Economics: Understanding Average Product

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We've been describing the technology of the firm, and we've been focusing on the marginal product, the change in output that results from the change in the variable input when you hold everything else constant. Now we're going to look at another measure of productivity that becomes important later in the story. I'll give a little hint about where we're going. Remember, our main concern is being able to recommend to a firm how much output to produce if it wants to maximize its profits. Well, the marginal product turns out to answer that particular question. The average product, on the other hand, the concept that we're about to introduce, tells the firm whether it's able to make a positive profit or not.
That is, when a firm is doing the best it can, is it making a profit or a loss? So let's go ahead and introduce now the concept of average product of labor. That is, the total output divided by the total labor input. When you read the newspaper or hear discussions of labor productivity on the TV news, what people are talking about is average product of labor, how much output is a typical worker at a firm producing, the average worker. We define the average product of labor, again, as total output divided by the total number of workers employed. So, if we look back at the tables we've been looking at, the particular television firm we've been considering, if we have one worker producing two televisions then that means on average, workers are producing two TVs apiece. Two workers producing ten televisions gives us an average product of labor of five TVs per worker. Three workers producing 30 has an average product of labor of 10, 4, 40, also an average product of 10, 5, 45 gives us 9 TVs per worker and so forth, on down the list.
These numbers represent the average product of labor for different levels of employment inside the firm. That is, for different quantities of workers hired and different numbers of televisions produced. I'll move all these numbers now, next door and we will draw a picture of the average product of labor. We will draw a graph below the total product curve that represents the average product of labor. Now, I use the red for product. I kind of like red for output for some reason and I used the red a minute ago to draw the marginal product curve. So in order to avoid confusion, I'm going to switch to green here, to represent the average product of labor.
So, let's do that. The average product again, is total output divided by the total number of workers. So, up here we see that a total output of two televisions when we have one worker gives us an average product of labor of two TVs per worker. So, I'll put this in at two TVs per worker and here we've got two workers producing ten TVs for and average product of labor of five TVs per worker. Then three and 30 gives me an average of ten per worker, which is exactly what I get with four workers producing 40 TVs and five workers producing 45 takes my average down to nine TVs per worker and then eight and then seven and then six. So, if I connect the dots here, I'm going to get an average product of labor curve that looks something like this. First it's increasing, then it levels off, and then it's decreasing. And, I'll label this APL for the average product of labor. It's the output per worker or the average--the amount of output that the average worker produces, output per worker or labor productivity.
Now, before, remember we said that the marginal product of labor was the slope of this curve at any given point? There's also a geometric way to calculate the average product of labor, but it doesn't make as much intuitive sense. It's actually the slope of a line from the origin up to the curve. The rise would be output and the run would be labor. So, output divided by labor would be the average. If you're interested, you can find the average product of labor by taking the slope of a line that goes from the origin up to any point on the curve and as the points on the curve change, the slope of the line from the origin also changes and that changes your average. That seems a little complex and not a lot of, you know, intuitive assistance do we get from that. So, I'm going to leave that alone and go back to the curve that I drew from the numbers that I got from my table, that's just as easy a way of doing it.
I want to notice a few things about this average product of labor curve. I want to notice a few things about it. First of all, again, it's kind of U-shaped. That is, first the curve slopes upwards and then it slopes downward. You reach a point of maximum labor productivity at some point. At some point, average product of labor reaches a maximum. That is, at some point we are getting the maximum number of televisions per worker that we can get out of this factory, given its size, given the number of tools, given our technology and so forth. That's thing one I want to notice. The average product of labor curve simply gives us, like an upside down U. At first, it increases and then it decreases. It's like a hill.
The next thing I want to notice is, I'm going to put the marginal product curve back in this picture, I'm going to draw it again and it looks like this, you'll recall. So here's my marginal product of labor, and I've got it in red. Notice again that the marginal product curve first slopes upwards then the curve is convex and downwards when the curve is concave and then it goes below zero when the curve, the total product curve tips downwards. Well, notice something about the average product of labor. This is something kind of interesting, and that is, when the marginal product of labor curve is above the average product the average product curve is rising. And, when the marginal product of labor curve is below the average product the average product is falling.
Now here's the intuition. If you're adding workers that are more productive than average you're pulling up the average. Kind of like, when you have a really good semester at school and you make a grade point, an overall grade point average that's higher than your cumulative GPA, you pull up your cumulative average, by adding a semester that's above average. Over here, when we've got workers that are less productive, than average, we're pulling the average down. Kind of like when you make a bad exam grade, an exam grade that's below your class average, you pull your class average down. You pull your own average for the course down by a below average score.
When the marginal is above the average, it pulls the average up. When the marginal is below the average, it pulls the average down. That means that the marginal product curve is going to intercept the average product curve when the average product curve is at it's maximum. That is, the marginal pulls it up and then pulls it down and it intersects it, therefore, at the maximum of the average product. The intersection of the marginal product with the average product occurs at the point where the average product curve is at a maximum. Now, that piece of information is going to become important, later, knowing where the marginal product curve cuts into the average product curve. It cuts into it at the point where workers are producing, on average, the most televisions per worker that can be produced, from this particular factory.
This is the point when labor productivity is at its highest. There was a joke that we told at my school growing up about a rival school. Did you here about the guy from our school who left to go to a rival school? He raised the IQ at both schools. Now, this is a joke about marginals and averages. That anybody who would leave our school, must be someone whose IQ is below average, but he was still smarter than the average at the other school. So, he raised the IQ at both places. Now when you here that joke and you laugh, what you're really laughing at is mathematics. You're laughing about this funny relationship between averages and marginals, that makes it possible for you to take someone who's below average, move him over into another pool that has still a lower average and raise the average in both pools.
That's what this relationship between marginals and averages is all about. Well, that then completes our steps of product curves. We've now done as much as we can to explain the technology of a firm in the short run. What we've done here is we've described the possibilities of a television factory that produces television sets using labor and some other fixed inputs. The firm can increase its output, in the short run, but it can only do so by adding more labor. And we've described the productivity of labor as two concepts, the marginal productivity of labor, which depends on teamwork and specialization and on congestion and the average productivity of labor, which is what we usually call labor productivity or output per worker.
We also described the relationship between marginals and averages. When the marginal is above average, it pulls it up. When it's below average, it pulls it down. What's next? Next we're going to take these notions of productivity and couple them with some information about input prices and we're going to come up with a set of cost curves, a representation of the firms cost of producing any given amount of output.
Production and Costs
The Basics of Production
Understanding Average Product Page [2 of 2]