Deadweight loss
Rent Control and Deadweight Loss How instituting a price ceiling lower than the equilibrium price reduces the total surplus (dead weight loss)
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- what I have here is a supply and demand curve that represents
- you can view as a model for the housing market
- or the rental market in a given city
- this vertical axis right here is the dollar rented in terms of dollar per squared foot per month
- so if you have a 1000 sqft apartment and the price right over here
- that means it's being charged 1000 dollar/ month
- this axis right here is the squared feet per month in terms of
- million squared feet, so 1 million squared feet, 2 million squared feet, 3 million squared feet and so on
- and like what we have done in the last few videos
- we have been talking about
- consumer and producer surplus.
- I want to view the demand curve right over here
- I want to view that as a marginal benefit curve
- so, for the very first squared feet right here
- how much benefit is it for the renters, the consumers.
- for them it is a huge benefit.
- over 4 dollar per foot that is not what they are gonna pay for
- but that's what it worth to them. and I am gonna view these this supply curve
- as a marginal cost curve or the opportunity cost for producing that extra incremental unit.
- so, right down here. where you have very few squared feet.
- may be the land is cheap for all this land is available
- you just start or the land is most suitable for the building
- and so the cost, the opportunity cost for supplier that the few squared feet are very low.
- so it makes sense that they will supply it
- because they will produce it. the cost to product it is very low
- the benefit to the consumers is very high
- so the price, the price is anywhere between these two things
- the consumer will get some surplus
- so the price let's say there
- consumer will get some surplus
- and the producer will get some surplus
- right over there. so the market as a whole
- will get a ton of surplus depending on how it's divided
- and now we haven't talked about how that price is
- just yet, although you see where this is going
- so the producer will keep producing more and more units
- as long as the marginal benefit is higher than the marginal cost
- there is this surplus there that can be divided up
- between the consumers and the suppliers
- depending on where the price is.
- marginal benefit higher than the marginal cost
- marginal benefit marginal cost all the way up to that point
- all the way till we get to 3,000,000 squared foot per month
- after that it doesn't make sense if there is some builder
- says, hey let me add some more squared feet to the market
- this what it costs, it's gonna cost them over 3 dollars
- people are not gonna get 3 dollar benefit from those incremental
- squared feet. so no one is gonna get it
- so, no reason for anyone to build beyond that point
- so that's why this ends up being the equilibrium quantity
- and the price where that happens
- the price where that happens, I erase this so we
- get nice clean numbers, is 3 dollars per squared foot per month
- now, 3 dollar per squared foot per month is a pretty
- pricy rent. if you've got a 1000 squared foot apartment
- 1000 squared foot that's my old apartment
- that's a 2 bedrooms 2 baths apartment
- that's roughly $3,000 per month for that apartment
- so that's pretty pricy. so this is type of rent that you will see
- in some places in San Francisco
- and let's say that the mayor doesn't like this.
- this is unaffordable, people aren't gonna be able to live in
- our city. and so they, institute rent control
- rent control, which is essentially a price ceiling
- basically the rent per squared foot can not be above
- a certain amount. that's not normally how rent control is instituted
- but just for the sake of our model.
- normally they say you can increase rent beyond a certain
- amount. but let's say rent control. they essentially put
- a price ceiling on what rent can be charged
- so they put a price ceiling, a price ceiling
- or a rent ceiling. a price ceiling at $2 per squared foot per month
- $2/sqft/month. so let's think about what's going to happen
- and also think about what's happening to the total
- surplus. producer and the consumer surplus. so before
- actually before we even think about the rent control
- let's think about what the total surplus is
- you had the consumer surplus. so this is the price right
- over here. you had a consumer surplus of this area
- right over here. and I don't know if this
- if this right over here. let's call it 4 and half.
- if this is 4.5
- then this side of the triangle right over here is going to be 1.5
- that is 1.5
- this right over here is 3,000,000
- 3 million times 1.5 is 4.5 Million
- and then you divide by 2
- you get 2.25 million
- 1.5 times one half of 3 you get 2.25 million dollar
- so in the equilibrium, if you just let the market be
- before the rent control, at this equilibrium price and
- equilibrium quantity the consumer surplus is $ 2.25 million dollars
- that's how much more benefit the consumers are getting collectively
- vs what they have to pay for living in that,
- living in those houses. the producer surplus, this entire area
- right over here and if we assume. let's say this right over here
- i know it doesn't look like, but to make the math easy
- let's say that is 50 cents
- so this whole side right over here is gonna be $2.50
- so this is gonna be 2.5 right over here
- this length right over here is still 3
- so it's gonna be 2.5 times 3 times a half
- 2.5 times 3 will give you the area of the whole
- rectangle, you have to multiply by a half to get the area of that triangle
- so 2 times 3 let me just write this down
- so it's 2.5 times 3 is, that is 7.5
- 25 times 3 is 75
- and then 75 divide by 2 get you what it's 37.5
- so this is gonna be 3.75. so this the producer surplus is 3.75 million
- so this is $3.75 million dollars
- and so that's the total value that the producer are getting above and beyond the cost of production
- and so the total surplus, the total benefit that the market
- as a whole if you add the consumer's and the producer's
- 2.25 + 3.75 so that gets us to what
- that gets us to $6 million dollars of total surplus
- so there are $6 million dollars total surplus
- so that's good
- because we are at efficient price, efficient equilibrium price
- and production. we are able to produce all this total surplus.
- now let's go back to the rent control situation. where
- instituting a price ceiling of $2 per squared foot so the price
- is by government mandate being set at $2 per squared foot
- $2/sqft right over there
- now if the price is set for $2/sqft, what is the quantity is
- going to be. how much rent is going to supply
- if you can only get $2/sqft maybe some of the landlord say
- no I will break down this wall and expand my own apartment
- or I'm not going to rent these out as much
- or maybe people who are renting out spared bedroom
- say, oh i'm not going to rent out those spared bedrooms
- anymore, I'm just gonna keep them as guest's room
- so the total quantity goes down. total quantity goes down to 2 million squared foot per month
- now this is a interesting situation. because 2 million squared
- feet a month. the marginal benefit is much higher than the marginal cost
- the marginal benefit of one extra unit is over $3 dollars
- the marginal cost of an extra unit is right around $2 dollars
- so in a open market, an efficient market, unfeded market
- people say, oh, just build more unit because people
- are going to get benefit from them and we can have a price
- between and we both will be ale to experience some surplus
- but now you won't. even though there is benefit that's
- in excess of $3 dollars, because the price can't be higher
- than $2 dollars there is no incentive for any of these
- people to either build more unit or maybe offer the units
- that they have up for sale. and we shouldn't be talking about
- building this for the long run
- but even if units are there
- I won't want to rent my gust's room out because I'm like
- oh, it's too much of that, I'm not going to get my marginal cost
- my marginal cost here is over $2 dollars and all I am allowed
- to get is is $2 dollars. so I don't want to offer that extra unit
- so what happens in this situation. when the price is set right
- over here, the consumers who happen to be able to rent at
- this price who are able to get these 2 million squared feet
- per month. they get even larger at least for those 2 million
- squared feet. their consumer surplus is this whole thing right
- over here is this thing right over there
- and the producer surplus unambiguously shrinks
- producer surplus is this stuff right over here
- but you see that total surplus is smaller than the total surplus
- was when we had the unfedded market. we no longer are able
- to access this part right over here of the surplus.
- so this right over here you could view this as lost benefit to
- society. benefit above the cost. lost surplus
- we call this in economic terms. we call this right over
- here: the dead weight loss
- the dead weight loss
- this is benefit to the market that could've gone
- to either the consumers or the producers that are somehow
- are taken away from the market because the market was
- made less efficient by this artificial price ceiling right over here
- and you could measure the dead weight loss
- once again it's only the area this triangle right over here
- and if you say, this right over here,
- this length right over here is clearly just one
- that's one, and if we say that this height
- this height right over here it looks like is
- this is about 1 and half
- then the area of this white triangle right over here
- the dead weight loss is going to be equal to
- 1 times 1.5 times 0.5.
- 1 times 1.5 is double the area of the triangle
- you multiply it by a half to get the area
- so that becomes half times 1.5 which is 0.75
- so that gives us the dead weight loss that is 0.75 million
- so 750,000 dollars which is lost to the market
- so now the total surplus is going to be 750,000 dollars less
- than the 6 million dollars
- so because of that rent control. it will now go down to 5.25 million
- I took 750,000 out of this. So it might have benefited
- the renters who happened to who are able to get apartments
- it won't benefit the renters who now they are not going to be
- able to find any apartment. it unambiguously reduced the producer's surplus
- and it reduced the total surplus. the total amount of benefit that the market as a whole was getting
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