 Next, the index. I want to take, this is a new one. I want to take the ratio of the raw materials used per labor hour. This is a technical ratio. In this case, every labor hour, we have 200 labor hours. The workers require $80 of value of what? Of means of production. This is the value of the means of production per labor hour. So in this case, it's 4208 for two-fifths. So every single labor hour that the workers work, they require $2 of means of production to produce whatever is they're producing. So these are the numbers that I'm going to play with now. Now let's assume everything stays the same. Save for one change. I'm going to now have employment grow from 20 to 30. I'll call this the new. The age will stay the same. I could change it, but I'm going to just focus on this. So I'm going to have an expansion of employment by what percentage? Well, you can do this. The employment is going to grow by, let's see, that's 30 minus 20 over 20, 50%. So what the delta L, the Greek letter delta, what that stands for is the new employment, I'll write it out, the new minus the old. So that's the change in jobs, employment of what? Of productive labor. Labor that's productive of surplus. So I'm assuming that the capitalists go out and they expand employment, they now hire 30 rather than 20 workers, giving me a percentage increase of 50%, a hefty rate of increase. So I have employment growing by 50%. So let me get rid of this. The question is, if we have now 30 workers, how much new value do those workers add if they're working the same hours of 10? Well, we have this formula that we can make use of now. We have, let's see, we have a question. What is this? We don't know. If I assume that the I remains unchanged, so the intensity, it could change, but if I assume for the moment it remains unchanged, then I have a new pool of labor hours, I'm just solving this equation here, and this is new. The H remains the same by assumption. So I can plug in the numbers here. So this is one-fifth, because I'm assuming there's no change in the intensity of labor, there's no speed up, it stays the same. But I now have L times H. Let me see, this is 30, this is 30 times 10, so I have now 300. The use value of labor power has grown, this is now 300, and I have therefore $60 of value added by these workers because we're employing more productive labor. We have more value. If the rate of exploitation remains the same, and if we have $60, then the new equation here has to be 30 here plus 30. Why? Because I'm assuming the same rate of exploitation. So if it's the same rate of exploitation, the rate of exploitation can't change, the surplus has to grow at the same proportion as the value of labor power, hence to get an unchanged rate of exploitation that gives me the 30 plus the 30 unchanged rate of exploitation. The only last one I need is what is the C? Well, if I assume that the index, this index remains unchanged, there's no change in the technology. So I can calculate the new C, I'm going to erase this now, and calculate the new C that's needed from this. Don't forget what this is. This is the C divided by LH. So I can calculate the new C, which is two-fifths, I'm assuming an unchanged technology, so it could change, I'm assuming it's unchanged, times the new labor, which is 30, times the hours that they work, which is unchanged is 300. So what is that? Two-fifths times 300 is 60. So the new C is $120 of value. Not terribly surprising that it grows because we have a growing employment. So this is the new value being produced by the capitalists when they employ more, 150, 180, sorry, when they employ more workers. So this has grown from this to this. This is the new equation. This is the old equation. Notice the surplus has grown from 20 to 30. Value of labor power grows from 20 to 30. The value of the means of production grow from 80 to 120. We're employing more productive labor. Now in the last few minutes, let's examine this a bit more carefully to see what Marx has produced here. So I'm going to erase all this. Let's go back to some of our indices. First, let me see. 80 plus 20 plus 20 is 120. What did I have here? 120 plus 30 plus 30, 50 is 180. This is the old. This is the new. What's the growth in capital accumulation? Well, let me see now. We have delta C is equal to 40. Delta V is equal to 10. So let's do this. Delta C plus delta V over C plus V, that was your K star, is equal to 40 plus 10 divided by 100. That's 50%. How about delta surplus value, the change in surplus value, the rate of growth of surplus value? Well, that's 10 over 20. That's 50%. This is a remarkable result. What Marx has shown here is that if you hold everything constant, save for, except for the growth of employment, you get the following result. The rate of growth of employment, change of L over L, is exactly equal to K star, which is exactly equal to the rate of growth of surplus. So I'm starring these to indicate this is a rate of growth. Well, by the same logic, I can star this too, I suppose. Now let me quote Marx. A theory of capital accumulation, a theory of capital accumulation is a theory of employment growth. And is a growth of profits as well. So if the capitalists accumulate capital, they take a portion of their surplus that they pumped out of the workers, they purchase more workers and more means of production, as I just showed you in this example. So they're employing more workers, they're taking their surplus again, they're accumulating more C, accumulating more V, they're growing employment, they're also growing their surplus, and the rate of growth of capital is the rate of growth of employment. So in the case you all know when you're going to hear this, we have a recession. So let's make use of this. A fall in the rate of accumulation. If K star falls, employment is going to fall, bingo, we have a recession. So we now have an explanation of one part, there are many possibilities. So one reason why we might have a recession, capitalists don't accumulate as much as they might otherwise, employment's going to grow, the demand for means of production, the demand for consumer goods is going to fall, bingo, we have a recession. So Marx develops then, he gives an explanation of how we can have more employment or less employment in the society. And the reason is, it's connected to what capitalists do with the surplus that they pump out of workers. The next step then, and I'm going to do this, develop this the next time, is to discuss the consequences. What's the consequence of growing capital accumulation and growing employment on the economy? So we have to back it up, just to make sure. If capitalists accumulate, they take out of their surplus and they do this K star, they employ more, they get more profits, what's the result of that? That expansion, which is quite wonderful, what's the result of this expansion on the capitalist economy? And what Marx is going to to anticipate what we're going to do, what Marx is going to show is that expansion, that growing capital accumulation, growing employment, growing in profits, growing demands by workers in the economy is going to set the conditions for a contraction, for a recession. So let's put it together. An expanding economy, K star is equal to L star and equal to surplus value star. An expanding economy is going to create the conditions for a contracting economy, that's the business cycle, the ups and downs of the economy under which we live. And the way he's going to develop this is to show how this growing capital accumulation and growing employment is going to impact two markets. There are many markets, but he's going to show in these two, the labor power market and the means of production market. So the growing K star in English, the delta C plus the delta V divided by C plus V, the delta C is going to affect the means of production market, the delta V is going to affect the labor power market and basically what's going to happen in those two markets is that the demands for labor power, for workers are going to rise, the demands for machines and raw materials are going to go rise. That's going to cause in turn, if there's no change in the supply of those inputs, rising prices, those rising prices are going to in turn cause rising costs to the capitalists, rising costs of wages, rising costs of raw materials and machines, and that rising costs, if there's no other changes, is going to undermine capitalist expansion and produce a contraction. So when the seeds of expansion by the possibility, because as I'll show you also, it's not inevitable, by the seeds of the contraction, inside capitalism is not just exploitation, that is the business cycle and we shall stop there.