In the previous session, we looked in the setting of table 7.1 and, and by the way, this week we're going to be covering most of chapter 7, for those of you that are following around, following in the textbook, and the first three sections of chapter eight. So, if we looked at table 7.1 in the last session, it was from a table setting the relationships between total product, average product, marginal product. Now we're going to look from a geometrical perspective at these relationships between total, average, and marginal product curves. Let's first turn to figure 7.1. And these figures correspond to table 7.1, the numbers in that table. What we see in the first panel, the top panel, is Total Product is basically an upside down bowl. No Labor, which is measured on the horizontal axis, produces no units of total output, or TP. As we keep adding labor, the height of this curve rises. It ends up peaking at eight units. And that was the point where adding an additional unit of labor on table 7.1 added nothing to total output. After that it declines. Panel B is a per unit product curve. Instead of measuring totals. It measures the per unit effect in a particular way of additional units of labor. And again, capital's the other input being held constant. And what we see here is both the marginal product of labor and average product of labor curves. The marginal product of labor first rises. And we see this in many settings. There's some advantage to having two workers as opposed to just one. There's, there are times where having a team to move a piano. You can do it more effectively than having one person try to lift the entire piano by herself or himself. But then after a certain point and in this case after two units of labor, the marginal product curve starts to decline. It actually becomes negative at the point where total product turns negative. Average product also has an upside down bowl shape to it. It first rises. And then falls. And here's another important characteristic or feature of these curves and how they're related. So long as marginal product is above average product, so long as the marginal unit is adding more than the average unit, the average keeps rising. So below four units of labor, average product is still increasing. And that happens because the marginal product curve is above it in height. Beyond four units of output, when the marginal comes in below the average, average is decreasing. And right where marginal intersects average product of labor, average is flat. Now why might that be? One example, think about the heights of a number of people in the room. Say we have 30 people in this room. And the average height was five foot seven inches. If the marginal person coming into the room was six foot seven inches. He would raise the average, so whenever the marginal height comes in above the average height, the average will be increasing. If the marginal person comes at four foot seven, below the existing average, she will lower the average. And if the marginal person comes in right at five foot seven she won't change the average. The average will remain the same as before, five foot seven. As another example, think about grades on a four point scale here in the United States. say going into a particular term at college, your average GPA on a four point scale was 3.0. After two years at college you'd earned the 3.0 average. Say in your junior year, in your third year, you really decided to challenge yourself. You decide to take a course on particle physics, organic chemistry. A very difficult philosophy course, conversational Latin. You learn a lot, but say your GPA in that marginal term comes in at 1.5. That marginal GPA, because it's below the existing average GPA, will end up pulling down your average. By contrast, if you take it easy and take a basket weaving course. Or a very easy interact movie appreciation course. You may not learn as much, but say your marginal GPA comes in at a perfect 4.0. That marginal GPA because it's above the existing average, will end up driving up the average. So very important relationships that we'll see through the coming weeks as well between marginal and average. And it'll apply not just to product of labor but also, as we'll see, cost curves. Figure 7.2 shows another way of relating marginal product, and average product, and total product. In this case, we're just showing the total product curve. How can we show the marginal product just by employing this curve? How we can do it is by looking at the slope at any particular point, because what the slope of the total product curve gives you is the rate at which total output changes per unit of labor on the horizontal axis. So the point like a, the slope, we pick up five units of output per each additional unit of labor. That slope right at point a is the marginal product of point a. And what we can see is that the slope first increases. As we go from point a, to point b, to point c, the slope is increasing. And then beyond point d, the slope starts to taper off. So marginal product first increases, as we saw in the previous figure, and then decreases. How can we depict average product? Average product is the slope of the cord that connects the origin to a particular point on the total product curve. Say at point b. The height of the total product curve is 18 units of output. If we divide that height, the rise as we move from the origin, by the run, two units of labor to get that total output, the slope of that cord from zero to b, is nine. That's the average product at two units of labor being used. Now noticed what happens to this average product, as we connect each point from the origin to the total product curve. That's slope of the cord first increases in height. And then beyond point d it starts tapering off. The average product beyond point d diminishes. So average product as we see from this perspective also has this upside down bowl shape, also has this first increasing then decreasing property. Notice too at point d, when average product is at its peak, when you just touch the outer most edge of the total product curve with the cord from the origin. At that point, the slope of the cord connecting the origin to the total product curve, or average product, is the same as the slope of the actual total product curve, or marginal product. So an average product is just at its peak, the marginal equals the average.