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# Rent control and deadweight loss

Let's step through some details on how one kind of regulation can reduce economic efficiency. Created by Sal Khan.

Video transcript

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