen and I'll show it for you. At that output price I know consumer surplus would be the area below demand but above price, it's the net of what consumers would be willing to pay less what they actually had to pay,. And there's a whole bunch of consumers there and they had it all up, and this area would be consumer surplus. And what would producer surplus look like? Well, producer surplus is the area below price but above what the true marginal cost is. That's because for all of these units, Firms would have produced this unit. Let's call this Alpha. Firms would have had produced this unit, but they get this price instead, that firms would have purchased this unit for this price, that's what the supply curve says. But instead the market actually gives them this amount. So all of these little distances add up to this triangle, which we call Producer Surplus. We knew that, we looked at that, we understood that's the market outcome. But now we see the total value to consumers is that blue triangle. The total net value of consumers is that blue triangle consumer surplus and the net value to producers is that green triangle producer surplus. And that's the outcome of the competitive market. But wait, what about our benevolent dictator? Our benevolent dictator looks at that and goes amazing. The competitive outcome is exactly the same. As what I want to do produce. The socially optimal output turns out to be Q0, we proved that earlier when we had this understanding that the benevolent dictator wants to go all the way out to that point. That point is socially optimal, no more, don't go over this direction, bad, all right? Don't stop short of that, that's also bad, go right to that point. Well, it turns out, That yardstick that we have, the benevolent dictator's yardstick, which says maximize the size of the pie. Guess who does it? The competitive outcome. This is a very important result in economics, okay? There's a set of fundamental theorems and economics and if you go onto yourself a PhD, you can in economics you can bet that you're going to spend at least a week and a half on the proof of this particular result, which says that a perfectly competitive outcome, the perfectly competitive industry. A bunch of greedy profit-maximizing firms and a bunch of scheming consumers who want to pay as little price as possible. That set of decentralized characters will actually end up finding the exact point, the exact output point that maximizes the size of the pie. I remember, as we talked about it, there's not a lot of markets that is fit. All of those conditions, those four conditions we had for perfect competition, lots and lots of relatively small buyers and sellers, homogeneous product, free entry and exit and perfect information. But if they do fit that and we do see a competitive outcome, it turns out that competitive outcome is the best outcome we could ever hope for, okay? Regardless of who is to make the decision, whether it's the dictator, whether it's the king, whether you're throwing darts at the wall, the best outcome is the competitive outcome. And what we're going to do in all of our remaining videos is look at what happens when we no longer meet all those conditions of the competitive outcome. Something is different either there's not a lot of firms like say a monopoly or there's bad information, we have information failures. All of these things is going to cause the outcome to be at a smaller sized pie than what a pure competitive outcome is all about. Thanks.
