Maximizing Profit and the Average Cost Curve

Now that we know how to find the profit maximization point, we're going to show the amount of profit on the diagram using the average cost curve.

So as I said in the last lecture, average cost is the cost per unit of output. That is, average cost is total cost divided by Q. Now remember also that total cost can be broken down into fixed costs plus variable costs. So we can also write average cost in a slightly longer format. Average cost is equal to fixed cost divided by Q plus the variable cost divided by Q, the units of output. That's a little bit useful because we're able to see, get some intuition, for the shape of a typical average cost curve.

Notice that the fixed costs don't change with Q. That's why they're fixed. So when Q is small -- this number, suppose fixed cost is 100, and Q is small -- then this number is going to be big like 100 divided by 1. As Q gets larger, however, this number -- fixed cost divided by Q -- is going to get smaller, So when Q is 10, this number 100 divided by 10 becomes 10. So it goes from 100, and it goes down, down, down, down, gets lower and lower and lower all the time as you divide by a bigger quantity. On the other hand, the variable costs increase with quantity.

Moreover, what we saw with the marginal cost curve is that at some point, your variable costs are going to increase faster than quantity. So what's going to happen is that this number at some point -- variable cost divided by quantity -- is going to get bigger and bigger and bigger. So you have two things, one force is driving average cost down. That's going to be particularly strong at the beginning. Eventually, however, the second force here is going to drive average cost up. So that's going to be our typical shape of an average cost curve -- falling, reaches a minimum, and then rising.

So let's draw it like that. Okay, here's our typical marginal cost curve, and here is our marginal revenue curve, equal to price. We know that the profit maximizing point is where marginal revenue is equal to marginal cost. Here is our average cost curve, and notice it has the shape which I described -- it starts off high, it falls, reaches a minimum, and then goes right back up again. Couple of other points to notice is that the minimum point, the marginal cost curve goes through the minimum point of the average cost curve. Now that's just a mathematical fact, but let me give you some intuition. Instead of cost, I want to talk about average grade and marginal grade. So suppose that your average grade is 80%. You're doing really pretty good, but then on your next test you only get 60% -- lower.

What is that going to do to your average? Well, it's going to drive your average down. Indeed whenever your marginal is below your average, the average must be falling. On the other hand, suppose that you're getting 80%, and on your next test you get 90%. Great, but what does that do to your average? It drives your average up. Indeed whenever your marginal is above the average, the average must be rising. Now suppose what happens when you're getting let's say 80%, and on your next test, you also get 80%. Well then your marginal is equal to your average grade, and your average grade is flat -- it doesn't change, it's flat. But what is true for average and marginal grades is also true for average cost and marginal cost. Whenever the marginal cost is below the average, the average is falling. Whenever the marginal cost is above the average, the average is rising. And where marginal is just equal to average, the average is flat. In other words, we are at the minimum point of the average cost curve.

Okay, now I said we could use the average cost curve to figure out profit -- show profit on the diagram. We can do that with just a little bit of rearranging. Remember that profit is equal to total revenue minus total cost and total revenue is price times quantity -- P times Q. We also know that average cost is equal to total cost divided by quantity. Let's just rearrange that to tell us that total cost is equal to average cost times quantity. So just take this one and multiply both sides by Q.

Let's now make these substitutions into our profit equation. If we do that, then profit is equal to total revenue -- price times quantity -- minus total cost -- average cost times quantity. Now let's take Q out of both parts of this equation, and we find that profit can also be written as price minus average cost, all of that times quantity. That's nice because we can find all of these elements on our diagram. Here's the price. Here's the average cost at the profit maximizing quantity. Let's just show that. There's the price. There's the average cost at the profit maximizing quantity. So profit at the profit maximizing quantity is this green area right here -- price minus average cost times quantity. So now we have a nice way of showing in a diagram exactly how much profit is. Let's use this tool some more.

Here's another example of the average cost curve in action. Remember, I said that profit maximization doesn't necessarily mean the firm is making a positive profit. Sometimes the best you can do is to minimize your losses. You may have to take a loss. For example, suppose that the price is below $17. That is, here's the market price, which is equal to the firm's marginal revenue curve. How does the firm profit maximize? It chooses the quantity where marginal revenue is equal to marginal cost. In that case, this quantity is one.

Now what's the profit for the firm? Well, as usual we measure profit as price minus average cost times quantity. But notice that price is below the average cost at the profit maximizing quantity of one. Since price is below average cost, this is a loss. It's a negative quantity. It is a loss. In fact, notice that the breakeven price is $17, which is the minimum of the average cost curve. In order to make a profit, the firm at least has to meet the minimum of its average cost curve. So at any price below $17, we'll be profit maximizing at a point where price is equal to marginal cost, and notice that all of these prices are below average cost. So all of this area down here, even the profit maximizing quantity, will mean a loss.

On the other hand, once we get above $17, above the minimum of the average cost curve, then we can price equal to marginal cost. We can choose the quantities such the price is equal to marginal cost. That price will be above average cost, so we'll be taking a profit. Therefore, $17, the minimum of the average cost curve, is the breakeven point. If the price is less than the minimum of the average cost curve, we're going to be taking a loss. If the price is bigger than the minimum of the average cost curve, then we can make a profit.

So when should a firm enter or exit an industry? In the long run, the firms will enter when price is above average cost. If price is somewhere above the average cost curve then the firm can make a profit by entering, and that's what firms want to do. They want to find profit, so they will want to enter wherever a profit is possible. Firms will exit the industry when the price is below the average cost curve. Then they're going to be taking a loss, and they're going to want to exit. Finally, when the price is equal to the minimum of the average cost -- it's just equal to the bottom of the average cost curve, profits are zero, and there's no incentive to either exit or enter the industry.

Now you might ask, why would firms remain in an industry if profits are zero? Zero profits, this is just a matter of terminology, means that at the market price the firm is covering all of its costs, including enough to pay labor and capital, their ordinary opportunity cost. So zero profits means everyone is being paid enough to make them satisfied. Zero profits, in other words, is what normal people mean by normal profits. So when an economist says zero profits just substitute normal profits.

One more point about entry and exit. It doesn't always make sense to exit an industry immediately when price falls below average cost, or to enter immediately when price is above average cost. Why not? Well, there are also entry and exit costs. For example, suppose that that the price of oil is currently above the average cost of pumping oil, if you've already got a well. Should you enter the industry? Well, maybe not necessarily. Because entry requires you to drill an oil well, and drilling an oil well is a sunk cost -- literally in this case. A sunk cost is a cost that once incurred can never be recovered.

So if you enter the industry and drill the oil well, you don't get that money back when you later exit the industry. What this means is you don't want to enter unless you expect the price of oil to stay above the minimum of the average cost curve long enough so that you can also recover your entry costs. So just because the price goes above the average cost a little bit, you don't immediately want to jump into that industry. You have to expect that that price is going to stay above average cost long enough for you to recover your entry costs.

For the same reasons, if there are exit costs -- for example, if you have to shutter up the well or fill the well with cement when you exit the industry as you do in the United States -- then when price falls below average cost, it may be best to weather the storm at least for sometime before you exit. Only if you expect the price of oil to stay below your minimum of average cost for an extended period of time will you want to exit the industry. After all, if the price of oil falls below the average cost just for a little bit, and then it goes back up, the lifetime profits can still be possible.

So, entry and exit could be quite complicated because you've got to be thinking about the lifetime profits, not just your immediate profits. However, the bottom line is pretty simple. Firms seek profits, and they want to avoid losses. As a result, firms will enter industries when the price is above the average cost and they can make a profit, and they will exit when the price is below the average cost. Thanks.