 Good day. It's Professor Resnick again, and I want to continue to develop this interesting equation of C plus V plus S that Marx developed here. Let me get it on the blackboard again. C plus V plus S, surplus value is equal to W. The numbers that we used last time was $2, the value of means of production, plus a dollar of labor power, plus a dollar of surplus, plus and the product cost and sold for $4. Notice something the following just as we have it on the board here. Every single commodity that's produced and sold in capitalism, according to Marx, contains within it exploitation. That's a very different idea than exists in non-Marxian theory. I want to make use of these and produce for you a few indices that Marx talks about. Just before I do that, let me put the hours on again. Four hours plus two hours plus two hours is eight hours. Let's have our hours over here and our dollar dimensions, two different dimensions to measure a commodity. I want to go back to something we did before, before I develop for you these indices. Notice that the value of labor power. The worker gets a dollar. The question is what does the worker do with it? Well, the worker goes out and purchases means of subsistence, consumer goods, to reproduce his or her labor power. So the worker goes out and buys commodities whose value is, don't forget, it's an exchange of equivalents whose value is a dollar. So the worker goes out and buys, purchases means of subsistence. That's in your reading. Consumer goods, the value of which is a dollar. The value of which is a dollar. So the worker gets a buck, goes out and buys, let's say, apples. Let's assume apples are the consumer goods. Well, the cost of an apple is four dollars. Hence the worker buys a quarter of an apple. And what we're assuming here is the quarter of an apple is what is socially required to reproduce the labor power. How much labor does it take to produce a quarter of an apple? Well, it takes two hours, right? So the value of the means of subsistence, this quarter of a, you know, the total value or the one quarter of an apple, it takes two hours of what? Necessary labor to produce the means of subsistence to reproduce the labor power which the worker is going to sell the next day to the capitalist. So I'm trying to show you we're going back again. It takes two hours of necessary. The worker goes to work for four hours, the used value of labor power. A portion of that is two hours of necessary labor. What is that? That's the labor required to produce the means of subsistence, the consumer goods, to sustain the laborer, that is to reproduce his or her labor power. And then the worker goes to work for two hours more above and beyond than necessary doing that surplus. So another way of looking at this is this is the necessary labor. And here is your surplus labor. And this again is the labor already materialized in the means of production. So let me now develop with all this in mind, let me now develop these indices. The first one is, not in order for necessary importance, but the first one that Marx talks about is what is called the rate of exploitation which is the relationship of your surplus labor to the value of labor power which in this particular case in dollar terms it would be one dollar over a dollar or 100%. The rate of exploitation. Let's use a more provocative term. This is the relationship of unpaid which I developed last time for you over paid labor. It's an index of the rate of exploitation or its rate, how it changes over time. Unpaid to paid labor. The total of the unpaid plus the paid plus the unpaid is what the value added of the worker but the worker only gets a portion back. So the ratio is measuring how that portion changes over time, rate of exploitation. Another measure, excuse me, by Marx is the relationship of the total value of the means of production to the total cost of production which in this case would be $2 over $3 or 67%. So the first one again is the rate of exploitation. This one is an index of mechanization. Mechanization. Why? Well, the bigger the ratio here, the larger of the total cost is formed by means of production. So the higher the ratio, the more mechanized the society because the more that society is spending on machines and tools and so forth as a proportion of its total capital C plus V. So you would expect in capitalism for this ratio C over C plus V to rise because part of the theme of capitalism is the growing value of machines and raw materials and so forth to produce all these commodities. The last one is what's the return to the capitalist? Well, the last one that Marx develops is the ratio of surplus to the total capital that the capitalist has to expend. Don't forget, the capitalist has to expend on means of production plus the value of labor power and this is the return. So this is called by Marx the profit rate. I'll call it little r. The profit rate, which in this particular case is $1 over 2 plus 1 is $3, 33%. 33 to the third percent. So if the capitalist is successful, the capitalist would be putting in costs, C plus V, production costs, and getting out a higher and higher numerator. The profit rate would be going up. That's a success if that rate of return to the capitalist is increasing. So these are your three famous indices. And I just now want to combine them together in one kind of neat formula. Marx didn't do this. An American Marxist did this formula. His name was, he died a few years ago, Paul Sweezy. So the next step is to combine these into one formula which will find useful to analyze capitalism. So let me start with the rate of profit here. The rate of profit is surplus divided by the costs of capital. Divide the numerator and denominator by the value of labor power. So I'm going to divide the numerator and denominator by same V. And I'm going to rewrite this then as S over V, V over C plus V. You know, a little bit of algebra. You can do this after the lecture. You can multiply the numerator by V divided by C plus V, V divided by C plus V. That'll cancel out, that'll be one, and that'll give me this. Add C and subtract C. So as you know from high school, C minus C is zero.