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♪ [music] ♪

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- [Alex] We learned last time[br]that a firm

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in a competitive market[br]doesn't have much control

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over it's price.

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It must accept the market price.

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So its decision about profit[br]maximization turns into a decision

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about what quantity to choose,

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and that's what we're going[br]to be focusing on now.

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So what is profit?

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Profit is total revenue[br]minus total cost.

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Total revenue is just price[br]times the quantity sold.

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Total cost has two parts.

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First are the fixed costs.

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These are costs[br]that do not vary with output.

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So, for example, suppose you[br]are the owner

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of this small oil well[br]and you have to pay rent

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for the land[br]on which the oil well sits.

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Those rental costs --[br]you have to pay them

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regardless of how much[br]the oil well is producing.

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Every month you have to pay[br]some rental cost

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whether you're producing[br]one barrel of oil per month,

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10 barrels of oil per month,[br]11 barrels of oil per month.

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It doesn't matter.

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You still have to pay[br]the same rental cost.

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Indeed, even if you don't produce[br]any oil that month,

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if your oil well breaks down,[br]you still have to pay

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those rental costs.

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So the rental costs[br]are fixed costs.

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They don't vary[br]with the quantity produced.

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By the way, notice[br]that even if you owned the land,

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if you could have rented it[br]to someone else,

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then that would be[br]an opportunity cost.

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So your calculation of profit[br]should also include

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opportunity costs.

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That's what makes the economic[br]calculation of profit, by the way,

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differ from the accounting[br]definition of profit.

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The economic notion of profit[br]includes opportunity costs.

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Okay, what else?

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Well, variable costs --[br]these are the cost

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that do vary with output.

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So for example, the electricity cost[br]for pumping oil --

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the more oil you pump,[br]the faster you get your rig to go,

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the more electricity[br]you're going to use up.

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If you run it 24 hours a day,[br]you're going to use

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more electricity[br]than if you only run the pump

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12 hours a day.

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Transportation cost --[br]you got to go and get the oil,

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truck it out of there,[br]move it and so forth.

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So these costs are all costs[br]which vary with output,

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which typically will increase[br]the more output that you produce.

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Those are your variable costs.

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So just to summarize on cost,[br]total cost is equal

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to your fixed costs[br]plus your variable costs

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and these depend upon output.

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Okay, so how do we maximize profit?

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Well, we're not going[br]to use calculus in this class,

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but for those of you[br]who do know calculus,

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I want to do a quick aside --[br]show you actually how useful

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calculus is and show you[br]an easy way

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of answering this problem.

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So we know the profit[br]is total revenue minus total cost

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and both of these are functions[br]of the quantity produced.

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Now in calculus[br]how do we maximize a function?

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Think back to your calculus class.

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You take the derivative[br]of that function

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and you set it equal to zero.

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So in this case,[br]we want to take the derivative

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of profit with respect[br]to quantity and set that

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equal to zero.

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So derivative of profit [br]with respect to quantity --

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that's just the derivative[br]of total revenue

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with respect to quantity[br]minus the derivative of total cost

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with respect to quantity.

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Now in economics,[br]we have special names

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for these two derivatives.

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The derivative of total revenue[br]with respect to quantity

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is simply called marginal revenue.

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And the derivative of total cost[br]with respect to quantity

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is called marginal cost.

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So we want to find the quantity[br]such that marginal revenue

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minus marginal cost is zero,[br]or in other words,

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we want to find the quantity[br]such that marginal revenue

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is equal to marginal cost.

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In other words, the quantity,[br]which maximizes profit,

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is the one where marginal revenue [br]is equal to marginal cost.

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Now I'm about to give you[br]a more intuitive explanation,

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especially for those of you[br]who don't get no calculus,

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but for those of you who do,[br]this is just exactly

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what you were to do in calculus --[br]you take the derivative,

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set it equal to zero.

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Okay let's get to more intuition.

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When the firm produces[br]an additional unit of output,

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there are additional revenues[br]and additional costs.

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Profit maximization[br]is all about comparing

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these additional[br]revenues and costs,

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and we have names for these.

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Marginal revenue is the addition[br]to total revenue

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from selling an additional[br]unit of output.

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Marginal cost is the addition[br]to total cost from producing

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an additional unit of output.

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Profits are maximized at the level[br]of output where marginal revenue

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is equal to marginal cost.

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Now why is this?

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Well, let's suppose[br]that marginal revenue

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is not equal to marginal cost[br]and let’s show

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that you can't be profit maximizing[br]if that's the case.

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For example, if marginal revenue[br]is bigger than marginal cost,

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you're not profit maximizing --[br]producing more

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will add to your profit.

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Why? Well, remember marginal[br]revenue is the addition

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to revenue from producing[br]another unit.

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Marginal cost[br]is the addition to cost

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from producing another unit.

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If marginal revenue is bigger[br]than marginal cost,

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that says producing that unit[br]adds more to your revenues

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than it does to your costs.

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In other words,[br]you could increase profit

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by producing more.

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So if marginal revenue[br]is ever bigger

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than marginal cost,[br]you want to produce more.

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On the other hand,[br]suppose marginal revenue

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is less than marginal cost,[br]or to put it the other way,

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suppose marginal cost is bigger[br]than marginal revenue.

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Well then, you're not[br]profit maximizing

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because producing less[br]will add to your profit.

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Why is this?

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Well, think about marginal cost.

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If you were to produce[br]one unit less your costs would fall

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by marginal cost,[br]your revenues would also fall

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by marginal revenue,[br]but since marginal cost is bigger

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than marginal revenue,[br]your costs by producing

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one unit less fall by more[br]than your revenues fall.

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So if your costs are going down[br]by more than your revenues

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are going down,[br]you're again increasing profit.

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So if marginal revenue[br]is ever less than marginal cost,

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you want to produce less --[br]you'll be increasing your profit

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by producing less.

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So, if marginal revenue[br]is bigger than marginal cost,

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you're not profit maximizing.

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If marginal revenue is less[br]than marginal cost

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you're not profit maximizing.

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You can only profit maximize[br]if marginal revenue

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is equal to marginal cost.

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Now let's put all this in a diagram[br]beginning with marginal revenue.

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Now for a competitive firm,[br]this is going to be easy

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because remember,[br]that a competitive firm

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is small relative[br]to the total market.

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That means it can double[br]its production easily

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and not push down the market price.

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As a result,[br]for a competitive firm,

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marginal revenue is equal[br]to the market price.

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So for example, suppose the firm[br]is producing two units of output

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and it decides to produce[br]a third unit,

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what's the additional revenue[br]from that third unit?

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It's the price.

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It's the price it gets[br]for that barrel of oil.

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What about if it produces[br]a fourth barrel of oil?

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What does it get?[br]What's the addition to revenue?

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It's the price of a barrel of oil.

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What about the fifth unit?

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Again, the price is the addition[br]to revenue, is marginal revenue.

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So, marginal revenue[br]for a competitive firm

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is equal to the price[br]and it's flat --

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it doesn't change when the firm[br]changes its output

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because the firm is small[br]relative to the market.

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Now what about marginal cost?

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Well, a typical shape[br]of a marginal cost curve

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would be upward sloping like this.

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Again, think about[br]our stripper oil well.

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We can produce more[br]from that oil well,

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but there's a limit.

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We can only run it so quickly.

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We have to push it really hard[br]when we start to produce more.

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So we can easily produce,[br]you know, three, or four units,

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but in order to produce six,[br]seven, eight, or nine barrels of oil

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from that oil well,[br]we're going to have to run it

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really quickly, we're going[br]to have to put in

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a lot of electricity,[br]we're going to have to do

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a lot of maintenance and so forth.

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So our costs will tend to increase.

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We can't produce[br]an unlimited amount of oil

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at the same cost[br]from this oil well.

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Our costs are going to go up,[br]are going to rise,

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our additional costs[br]are going to rise

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the more we want to produce[br]from that oil well.

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So this is a typical shape[br]of a marginal cost curve.

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Now, where's profit maximization?

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Well, profit is maximized[br]where marginal revenue

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is equal to marginal cost.

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In this case,[br]for a competitive firm,

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marginal revenue is equal to price.

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So profit is maximized[br]where price is equal

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to marginal cost[br]or at this point right here.

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Now let's think[br]about that intuitively.

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On the left hand side,[br]this is the additional revenues

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from selling a barrel of oil.

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These are the additional costs[br]from selling a barrel of oil.

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So you want to compare --[br]revenues bigger than costs,

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therefore sell more.

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Revenues bigger than costs,[br]therefore sell more.

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Revenues bigger than costs.

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You keep selling more[br]until you reach this point.

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Do you want to go further? No.

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Here, costs are bigger[br]than revenues.

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So by selling less,[br]you can reduce your costs

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by more than you'd reduce[br]your revenues

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and therefore profit goes up[br]going this way

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and that's why this point,[br]where marginal revenue

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is equal to marginal cost,[br]or price is equal to marginal cost,

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that's the point where profit[br]is maximized.

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Now remember way back[br]in the first talk,

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we wanted to explain[br]a firm’s behavior.

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So let's look how maximizing profit[br]explains the firm’s behavior.

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Suppose the market price[br]is $50 per barrel.

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Well, then in order[br]to maximize profit,

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the firm chooses the quantity --[br]in this case,

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about eight barrels of oil --[br]such that marginal revenue

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is equal to marginal cost,[br]bearing in mind

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that for the competitive firm,[br]marginal revenue is equal to price.

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So to profit maximize[br]the firm produces a quantity

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of about eight barrels of oil.

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Now suppose that the market price[br]goes up to $100.

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Now in order to profit maximize,[br]the firm increases its production

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along its marginal cost curve[br]keeping this relationship the same

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so price is still equal[br]to marginal cost.

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Price has gone up to 100,[br]but because the firm has expanded

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along its marginal cost curve,[br]marginal cost has gone up as well.

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So this again is the profit[br]maximizing point

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when the price is equal to 100.

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When the price is equal to 100,[br]the profit maximizing quantity

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is just under 10 barrels of oil.

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So profit maximization explains[br]what the firm does when the price,

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when the market price, changes.

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We now know how to find[br]the profit maximizing quantity --

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look for the quantity[br]where marginal revenue

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is equal to marginal cost,[br]which is the same

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for the competitive firm[br]where price is equal

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to marginal cost.

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Now we want to ask,[br]what is the size of the profit?

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This raises a subtle point.

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You can be maximizing profits[br]and actually have a loss.

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That is, the best that you can do[br]might be a loss.

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So we want to show on the diagram[br]how large your profits

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or how large your losses are[br]when you are maximizing profits.

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In order to do that,[br]we need to introduce

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another concept[br]and another curve --

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average cost.

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Average cost is simply[br]the cost per unit of output.

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That is the total cost[br]divided by Q,

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the quantity of the output.

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So average cost again --[br]total cost divided by Q.

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Adding the average cost curve[br]to our graph

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will let us show profit[br]on the graph.

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And that's what we want to do,[br]and that's what we'll do

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in the next talk.

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Thanks.

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- [Narrator] If you want[br]to test yourself,

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click, "Practice Questions,"

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or if you're ready to move on,[br]just click, "Next Video."

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♪ [music] ♪