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- [Alex] Now that we know [br]how to find the profit

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maximization point, [br]we're going to show

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the amount of profit on the diagram [br]using the average cost curve.

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So as I said in the last lecture,

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average cost is the cost [br]per unit of output.

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That is, average cost is[br]total cost divided by Q.

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Now remember also [br]that total cost can be broken down

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into fixed costs plus [br]variable costs.

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So we can also write average cost[br]in a slightly longer format.

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Average cost is equal [br]to fixed cost divided by Q

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plus the variable cost divided [br]by Q, the units of output.

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That's a little bit useful [br]because we're able to see,

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get some intuition, for the shape [br]of a typical average cost curve.

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Notice that the fixed costs [br]don't change with Q.

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That's why they're fixed.

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So when Q is small -- this number,

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suppose fixed cost is 100,

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and Q is small -- then this number [br]is going to be big

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like 100 divided by 1.

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As Q gets larger, however,[br]this number --

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fixed cost divided by Q -- [br]is going to get smaller,

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So when Q is 10, this number [br]100 divided by 10 becomes 10.

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So it goes from 100,[br]and it goes down, down, down, down,

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get's lower and lower and lower[br]all the time as you divide

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by a bigger quantity.

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On the other hand, the variable [br]costs increase with quantity.

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Moreover, what we saw [br]with the marginal cost curve

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is that at some point,[br]your variable costs are going

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to increase faster than quantity.

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So what's going to happen is [br]that this number at some point --

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variable cost divided by quantity --[br]is going to get bigger

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and bigger and bigger.

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So you have two things, one force [br]is driving average cost down.

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That's going to be particularly [br]strong at the beginning.

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Eventually, however, [br]the second force here is going

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to drive average cost up.

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So that's going to be our typical [br]shape of an average cost curve --

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falling, reaches a minimum,[br]and then rising.

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So let's draw it like that.

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Okay, here's our typical[br]marginal cost curve,

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and here is our marginal [br]revenue curve, equal to price.

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We know that the profit maximizing [br]point is where marginal revenue

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is equal to marginal cost.

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Here is our average cost curve [br]and notice it has the shape

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which I described --[br]it starts off high, it falls,

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reaches a minimum, [br]and then goes right back up again.

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Couple of other points to notice[br]is that the minimum point,

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the marginal cost curve goes [br]through the minimum point

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of the average cost curve.

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Now that's just a mathematical fact, [br]but let me give you some intuition.

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Instead of cost I want [br]to talk about average grade

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and marginal grade.

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So suppose that your [br]average grade is 80%.

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You're doing really pretty good,[br]but then on your next test

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you only get 60% -- lower.

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What is that going to do [br]to your average?

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Well, it's going to drive [br]your average down.

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Indeed whenever your marginal [br]is below your average,

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the average must be falling.

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On the other hand, suppose [br]that you're getting 80%,

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and on your next test you get 90%.

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Great, but what does [br]that do to your average?

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It drives your average up.

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Indeed whenever your marginal[br]is above the average,

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the average must be rising.

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Now suppose what happens [br]when you're getting let's say 80%,

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and on your next test,[br]you also get 80%.

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Well then your marginal is equal [br]to your average grade,

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and your average grade is flat -- [br]it doesn't change, it's flat.

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But what is true for average [br]and marginal grades is also true

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for average cost and marginal cost.

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Whenever the marginal cost is [br]below the average,

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the average is falling.

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Whenever the marginal cost is [br]above the average,

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the average is rising.

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And where marginal is [br]just equal to average,

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the average is flat.

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In other words, we are [br]at the minimum point

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of the average cost curve.

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Okay, now I said we could use [br]the average cost curve

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to figure out profit -- [br]show profit on the diagram.

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We can do that with just [br]a little bit of rearranging.

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Remember that profit is equal [br]to total revenue minus total cost

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and total revenue is [br]price times quantity -- P times Q.

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We also know [br]that average cost is equal

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to total cost divided by quantity.

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Let's just rearrange that [br]to tell us that total cost is equal

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to average cost times quantity.

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So just take this one [br]and multiply both sides by Q.

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Let's now make these substitutions [br]into our profit equation.

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If we do that, then profit is equal [br]to total revenue --

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price times quantity --[br]minus total cost --

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average cost times quantity.

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Now let's take Q out [br]of both parts of this equation,

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and we find that profit [br]can also be written as price

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minus average cost, [br]all of that times quantity.

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That's nice because we can find

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all of these elements [br]on our diagram.

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Here's the price.

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Here's the average cost[br]at the profit maximizing quantity.

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Let's just show that. [br]There's the price.

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There's the average cost [br]at the profit maximizing quantity.

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So profit at the profit [br]maximizing quantity is

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this green area right here --

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price minus average cost [br]times quantity.

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So now we have a nice way [br]of showing in a diagram

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exactly how much profit is.

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Let's use this tool some more.

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Here's another example [br]of the average cost curve in action.

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Remember, I said that profit [br]maximization doesn't necessarily

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mean the firm is making [br]a positive profit.

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Sometimes the best you can do [br]is to minimize your losses.

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You may have to take a loss.

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For example, suppose [br]that the price is below $17.

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That is, here's the market price, [br]which is equal to the firm's

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marginal revenue curve.

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How does the firm profit maximize?

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It chooses the quantity [br]where marginal revenue is

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equal to marginal cost.

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In that case, this quantity is one.

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Now what's the profit [br]for the firm?

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Well, as usual we measure [br]profit as price minus

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average cost times quantity.

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But notice that price is [br]below the average cost

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at the profit maximizing [br]quantity of one.

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Since price is below average cost, [br]this is a loss.

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It's a negative quantity.

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It is a loss. In fact, notice [br]that the breakeven price is $17,

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which is the minimum [br]of the average cost curve.

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In order to make a profit, [br]the firm at least has to meet

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the minimum of its [br]average cost curve.

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So at any price below $17,[br]we'll be profit maximizing

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at a point where price is equal[br]to marginal cost,

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and notice that all of these [br]prices are below average cost.

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So all of this area down here,

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even the profit maximizing [br]quantity, will mean a loss.

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On the other hand, once we get [br]above $17, above the minimum

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of the average cost curve, then we [br]can price equal to marginal cost.

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We can chose the quantities such [br]the price is equal to marginal cost.

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That price will be above average [br]cost, so we'll be taking a profit.

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Therefore, $17, the minimum[br]of the average cost curve,

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is the breakeven point.

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If the price is less [br]than the minimum

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of the average cost curve, [br]we're going to be taking a loss.

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If the price is bigger [br]than the minimum

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of the average cost curve, [br]then we can make a profit.

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So when should a firm enter [br]or exit an industry?

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In the long run, the firms will [br]enter when price

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is above average cost.

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If price is somewhere [br]above the average cost curve

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then the firm can make [br]a profit by entering

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and that's what firms want to do.

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They want to find profit, [br]so they will want to enter

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wherever a profit is possible.

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Firms will exit the industry [br]when the price is below

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the average cost curve.

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Then they're going [br]to be taking a loss,

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and they're going to want to exit.

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Finally, when the price is [br]equal to the minimum

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of the average cost --[br]it's just equal to the bottom

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of the average cost curve, [br]profits are zero,

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and there's no incentive [br]to either exit or enter the industry.

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Now you might ask, why would[br]firms remain in an industry

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if profits are zero?

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Zero profits, this is just [br]a matter of terminology,

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means that at the market price [br]the firm is covering all of its costs

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including enough [br]to pay labor and capital,

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their ordinary opportunity cost.

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So zero profits means everyone[br]is being paid enough

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to make them satisfied.

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Zero profits, in other words,[br]is what normal people mean

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by normal profits.

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So when an economist [br]says zero profits

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just substitute normal profits.

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One more point [br]about entry and exit. [br]

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It doesn't always make sense [br]to exit an industry immediately

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when price falls [br]below average cost.

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Or to enter immediately [br]when price is above average cost.

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Why not? Well, there are [br]also entry and exit costs.

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For example, suppose that that the price[br]of oil is currently above the average cost

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of pumping oil, if you've already got a[br]well. Should you enter the industry? Well,

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maybe not necessarily. Because entry[br]requires you to drill an oil well, and

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drilling an oil well is a sunk cost -[br]literally in this case.

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A sunk cost is a cost that once incurred[br]can never be recovered. So if you enter

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the industry and drill the oil well, you[br]don't get that money back when you later

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exit the industry. What this means is you[br]don't want to enter unless you expect the

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price of oil to stay above the minimum of[br]the average cost curve long enough so

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that you can also recover your entry[br]costs. So just because the price goes

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above the average cost a little bit, you[br]don't immediately want to jump into that

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industry. You have to expect that that[br]price is going to stay above average cost

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long enough for you to recover your entry[br]costs. For the same reasons, if there are

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exit costs, for example, if you have to[br]shutter up the well or fill the well with

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cement when you exit the industry as you[br]do in the United States, then when price

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falls below average cost, it may be best to[br]weather the storm at least for sometime

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before you exit. Only if you expect the[br]price of oil to stay below your minimum of

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average cost for an extended period of[br]time will you want to exit the industry.

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After all, if the price of oil falls below[br]the average cost just for a little bit, and

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then it goes back up, the lifetime[br]profits can still be possible. So, entry

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and exit could be quite complicated[br]because you've got to be thinking about

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the lifetime profits, not just your[br]immediate profits. However, the bottom

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line is pretty simple. Firms seek profits[br]and they want to avoid losses. As a

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result, firms will enter industries when[br]the price is above the average cost and

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they can make a profit, and they will exit[br]when the price is below the average cost.

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Thanks.

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