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Economics: Marginal Cost and Marginal Product

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  • Type: Video Tutorial
  • Length: 10:29
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 113 MB
  • Posted: 03/30/2010

This lesson is part of the following series:

Economics: Full Course (269 lessons, $198.00)
Economics: Production and Costs (24 lessons, $39.60)
Economics: Marginal Costs (3 lessons, $4.95)

This video lesson will look at the concepts of marginal cost (MC) and marginal product (MP). You'll learn what each of these constructs are as well as why they're important and how they relate to each other. Taught by Professor Tomlinson, this video lesson was selected from a broader, comprehensive course, Economics. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/economics. The full course covers economic thinking, markets, consumer choice, household behavior, production, costs, perfect competition, market models, resource markets, market failures, market outcomes, macroeconomics, macroeconomic measurements, economic fluctuations, unemployment, inflation, the aggregate expenditures model, banking, spending, saving, investing, aggregate demand and aggregate supply model, monetary policy, fiscal policy, productivity and growth, and international examples.

Steven Tomlinson teaches economics at the Acton School of Business in Austin, Texas. He graduated with highest honors from the University of Oklahoma and earned a Ph.D. in economics at Stanford University. Prof. Tomlinson's academic awards include the prestigious Texas Excellence Teaching Award given by the University of Texas Alumni Association and being named "Outstanding Core Faculty in the MBA Program" several times. He has developed several instructional guides and computerized educational programs for economics.

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Thinkwell
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Here we are in the middle of a series of lectures on productivity and costs, and this stuff sometimes is pretty heavy sledding. So let's take a moment and review what we've done and what we're going to do next. We're talking about marginal cost and marginal product. Remember, marginal product is the extra output that can be produced when you hire another worker. That is, anytime you increase your variable input, the input that you can change in the short run, how much extra output do you get? This is a matter of your technology, and we call that measure the marginal product of labor.
Also, marginal cost is the cost of producing an extra unit of output. How much do your costs change when you hire the labor that you need to produce one extra television? Now, I'm stopping right here in the middle of these lectures to make a point about the relationship between costs and productivity. I've talked about this before. The relationship is reciprocal. When productivity goes up, costs fall. And when productivity goes down, costs increase.
I'm going to write a few steps of math out right now that I think will make this very, very clear. For those of you who get kind of nervous when I start doing mathematics, just take a moment and take some deep breaths and we're just going to go right ahead with this. I think it will actually help if you'll just be patient with me.
So let's start with marginal cost. Marginal cost is defined as--so I'm just putting an equal sign here because by definition this is true. The change in variable cost that results from a change in output. So we'll call that output total product. Remember, that's the total number of television sets that you produce. So if you change your output, how does variable cost change, that's what marginal cost is. Well, how does variable cost actually change? If you hire another worker, how does your variable cost change? Well, you're going to have to pay that worker the wage, and we're going to imagine, for the sake of the stories we're telling here, that the wage is constant. You can hire as many workers you want to at $1,000 per week. So I can write in here, wage, which is $1,000 a week, times the change in labor, and that's my variable cost. We'll have to divide that now by total product.
So again, all I've written here is the change in the variable cost which occurs when you hire an extra worker or some extra workers, multiplied by the wage, and now divided by the total product. Now, let's see if I can make this a little bit easier. Take this number that's upstairs and divide it into the number that's downstairs. What I'm doing is, I'm going to take this and put it downstairs as a reciprocal. I'm dividing the top fraction and the bottom fraction by the change in labor. And when I do that I get this--I get the wage divided by the change in total product that results from a change in labor.
Does this term right here look familiar? What is this term? What is this little fraction that I have downstairs? What is this expression that's in the denominator? It's the marginal product of labor, the change in output that results from a change in labor, the extra TVs that you get when you hire extra workers. So I can finally rewrite my expression this way--that the marginal cost is equal to the wage divided by--and I'm going to try to stick with my color coding here--the marginal product of labor.
Ah, what have I just proved? I've just proved with a few steps of logic and math that the marginal cost is equal to the wage divided by the marginal product. Now, you can go back and check the numbers that we've used before and see, in fact, that this is true. I'll do that in a little bit. But I want you to notice that marginal product and marginal cost are reciprocals. Marginal product is over here in the reciprocal or the denominator of this fraction that is defining marginal cost--they're reciprocals. Now, that's kind of "mathy," that's not real intuitive, but at least it's precise.
Now, what I'd like to do is to try to make this very, very intuitive. Let's suppose that I've got workers producing television sets. And let me put my television set over here. And let's suppose right now that the marginal product of labor is such that one worker can produce one-fourth of a television set. So the marginal product of labor, the extra worker hired, can produce one-fourth of a television set. If we want to produce a whole television set right now, we're going to have to hire four workers. Why? Because the marginal product of labor is one-fourth of a television set. So to get a whole television set, you've got to hire four workers. Each of them can produce one-fourth, and then you've got a whole television set. And you've got to pay each one of those four workers the going wage.
Now look over there at the numbers that we just derived. Look over there at the formula that we just set up. If one-fourth is the marginal product of labor, that is, one worker can produce one-fourth of a television set and the wage is $1,000 a week, then 1,000 divided by one-fourth means it's going to cost you $4,000, four workers that you're going to have to hire to produce one whole television set. The extra cost for your factory of producing a television set right now is four workers times $1,000 equals $4,000. That's the marginal cost of a television set.
I hope I've made this clear that cost and productivity are reciprocals. The marginal cost is the reciprocal of the marginal product. In fact, it's quite precise. The marginal cost is equal to the wage divided by the marginal product of the next worker. Well, now that we've got it established that marginal cost and marginal product are inversely related, that is, they are for all practical purposes reciprocals, it should be very clear why the curves have the similarity that they do. Look at the curves for marginal product and marginal cost. We've drawn them before, but I'm putting them here together in a double-decked graph.
Now here's a warning. In this case the double-decked graph is not measuring exactly the same thing on the two horizontal axes. I'm not saying that these graphs can be mapped perfectly into each other. I'm just setting them beside each other for comparison. This is an important difference. Because I have labor on the horizontal axis up here and I have televisions on the horizontal axis down below. But you know that as you hire more labor, you're going to be producing more television sets, so in some ways, these two graphs are not incompatible. I can set them on top of each other and be measuring the same idea, even if I'm not measuring the same variable.
Well look, up here, when the marginal product is increasing, when each additional worker is producing more output than the worker before, what's happening down below? The marginal cost of production is falling. Here, it takes, let's say one worker can produce one-fourth of a television set, so it takes four workers to produce one television set and that's expensive. Up here, one worker can produce half of a television set, so it only takes two workers to produce a whole television set and the marginal cost is lower. Up here maybe one worker can produce a whole television set by himself. In that case, down here you only have to hire one worker to produce a television set and the marginal cost is at its minimum. As long as productivity is increasing at the margin, cost is falling at the margin. As long as workers can produce more television than the workers before, the cost of adding extra televisions to your output keeps falling. But when productivity at the margin begins to fall, then costs at the margin begin to rise.
One final thing to note. When marginal product is at its maximum, marginal cost will be at its minimum. Remember, marginal product is at its maximum when? When is it going to be that an extra worker is going to add the most television sets? That will be the case when teamwork and specialization are maximized. When the scope for teamwork and specialization has been fully enjoyed. Beyond this point congestion starts to take over. Workers are crowded, using the given number of tools and the fixed production space. Over here you get congestion and marginal productivity begins to fall as the workers get in each others' way and end up sharing the tools, and that gets hard, and we don't have enough fixed inputs here to accommodate all these workers. Well, once you're into declining marginal productivity, then the marginal cost of production starts to rise.
So what has this lecture been about? This lecture has been about the inverse relationship between marginal cost and marginal productivity. We saw first, mathematically, that marginal cost and marginal product are reciprocally related. Then we took an example to explain the intuition. And finally, we used that intuition to explain why the graphs look a lot alike, why they look like mirror images. Anytime marginal product is increasing, marginal cost of production is falling. Anytime your workers are getting less productive, the cost of adding extra televisions is going up.
Production and Costs
Marginal Costs
Understanding the Mathematical Relationship Between Marginal Cost and Marginal Product Page [2 of 2]

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