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Economics: Firm's Profit-Maximizing Output Level


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About this Lesson

  • Type: Video Tutorial
  • Length: 14:24
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 154 MB
  • Posted: 03/29/2010

This lesson is part of the following series:

Economics: Full Course (269 lessons, $198.00)
Economics: Perfect Competition (14 lessons, $26.73)
Economics: Calculating Profit and Loss (5 lessons, $9.90)

In this video lesson, you'll be focused on learning to identify a firm's profit-maximizing output level. At this level, the firm maximizes its profit. 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 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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Imagine you're running a television factory and you want to make maximum profits. You're trying to decide how many television sets to produce. What rule are you going to use to decide whether to produce one more television set? The answer is, you'll produce an extra television set any time that extra set adds more to your company's revenue than it adds to its cost. You're never going to produce a television set that costs you more, at the margin, than the revenue that it adds. That would be subtracting from your profits. But the rule of producing up to the point at which marginal cost is just equal to the price. That's the rule that a competitive firm uses to maximize its profits.
Let's look at how that rule looks in a graph. We're dealing with a firm, in the short-run, that's trying to maximize its profits and we've made a particular assumption about that firm. We've assumed that it is a competitive firm. Now, I haven't used this term before, but now is a good time to introduce it. A competitive firm is a firm that can take any action it wants to. It can produce as many television sets as it chooses to without influencing the price of its product. A competitive firm is a firm that can take any action without having an effect on the price of its product.
Therefore, the price of your product is a given, a constant, something determined in the market that you have no control over. We've imagined that our competitive firm, in this example, can produce televisions a price of $500 per television sold. That is, the price is constant at $500, no matter how many televisions you produce and sell. If that's true, will you produce another television set if you want to maximize your profits? The answer is, it depends on the cost of producing that television set. The cost of producing an extra television set is called the marginal cost of producing that set.
The marginal cost of production, if it's less than the price, signals you to produce the television set and thereby increase your profits. But if the marginal cost is greater than the price, producing that television set would actually reduce your profits, and therefore it's not something you should do. Let's look now at this story in the picture. Here's a picture that you're familiar with from our last discussion. The total revenue curve is a straight line, away from the origin, which represents the situation of a competitive firm. You can produce all the television sets you want to and sell them at a constant price of $500 a piece. The total cost curve now, has a shape that reflects the productivity of the firm. First, you have diminishing marginal cost, as marginal product increases due to teamwork and specialization, and then you have increasing marginal cost as congestion in the fixed inputs occurs.
We now want to represent this picture, this same information in this graph below. I'm using another one of my double-decker graphs, which means I have to be clear that on the horizontal axis I'm measuring the same thing. In this case, I'm measuring output on both of these axes and I'm using exactly the same scale. Now the first line that I'm going to draw in the diagram below, is the firm's marginal revenue. Marginal revenue is defined as the change in total revenue that results from a change in output. Now, how does marginal revenue change? How does the firm's total revenue earned change if it sells one more television set? The answer is, it changes by $500, the price of the television set. It doesn't matter whether it's your first television sold, your tenth or your 100^th. Each television sold would always add $500 to your total revenue. $500 is the marginal revenue, which in this case, the case of the competitive firm, is equal to the price of the television set.
A quick note. For a competitive firm that cannot influence the price of its good, marginal revenue is always equal to the price of the product. So, let me draw in a line that represents marginal revenue. In this case, marginal revenue is the price of a television set and the price of the television set will always be equal to $500. So, here I have a line with a slope of zero. It represents a constant, and this line is representing the price of a television set, in my story that's $500. Now, let's represent next the marginal cost of producing a television set.
Where do I get information, from this picture, on marginal cost? Where in this picture do I see the marginal cost of production? The answer is, it is the slope of the total cost curve. Remember, marginal cost is defined as the change in total cost that results from a change in output. It's the rise over the run, the slope of the total cost curve. So I want to graph a picture of the total cost curve and, let me see where the inflection point is. It looks like the inflection point might be right about here. This is the point where the total cost curve is no longer concave and becomes convex. That is, the slope stops decreasing and starts increasing instead. So if this is my point of inflection, this gives you the point at which marginal cost is at a minimum. The slope has decreased and decreased and decreased and decreased and it's just not going to get any lower. So here's the point of minimal marginal cost.
Now, two other things that I want to notice. First of all, this point right here, this output level, in our last lecture we called this output level Y*. This is an output level at which the slope of the total cost curve is the same as the slope of the total revenue curve. This is an output level at which price is equal to marginal cost. So marginal cost at this point would be equal to price and I can call this point Y*, just like I did before. That's Y*. Over here, is another point where the slope of the total cost curve is equal to the slope of the total revenue curve, and this point before I called it Y*. Y* is another point where marginal cost is equal to price. Y*. That's the point at which losses are maximized, by the way.
All right now, if I keep the marginal costs diminishing until I reach the inflection point, and then have it rise after that I would be drawing the slope of the total cost curve in this downstairs graph. So, let me do that. Here's diminishing marginal cost. Bam, then marginal cost increases, bam, and there's your marginal cost curve. Again, what have I drawn here? This marginal cost curve is simply the slope of the total cost curve at every point, and I had some points that I knew had to be on the curve, the point of inflection, where marginal cost is at a minimum, and these two points where marginal cost is equal to price. Y* and Y*.
Now, now, I can use this diagram down below to make an intuitive point about profit maximization. I argued before that this point, Y*, was the point of maximum profit for the firm. How did I know that? Well, if I look in the upstairs diagram, I know that because that's the point where the gap between total revenue and total cost is the biggest. That's the point where profit is maximized. But downstairs, I can tell the story a different way, using a different intuition. Let's suppose now that you run that television factory and you're producing, at this point, Y*. Is that a good point for you to be at? The answer is, yes.
If you increase your output beyond Y*, what's happening? You're adding $500 for that television. If you produce another television at that point, you're adding $500 to your revenue, but the amount that you're adding to your cost is greater. What does that mean? It means that that next television is actually shrinking your profits. Because it costs more to produce than it earns you in revenue. So you don't want to go past the point Y*. You also, however, don't want to decrease your output. If you decrease your output, you would lose $500 by not selling a television set. If you back off and produce one less television set, you're going to cost your firm $500 in lost revenue.
How much are you spending on the labor that you're not employing? Well, notice your savings is less than $500. The savings is less than $500. So you're sacrificing $500 in lost revenue, but you're only saving yourself maybe $450 in costs that you don't incur. It's not worth it to save $450 if it means you're throwing away a $500 sale. Therefore, you don't want to move backwards from that point either. If you're at this point, Y*, where price is equal to marginal cost, you do not want to produce an extra television set. You also do not want to produce one fewer television set. This is the point that is un-improvable. This is the point at which profit is maximized.
Suppose we were back here at another point. Let's say this point of inflection. Just pick it, for example. Is this a good place for your firm to operate? The answer is no. How do I know? How could you improve your situation if you were at this point, if you were producing this smaller quantity of television sets? How could you improve this situation? You could produce more television sets. If you produce more television sets, notice, each television set that you produce adds how much to your revenue? $500, the price of the television sets. Each one of them costs how much to produce? Well, some amount less than 500. Notice the green line is below the blue line at that point.
If marginal cost is less than marginal revenue, if marginal cost is below the price of the good, for a competitive firm, you can always increase your profit by increasing your output. As long as the cost is less than the price, by all means, make more television sets, drive up your profits. If you're over in this region and producing a large quantity of television sets and the marginal cost is greater than the price, by all means, back off; produce fewer television sets. Because the money that you save by not producing those television sets, the money you'd save by not employing the extra workers is greater than the money you lose from the lost sale.
You economize more by not hiring the workers than you would lose by not producing the television sets. So back off, save more than you lose in revenue. Save more by economizing on costs. It's only at the point where marginal costs equals price, it's only at this point that the firm cannot improve its situation. Now, one final note. Look over here at Y*. Y* is another point where price is equal to marginal cost. Y*, on the other hand, is a bad point, because anything you do, any movement away from Y* makes you better off. If you're at Y* and you increase your output, what happens? Well look, you're adding television sets that earn $500 apiece and the cost is less than 500. Get away from Y*, increase your output, because price is greater than cost. As you increase your sales, that's going to add to your profits. The televisions are bringing more in in revenue than they cost to produce.
Look. Even if you reduce your output, you're improving your situation. Because if you back off here, each of those televisions is bringing in $500, but they're costing more to produce at the margin. So, if you reduce your output away from Y*, then you're saving more in labor costs than you're losing in lost sales. Y* is an awful point. In fact, if you'll look at the picture, you can see it's the worst you could possibly do. It's the point of minimum profit, the point where cost is the highest above revenue that it ever gets.
So, let me summarize. The point at which profit is maximized is the point where price is equal to the marginal cost of production. This is the rule, the profit maximization for a competitive firm. Any competitive firm to maximize its profits must be producing at the point where price equals marginal cost. There's one additional condition and that is, it's not enough to be at the point where price equals marginal cost. You also have to be at a point where the marginal cost curve is sloping upwards. That is, you have to be at a point where marginal cost is increasing. That's what distinguishes Y* from Y*. Y*, where marginal cost is decreasing, is a terrible point. It's the point of minimum profits. Y*, where marginal cost is increasing, is actually the point of profit maximization.
So, our two conditions, our first, price equals marginal cost and next, that the marginal cost curve itself must be upwards sloping at that point. Marginal costs must be increasing. If those two conditions are satisfied, then the firm is maximizing its profits in the short run.
Perfect Competition
Calculating Profit and Loss
Finding the Firm's Profit-Maximizing Output Level Page [3 of 3]

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