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Rent control and deadweight loss | Microeconomics | Khan Academy - YouTube
Channel: Khan Academy
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Voiceover: Let's think about
the market for real estate
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in a given city.
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Here on the vertical axis
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I have plotted rent in terms of dollars
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per square foot per month.
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Here on the horizontal axis,
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is essentially the quantity of square foot
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square foot per month
available in millions.
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This is 1 million, 2 million, 3 million,
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4 million, 5 million.
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Here in blue we have the demand curve.
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You see as the price is high,
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one way to view it is that the demand
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for square footage is low and as the price
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is low the demand for
square footage is higher.
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But what I really want to
focus on in this video,
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is viewing the demand curve as the
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marginal benefit curve.
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Marginal benefit curve.
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When that first incremental square foot
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that is added to the market,
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that has a huge marginal benefit
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where people are desperate
to get an apartment.
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To get someplace where they
could rent and they could live.
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So it has a huge marginal benefit.
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Then the marginal benefit for every
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incremental square foot starts to go down.
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Likewise, we can look at the supply curve.
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We're going to look at this as the
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marginal cost curve.
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The marginal cost curve.
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The marginal cost of that very first
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incremental square foot for the suppliers
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for the landlords in the city is $1
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per square foot.
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One way to think about it,
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that very first square foot,
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we don't know what its
price would have been,
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but let's say its price
was at $3 if it was.
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I'm just making that up.
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In that reality,
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if that very first square
foot's price was at $3,
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there is definitely an
incentive for someone
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to make that first square foot
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because their marginal cost is only
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a dollar and they could
rent it out at $3 per month.
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There is definitely an incentive
for someone to rent it.
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The marginal benefit is
$4 and they just have
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to pay $3 for it.
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It could be rented out for anywhere
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or it would exist,
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or this kind of transaction would happen
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as long as its price
was between $1 and $4.
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You could imagine, based
on how this is drawn,
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where the actual equilibrium price is.
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The suppliers will keep
adding more and more
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square foot as long as they
can actually rent it out,
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all the way until the
point that the marginal
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benefit is equal to the marginal cost.
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Right over here marginal benefit is equal
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to marginal cost.
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It wouldn't make sense for suppliers
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to produce an incremental
square foot right over here.
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If they produce an
incremental square foot,
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their marginal cost has gone beyond $3,
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while the marginal benefit is below $3,
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no one is going to rent that thing out.
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We reach an equilibrium point at 2 million
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square feet per month on the market.
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Let me make that line a
little bit straighter.
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2 million square foot
per month on the market
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and at a price of $3 per
square foot per month.
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You can look at the total surplus here.
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In this equilibrium scenario,
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we can calculate the consumer surplus.
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So all of these folks,
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for this first incremental foot,
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someone was willing to
pay $4 per square foot.
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They only have to pay $3.
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The next one a little less than $4.
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Benefit they only have to pay $3.
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All the way to this point right over here.
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So the area of this
triangle right over here,
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this right over here is
the consumer surplus.
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So that right over here
is consumer surplus.
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Consumer surplus.
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We can calculate it.
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This is a triangle.
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I'm assuming actually both the
supply and demand curves are lines.
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So let's see this has a height of 1
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and it has a base of 2 so
its area is going to be
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1 times 2 times one-half.
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That is going to be equal
to 1 million dollars.
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We are multiplying $1 times 2 million
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times one-half.
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That's going to be 1 million dollars
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of consumer surplus per month.
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Let's think about the producer surplus.
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The producer surplus is
going to be this area.
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It's going to be this
area right over here.
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That first incremental foot it only cost
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those producers $1 but they are able
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to rent it out for $3.
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Then they will keep producing,
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keep producing all the way until they
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do 2 million square foot.
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For all of their square feet,
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they are able to rent it out for more
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than it was their cost to produce it.
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So the area of this triangle
is the producer surplus.
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This is the producer surplus.
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Producer surplus.
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We can calculate that as well.
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The height right over here is $2.
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$2 times this width is 2
million square feet per month.
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2 times 2 times one-half is 2.
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This is equal to 2 million dollars.
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If we were to talk about
what the total surplus is,
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it is 3 million dollars.
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Now, this equilibrium rent,
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$3 per square foot per month
is actually quite a lot
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for 1,000 square foot apartment.
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My last apartment was a two bedroom,
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two bath apartment.
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It was about 1,000 square foot.
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So that means you're
going to be paying $3,000
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per month for that.
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That's pretty high rent.
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That's the type of rent you might pay
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in a city like San Francisco.
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Let's say people start
complaining about it.
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So the government says,
"Okay that rent is not fair.
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"It's too high.
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"We want to introduce some
type of price control.
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"We want to introduce rent control."
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I'm oversimplifying how this works,
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but just so that we can deal
with this model right over here,
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Let's say that the city
just sets a ceiling
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on the price per square foot per month.
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Let's just say they set a price ceiling,
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a price ceiling of $2 per
square foot per month.
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$2 per square foot.
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Let me write it this way.
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$2 per square foot per month.
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So they set a price
ceiling right over here.
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Given that, what is going to happen?
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What is going to happen?
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What I really want to think about is what
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is going to be the new consumer surplus
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or the new producer surplus?
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I encourage you to pause the video
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and try to think about that on your own.
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Well let's think about
what's going to happen.
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From the producers point of view,
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it doesn't make sense for them to produce
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more than 1 million units.
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1 million square feet per month.
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I have to rent out more than a million
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square feet per month
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because that extra square foot above that,
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its marginal cost is going to be more than
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what they're going to get.
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The producers are just
going to stop there.
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The producer surplus
is going to be the area
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of this triangle right over here.
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Let's see, this is $1 times 1 million
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times one-half.
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This is now a producer surplus.
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Producer surplus.
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A new producer surplus
under the rent control
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of $500,000, half a million, of $500,000.
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So we see that the rent control
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immediately hit the producers pretty hard.
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The producer surplus has
gone down dramatically.
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Now what about the consumer surplus?
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We're talking about a million units,
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or a million square foot
per month I should say.
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So now the new consumer
surplus is the area,
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is this entire area.
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So you see that at least for this first
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incremental million square feet,
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the consumers have started
to win out a little bit.
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To figure this out,
what the total area is,
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we just need to figure
out what we could break
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this up into two sections.
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We could break this up into two sections.
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This is the point,
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1 million square feet at $3.50
dollars per square foot per month.
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This is right over here,
the point, the 3.5.
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We could use that to
figure out this new area.
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Actually let me do it
in a different color,
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in this green area right over here.
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What is it going to be?
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Well the area of this
thing right over here
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is one-half high.
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One-half times 1 times one-half.
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This right over here is 250K.
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We add that to this area right over here,
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which is one and a half times 1.
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$1.5 dollars per square foot per month
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times 1 million.
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Did I do that right? Yep.
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So that's going to be plus ... plus this,
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which is 1.5 million.
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You add these two together.
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The total consumer surplus ...
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So the total consumer
surplus is now 1.75 million.
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So the consumer surplus definitely
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did go up in total because it gained
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all of this from the producer,
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but let's think about what has now
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happened in our society or in our city.
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The producers definitely
don't want to put out
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as many square foot per rent anymore.
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It does look like we have lost some
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total surplus for our little city here.
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We have lost out on this entire area.
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We can calculate it by looking at what
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the total surplus was
before the rent control
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and what the total surplus
was after the rent control.
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The total surplus before,
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so before the total
surplus was the 2 million
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producer surplus plus the
1 million consumer surplus,
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so it was 3 million.
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After, it is the 1.75
million consumer surplus
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plus the $500,000 producer surplus,
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which is 2.25 million.
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What we've lost is the difference here,
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which is $750,000.
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So this area right over here.
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This is per month.
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This right over here represents
the lost total surplus.
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This lost total surplus
of $750,000 per month
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is referred to as the dead weight loss.
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You can debate about rent control.
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Is it good? Is it bad?
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Is it good for this kind of dynamic?
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Who gets what share of the surplus?
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This of course is an oversimplification
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of a market and even the way rent
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control would be instituted.
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This is a model for beginning to think
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about what happens to the total surplus
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when these types of price
controls are instituted.
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