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ECON20110 Fall 2013 - Lecture 9: Monopoly — Transcript

by Glen Weyl · 9,518 words · 1,436 segments · language en · Watch on YouTube

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0:01okay so um the basic
0:06idea uh of the monopo model is that
0:09firms want to try to reduce their
0:12quantity in order to raise the price
0:14that they receive for their goods in the
0:16industry and the reason is that um in
0:19order to sell more units a firm needs to
0:23lower its price but not just on that
0:25last unit but on all of the units that
0:28the firm sells
0:30and this of course wouldn't arise if
0:32firms could charge different prices to
0:34each purchase and each purchaser which
0:36is something we'll talk about uh just
0:39after the
0:40midterm um okay so the Monopoly um will
0:46tend to reduce quantity below the point
0:48where price is equal to marginal
0:50cost and that basic effect is something
0:54that shows up all over uh the world so
0:58um Adam could you give me some examples
1:00of cases where firms with Market power
1:02reduce their quantities below what you
1:04would might think is an efficient
1:08level maybe something like uh you VI
1:11like a like a organization like a union
1:14or something is like a kind of like a
1:16monopoly of the labor yeah so like they
1:19might have like um they may try to like
1:23compat others entering into the the
1:26Labor Field or have some like license
1:28for the that's a very good example
1:31occupational lure uh we didn't talk
1:33about that in the first class we did in
1:35the previous years uh labor unions who
1:38try to stop immigration or have closed
1:40shops that stop people from competing um
1:43Farm cooperatives try to prevent
1:45overproduction of farm products uh drug
1:48cartel's main job is not to produce
1:51drugs but to stop other people from
1:52producing drugs uh and this is the
1:55reason that when the drug bar in Pablo
1:57Escobar was killed the price of cocaine
1:59fell precipitously rather than Rising um
2:04uh drug companies make massive
2:06investments in trying to reduce the
2:10supply of the goods that um they sell by
2:15stopping re-importation from poor
2:17countries of their products uh strictly
2:19delineated territories Etc digital
2:22materials of All Sorts are basically
2:25free to copy but not free to copy
2:28because the law tries to stop you from
2:30doing that and companies invest a huge
2:31amount in trying to reduce the quantity
2:34uh that's supplied movie theaters it
2:36basically cost nothing if a movie isn't
2:39sold out for an additional person to
2:41come and yet they keep people out by
2:43charging a price uh which is also
2:46obviously
2:46inefficient okay so to
2:49represent uh this let's say that the
2:53revenue that a monopolist earns R of Q
2:56is equal to their price which depends on
2:58quantity times quantity now under
3:00perfect competition they would set price
3:01equal to marginal cost and now they're
3:03going to set marginal revenue equal to
3:05marginal cost marginal revenue is just
3:06the derivative of the revenue and uh
3:10where's
3:11Joan ah there she is hi by the product
3:14rule what is the derivative of Revenue
3:17what's the marginal revenue equal to
3:21um plus der
3:26PQ so
3:28PQ p Q um so what's the derivative of P
3:33of Q * Q yeah P Q Plus p q with Q time Q
3:41yeah so oh yeah P of Q yes P of Q um
3:46plus P Prime * Q that's right
3:49absolutely um so there are two terms
3:53here but you're going to set this equal
3:54to marginal cost now if this first term
3:56was the only thing here then you would
3:57set price equal to marginal cost that
3:58would be good right this is what happens
4:02this is the term that comes from how
4:03much benefit the firm gets from changing
4:05its quantity holding the price fixed
4:06taking itself as a price taker but
4:09there's a second term that comes from
4:10the impact it has on price experienced
4:13on all of its infam marginal units
4:15that's the second term which is called
4:17Market power or the Coro Distortion or
4:19sometimes um the marginal surplus of
4:23consumers because what this term is is
4:26how much when the quantity increases
4:28consumers benefit
4:30which uh The Firm doesn't get right so
4:33the price is the marginal value that um
4:38consumers place on getting the product
4:40but not all of that goes into Revenue
4:42some of that goes into consumer surplus
4:44and that's exactly what this term is
4:48here
4:50okay
4:52um so this term is proportional to how
4:55many infam marginal units The Firm has
4:57and how much impacts price and those are
5:00both measures of how large the firm is
5:01if the firm is very small it will have
5:03little impact on price and will have few
5:05units on which to uh have that impact
5:09okay so let's derive some simple
5:12examples of this for the most common
5:14demand curves let's first start with a
5:16concave demand
5:17curve
5:19um and uh philli could you derive the
5:23marginal revenue curve corresponding to
5:25this demand curve uh should I go up to
5:28the board sure that's probably easiest
5:30for people to follow all
5:40right
5:43oh
5:45okay I can yeah
5:49please okay so Mr the piece of Q
5:54equals P of Q equals um
6:001 -
6:02q^2 right yeah and
6:06then uh Revenue
6:09= QP
6:12= uh Q 1 - Q 2 = Q - QB exactly and so m
6:22r is just a derivative which is Q - 3 q^
6:252 1 - 3 q^2 right yeah exactly well done
6:31philli thank you
6:35um
6:36okay so um let me show you what that
6:42looks like so here's the concave demand
6:46function and you see that as the
6:48quantity increases initially marginal
6:51revenue and uh and price are at the same
6:57point but then they diverge increas inly
7:00rapidly as the quantity
7:02increases
7:04okay um Andrew Adair is not
7:09here
7:12um Can someone else derive this for
7:15linear
7:16demand uh so yeah sure so first you find
7:20Revenue which is 1 - Q * Q so that's Q -
7:24q^2 take the Der of that you get 1 - 2 Q
7:28exactly so so this is steeper than
7:31demand is so here's linear demand this
7:34is steeper than demand is but it
7:36diverges at a constant rate right
7:39whereas this diverges from demand at an
7:41increasing
7:43rate okay how about um exponential
7:47demand uh Rishi can you derive sure uh
7:51yeah sure
8:09I'm just going right up
8:10here C
8:13is uh
8:20pus
8:25yeah so you got uh
8:37Q mhm can I erase this part is
8:43yeah I don't think we have an eraser
8:45again oh there there it
8:51is right so if you derive this you get
8:551us the bar of this so you get 2 * 1 2
9:03yeah plus
9:07uh no he's got a minus around the whole
9:09time
9:11yeah * 1
9:15yeah so you get 1 - 1 + log Q which is =
9:22to log Q
9:26exactly uh actually negative log q but
9:29oh
9:30yeah but no that's
9:32right okay so this one notice that
9:36that's like log q and it was 1 minus log
9:39Q so this is just by a constant below uh
9:44price right so that is shown in this
9:48graph here you see there's always a
9:49constant distance between marginal
9:51revenue and price so here they were
9:53diverging at an increasing rate here
9:55they're diverging at a constant rate
9:57here there's a constant distance between
9:59them so guess what's going to be
10:01happening with the last case that I give
10:03you uh reishi I'm going to call on you
10:06again uh do it for the constant
10:08elasticity all
10:12right
10:21not cool so I'm just going toise one
10:33so we have one
10:35over 12 right
10:39yeah which
10:42is yeah so
10:47sorry so you take
10:51q q * Q you get Q * Q * 1
11:0112 yeah and uh if you derive this you
11:04get
11:0712 12 Q to the 12 which is equal to 1
11:13over 2K
11:15Q exactly so notice that this is
11:21half of the price
11:26right and it's decreasing in p uh
11:30quantity so that means that these things
11:32are going to converge together over time
11:34right because there's a constant ratio
11:36between them rather than there being a
11:38constant difference between
11:41them so that's shown here you see
11:44they're further apart up here because
11:46the ratio between the two of them is
11:48always
11:49constant okay now how do we find Optimal
11:53quantities well imagine that the
11:55marginal cost were the x-axis here just
11:58for fun
11:59then you intersect that with the
12:01marginal revenue curve you draw a line
12:03up to the demand curve and left over to
12:05price in order to get uh the optimal
12:08price for the firm to
12:09charge okay now another way to write
12:13marginal revenue is as price time
12:16quantity sorry price of quantity uh Time
12:191 minus 1 over the elasticity of
12:22demand and uh reishi I'm going to have
12:25you dve that again as well
12:34I swear it's
12:44[Music]
12:54random 1 - one Epsilon is that yeah okay
13:04um so no it's not P of Q equals that
13:06it's marginal I want to claim that
13:08marginal revenue is equal to P of Q * 1
13:12- 1 Epsilon the question is how could
13:14you prove that that's the
13:20case um times P of Q
13:26oh so we have a we had a form for
13:29marginal revenue before can you
13:30transform it into that um okay so we had
13:35from before that marginal revenue
13:39equals P Q Plus it's p Prime of Q * Q
13:46sorry I pime of Q * Q Plus p q yeah
13:52okay
13:56um so
13:59if
14:03you well here you've got your P of Q
14:06term right which shows up there so this
14:08much must correspond to this term
14:10somehow right okay so I mean if you got
14:14your cuz you don't have a p of Q um
14:18unless
14:20you so why don't you try factoring a p
14:23of Q out of the whole expression P of Q
14:26yeah okay
14:29then you get 1
14:33plus
14:37um yeah
14:391 p
14:44q q q over
14:47PQ okay now oh okay does that look like
14:51an elasticity yes it is so right which
14:56you which is equal to yeah yeah two
15:01* 1
15:05plus right except that the elasticity of
15:08demand is negative so yeah exactly just
15:12to be a little bit more explicit this is
15:14DP DQ which is 1 over uh DQ
15:19DP right and then it's divided by you
15:22know q and multiplied by P and that's
15:25exactly the elasticity
15:27formula what did you say
15:29no you're done you're done my
15:33friend um okay so one thing that
15:36immediately tells us is that marginal
15:37revenue is negative whenever the
15:39elasticity of demand is less than one
15:42which means that the monopolist will
15:44never produce in a region where demand
15:46is in elastic because he'd always have
15:48an incentive to reduce his
15:50quantity um which would also reduces
15:53cost so the elasticity of demand can be
15:57seen as one thing one way of formalizing
16:00the notion of Monopoly power if the
16:02elasticity is small then the relative
16:05importance of that firm is small um if
16:09the elasticity is large that firm is
16:12relatively important to the market and
16:14it summarizes the notion of being sort
16:16of a big player and rearranging this
16:18setting uh this equal to marginal cost
16:21yield that the price minus marginal cost
16:24divided by Price that's called the
16:25relative markup is equal to the inverse
16:27elasticity of demand so the smaller the
16:30elasticity is the larger the markup The
16:32Firm charge is which is a natural
16:33measure of Monopoly
16:36power okay now of course there's other
16:39measures of Market power you could also
16:41create it's not obvious this is the best
16:43one another one you could create is the
16:45markup divided by the marginal cost
16:47rather than divided by the price and
16:49that's equal to 1 over the elasticity
16:51minus one or you could do the price to
16:53marginal cost ratio which is equal to
16:54the elasticity over the elasticity minus
16:56one or you could do the absolute markup
16:59which is equal to the price divided by
17:00the elasticity these are all very
17:02similar ways of measuring Market power
17:05um and some are more useful than others
17:07depending on the context so the standard
17:10learner formula is useful because it's
17:12so simple and it uses elasticity so
17:15directly the price cost ratio is
17:18useful uh for profits um especially when
17:23you have a constant marginal cost um
17:26because it yields just like the ratio
17:30between whatever the cost is and however
17:32much uh profits the firm is making um
17:37the uh markup to cost gives a measure of
17:41profitability the absolute markup is
17:44useful when costs are not positive which
17:46can happen for example in credit cards
17:49you know your credit card subsidizes you
17:52for using your card you get points for
17:54using your card because they're earning
17:56money off of interchange fees from
18:00Merchants that pay them when they use
18:01the card and so denominating things by
18:04cost can be problematic then
18:08um okay now of course to set these
18:12prices firms need to know what the
18:13demand curve is otherwise the quantity
18:16that they produce will not match uh
18:18demand and um to so as a result firms
18:23need to be able to draw out their
18:25marginal revenue curve and it used to be
18:28that firms just had to guess about this
18:30and gradually learn but the internet has
18:32really created a revolution in this
18:34extent because many companies are
18:36experimenting with prices all the time
18:38to try to figure out what demand is this
18:40is particularly common on eBay where
18:43sellers all the time are experimenting
18:45with the reserve price that they can
18:46charge on their
18:48auctions you know sometimes the same
18:50seller will sell the same good on a
18:52different day or even at the same time
18:55uh at different prices or different
18:57Reserve prices uh in order to tryy to
18:59see what demand is like now this is an
19:03auction yeah Christian sorry what's the
19:05reserve price uh a reserve price um is
19:11the lowest price that you'll accept
19:13without calling the auction off oh so
19:16it's like a starting price
19:18basically um now changing the reserve
19:22price uh is a lot like changing a price
19:25and it traces out something like a
19:26demand curve why why is that true what
19:29sort of demand curve could you create uh
19:32Evan using uh Reserve changing around
19:35the reserve price to affect uh prices
19:38and and the probability of sale so you
19:40want so you want me to explain why it
19:42would look like a demand or or what yeah
19:45how you know this is a starting price
19:47for an auction it's not like a price
19:49that I charge you know and the number of
19:52sales I get but you can get out of this
19:54something that's like a demand curve
19:55well instead of the number of sales you
19:58you could could look at for example the
20:00number of people who are going to be
20:01willing to bid or you could look at what
20:05kind of price of how much you can expect
20:07it to go up right or if it's going to or
20:10the or the probability of it um that's
20:13going to actually clear yeah so I think
20:16the easiest thing to correspond to is
20:18the probability that it actually clears
20:20right because if you set a higher
20:21reserve price the chance that it clears
20:23is going to be lower but what's the
20:25offsetting benefit you get when you set
20:26a higher reserve price you get more
20:28money why the reason why you get well I
20:32suppose it's that you're more likely to
20:35get to get more money right and the
20:36reason why is because let's suppose that
20:39you have one auction where you have the
20:41same item with a lower reserve price and
20:44you have for whatever reason one person
20:47who bids that Reser that lower reserve
20:49price in the first auction that's what
20:51you're going to get the second option if
20:53that person is still willing to pay
20:55higher then you then you get that money
20:57you can't get the lower exactly right so
20:59basically there are two circumstances
21:01where the reserve price matters one is
21:03one one in which if you'd set a lower
21:05reserve price someone would have bid
21:07above it but because you said a higher
21:09reserve price no one bids above it
21:12that's the case in which the reserve
21:13price deterred a sale from taking place
21:16on the other hand if you there's another
21:19circumstance which is that the um the
21:23low the second highest bid if there was
21:26one was below the reserve price that you
21:29set but um the highest bid was above it
21:32in that case it raises the price that
21:34you get um and so you can look at the
21:39average price that you get for a good as
21:41a function of your reserve price graphed
21:44against the um the probability of sale
21:48and those things will have a negative
21:49relationship the higher reserve price
21:50you set the higher average price you'll
21:52sell it at but also the lower will be
21:54the probability of sale and that'll
21:56Trace out something like a demand curve
21:57Yeah Austin this is not I guess strictly
22:00the same thing but I know on eBay
22:02typically they'll tell you whether the
22:03reserve price was met or not or not
22:05whereas like an art auctions and things
22:06it's typically private that don't tell
22:08you with the reserve do you get any like
22:10discontinuities related to that people
22:13you know just trying to barely clear it
22:14or
22:15something so people always barely I mean
22:18it's always people's incentive to First
22:20barely clear it uh in in the art
22:22auctions that incentive doesn't exist
22:24and a reserve price doesn't actually
22:25raise your Revenue all it does is stop
22:27the thing from being sold at a
22:29inefficiently low
22:31price
22:36um so yeah okay so uh luron inov uh
22:43Teresa coer John Levan uh and Neil
22:48sueras got all of eBay's
22:51data and they found 500,000 cases in
22:56which people had run experiment
22:59so you you guys probably know John list
23:02here runs lots of experiments
23:04right but um what they found was that um
23:11you don't just need to be an economist
23:13who goes out and runs experiments
23:15yourself sellers on eBay are running
23:18experiments all the time and so rather
23:20than running you know I don't know five
23:21or 10 experiments you could look at
23:23500,000 experiments by looking at what
23:26the sellers are choosing to do
23:27themselves
23:28and so um what they did is they looked
23:32at cases where the same seller sold the
23:34same item on slightly different terms
23:38either at the same time or at slightly
23:39different times and they use this to
23:41draw out demand curves for the auction
23:44just as I was describing and the
23:47interesting thing is they found that all
23:48these demand curves at a very similar
23:50shape yeah Evan so on eBay is there a
23:53penalty for listing the same item
23:54multiple times and then canceling the
23:56$999 they get the lowest price before
23:58they close oh I think there is yeah so
24:02you you have to agree to sell so then
24:04what so then what are they doing are
24:05these sellers who who have an inventory
24:08and then list the inventory I think
24:09that's the point they're trying to
24:10figure out what the market price should
24:12be by trying out different prices and
24:14then for the future yeah
24:17okay um so the interesting thing that
24:20they found is that marginal revenue is
24:22actually increasing in some parts
24:25um and so
24:29uh the cost if you think about it in
24:32this case is the value you could get by
24:35trying to sell that object again or
24:36keeping it yourself right and there's a
24:39possibility of there being multiple
24:40intersections between marginal cost
24:42which is constant as a function of the
24:44probability right it's just the value of
24:46that good and the average and the uh
24:50marginal
24:51revenue okay so let me show you a
24:53picture of this and show you what we do
24:55to analyze these cases so here's what
24:57they found they found that for tons of
24:59different Goods if we divided the uh
25:03price of the Good by the um assessed
25:08value that um the demand curves looked
25:13very similar to one another and they
25:15looked like this they were sort of
25:18reasonably sloped here but then they get
25:20incredibly flat as you get out to high
25:22probabilities why is that well as a
25:26object is getting down to a low low
25:28probability of sorry a low price there's
25:31always going to be someone on eBay who's
25:33just looking for deals who's going to
25:36snap that thing up and go resell it
25:38right and so that makes demand really
25:41have a very sharp floor underneath it
25:45these people up here are people who are
25:46actually going to keep that good these
25:48people down here are people are just
25:49going to go and resell it again right um
25:54and uh you can fit a curve through this
25:58you can just you know use a polinomial
26:00fit on Excel and you can fit a third
26:02degree polinomial through this and you
26:04get a marginal revenue curve that is not
26:07just decreasing like all those marginal
26:09revenue curves we looked at before which
26:11means that if you had a marginal cost
26:13that was right here there would be three
26:15intersections between marginal cost uh
26:18and
26:19demand now does anyone want to guess
26:22imagine that marginal cost were here
26:26which point of these three would
26:28actually be the optimal quantity for you
26:30to
26:31sell the optimal probability with which
26:34a sale would
26:39occur marinal cost this way again sorry
26:42marginal cost let's say it's at 75 so
26:47it's just below that black line
26:54I what do you think so is the area like
26:56of those two little regions like the
27:00yeah between the pink and the black line
27:01are those equal yes that's the point but
27:04you have to figure out why that's the
27:05case that's what I'm trying to take you
27:07guys through
27:15now well notice that the profits that a
27:18firm earns is the area between the
27:20marginal revenue curve and the um
27:24marginal cost curve up to the point that
27:27they go to so if the firm produces here
27:30they get all this area and profits but
27:32they don't get anything over here if
27:34they produce over here they're going to
27:36actually take losses in this region down
27:38here and then they'll make gains over
27:41here but the gains are bigger than the
27:43losses here right the area above is
27:45bigger than the area below and so
27:47they'll produce over here on the other
27:50hand if they had a cost that was 85 like
27:53up here then if they produced over here
27:56they'd take losses over this full region
27:58here and only make gains over here which
28:00would not be worth it so they'd be
28:02better off producing over here so this
28:05line which is called the ironing line is
28:07a line where area above the line and
28:09below the curve equals the area below
28:11the line and above the curve and that is
28:15exactly the cost at which they would
28:18jump from producing from selling with
28:21this probability to selling with this
28:23probability so if the co if someone's
28:26cost went from you know know 79 to 82
28:31you would see the price jump from on
28:34average from about what is this
28:3882 up
28:40to uh
28:431.05 right so there would be a
28:45discontinuous change in price when there
28:47was a continuous change in the cost and
28:50the reason is that you're basically
28:53making a decision of which of two
28:54markets to serve are you going to try to
28:57just give this to the resellers and let
28:59them resell it in which case you'll set
29:00basically a zero reserve price or are
29:03you going to try to really sell this to
29:07a final consumer only in which case
29:09you'll probably set a reserve price
29:10that's about equal to its value does
29:12that make
29:14sense so this technique ironing is a
29:17more General technique you can use
29:18anytime you have a
29:20non-monotonic uh marginal revenue curve
29:22or really non-monotonic anything
29:24function that you have to optimize in
29:25economics you can always replace it with
29:27a mon iic one by using ironing
29:30procedures like this canceling out the
29:32area above and below
29:35yeah the IR line was determined by like
29:39who wants to resell wants to keep it
29:41finally you just talk a little more
29:43about well so I mean this is just a
29:45hypothesis but the reason these demand
29:47curves look they have this shape where
29:49they're like quite steeply decreasing
29:52and then you get out to about a0 five
29:54probability of sale and they're almost
29:56totally flat after that and the reason I
29:58think is that basically the people who
30:01are buying it and showing up with about5
30:05probability are people who actually want
30:06to keep that thing
30:08forever and they have like a decreasing
30:10demand curve but people who just want to
30:12resell it their value is completely
30:14constant because they all just have the
30:15same cost of reselling it
30:20right
30:22okay so Monopoly is two basic welfare
30:26related effects compared to
30:28competition the first is that it
30:31transfers resources um to the
30:35monopolist
30:38um from uh the consumers and the second
30:41is it inefficiently reduces the output
30:44in the
30:45industry so how do we know Mike fosco
30:49how do we know that this reduction in
30:51quantity is socially inefficient uh from
30:53the dead rate loss we're um the they're
30:56not producing uh Aral cost is equal to
30:59the price they're doing less than that
31:02okay so why does that create dead weight
31:03loss because there are more gains to be
31:06made for society in general if you
31:08produce more output um because then the
31:10benefit to the consumer is greater than
31:12the uh
31:15lower Yeah so basically this is a case
31:18in which at Price equals marginal cost
31:21the value the consumer gets is exactly
31:24equal to the cost of the firm of
31:26producing if the price is above the
31:28marginal cost the consumer gets a
31:29greater value out of the product than
31:31the than the cost of producing it and
31:34therefore it would be socially valuable
31:35to produce more of it and the firm is
31:38eliminating some sales that would be
31:40beneficial because the benefit to the
31:43consumers would be greater than the cost
31:46okay
31:48um now uh the inefficiency of Monopoly I
31:53think is quite apparent in real life
31:56it's the reason why information Goods
31:57like music aren't freely available right
32:01it's the reason why there are empty
32:02parking lots in busy cities uh that
32:07charge High rates right like it's
32:09completely crazy for there to be parking
32:11lots that are empty and people who are
32:13roaming around the streets looking for
32:15places to park right because there's no
32:17cost of have on the margin of putting
32:19one more person into that parking lot
32:21and there's a big uh cost of having them
32:24roaming around the streets right
32:28uh yeah Evan couldn't you see the high
32:30parking rates as as just a fee of the
32:34people who are going to park in that
32:36area are paying to increase the
32:38probability there is a
32:39spot because I'm from one of those very
32:41crowded areas and it's not normally the
32:43case people are driving around because
32:46there's not a spot in the parking lots
32:47because even with high prices it's
32:49usually
32:49full really I don't think that that's
32:52true I don't think it's usually true
32:54that parking lots usually have a fair
32:56number of vacancies in in almost all
32:59times of the day I mean there's a few
33:00parking lots that fill up at a few times
33:02of the day but it's very rarely the case
33:04that all the parking lots are actually
33:06full so uh yeah Austin are parking lots
33:10really monopolies though I mean I feel
33:12like for parking lots at least it's more
33:14of the case where it's yeah so that's a
33:15good question I don't think that
33:17structurally they're monopolies but I
33:19think it's basically they are monopolies
33:21because once you've turn you can't
33:22figure out what the price of the parking
33:24lot is until you've already turned into
33:26the parking lot and then I mean in other
33:28words like people have to invest like
33:30resources to learn the prices of the
33:32parking lot if there was complete price
33:34transparency I think it would
33:35effectively be perfect competition and I
33:37think that's starting to happen because
33:39of this app best parking I don't know if
33:41you guys have this I love this app and
33:43it like tells you the rates of all the
33:44parking lots and I think if everyone
33:46comes to have that app then there will
33:47be perfect competition but I think that
33:49not everybody has it yet and so there is
33:51effectively Monopoly are there any
33:52dynamically priced parking lots in
33:55Chicago well I mean there's almost all
33:57almost all parking lots have some amount
33:58of dynamic pricing they all have like
34:00you know special deals but not really
34:03intelligently dynamically priced ones no
34:06I mean they're like the way they
34:07dynamically price is better than none
34:09but it's not as intelligent as you could
34:10with a really adaptive system but to
34:12really make something like that work
34:13You' need price transparency on that as
34:15well so you'd need to have like the app
34:17linked to the prices and people would
34:20have to like have their apps telling
34:22them which lot to go to based on its
34:24current you know occupancy and your for
34:27a price I think I read San Francisco's
34:28doing that now yeah I think cities in
34:31California are trying that 100 yeah what
34:33what what things isn't California doing
34:35better than the rest of the world I mean
34:38I'm a Californian
34:41um um okay so
34:45effectively Monopoly means that
34:48consumers have an externality on the
34:52firm because if they purchase more the
34:54firm is going to make more profits
34:55because the firm is earning a markup
34:57over marginal cost on every unit that it
34:59sells and these extra profits that are
35:02created are not mediated through the
35:03price system so there are real
35:05externality and they suggest a standard
35:08pigouvian Solutions like subsidizing
35:10purchases of the goods by consumers or
35:13perhaps regulating the firm's price down
35:15to cost or mandating an efficient
35:18quantity uh to be produced and we're
35:20going to talk about some of these
35:22policies in practice on Thursday but
35:24they're far less common that you'd think
35:27and in lect 13 we're going to talk a
35:28little bit about why despite the
35:30ubiquity of Market power we don't have
35:32solutions that really uh address them
35:35that that often now you know another
35:38thing to keep in mind is that there are
35:40other solutions that you could use to
35:42address Market power which maybe are
35:45seem a little bit more dirty uh or less
35:49clearly cleanly lined up with economics
35:51but are you know from a social
35:53perspective just as valuable so for
35:55example advertising or creating Prestige
35:59for products can make people value them
36:03more and that can cause consumers to buy
36:08at prices that are above what they're
36:09willing to pay and therefore offset the
36:12Distortion associated with Monopoly so
36:14some sort of deceptive advertising or
36:17building hyper on a product might
36:18actually be socially beneficial because
36:20it offsets the Monopoly
36:23Distortion we consider that paying more
36:25than the what like that's considered
36:28paying more than their willing well I
36:29mean imagine you like a lot of people
36:31say oh they trick you into making you
36:32feel like you want the product when you
36:34don't really want it or you're willing
36:35to pay more than you're really willing
36:37to pay but that could actually be good
36:38in the context of a monopolized product
36:40because otherwise it would be
36:40inefficiently
36:42underconsumed uh yeah but like in that
36:44scenario though um although you'd be
36:46producing the right output like the
36:47right right quantity like the benefit
36:50would be transferred from like conser to
36:52the yeah that's true okay so but still
36:56from a social perspective
36:58in in aggregate it's still value and in
37:00fact it might even be good to transfer
37:01to the firm if the firm innovated in
37:03order to create that product because
37:06that gives more incentives for
37:07Innovation yeah Evan why is it that the
37:09soci social socially optimal quantity
37:12hasn't changed in response to the
37:14advertising because if now you change
37:15how people value it why well I mean it
37:17all depends how you think about
37:18advertising but some people think about
37:20advertising as sort of deceptive and
37:22making you feel like you want something
37:23more than you really want it and that
37:25wouldn't change the socially optimal
37:26quantity so you're saying that if you
37:28think of it there's like still a
37:30constant real want yeah so there there's
37:33a paper by Dixit and nor uh and Norman
37:37which is all about that uh yeah if we
37:40assume that people have a constant real
37:43want then uh be being able to
37:47deceptively advertise
37:50essentially someone allow it allows the
37:53monopolist to appropriate some money
37:56that
37:59is uh that consumers really aren't
38:02willing to pay so might it create too
38:04much incentive yeah so you'll typically
38:07want like you'll spend too much on
38:08Advertising but it will also typically
38:10be bad if you don't allow advertising at
38:15all
38:16so okay so the debt the like any tax or
38:20externality the value of extra
38:23production will be equal to the wedge
38:25the sort of like uh uh difference
38:28between price and marginal cost times
38:30the change in quantity uh that occurs
38:32when when something changes yeah ver um
38:35so even though that like allocates like
38:38a socially optimal level uh does it
38:40still create like negative externality
38:43because um consumers buy more than like
38:45they so advertising will have a negative
38:47externality because you'll be taking
38:49money from consumers and giving it to
38:50the firm and it's an action taken by the
38:52firm so it does have a negative
38:54externality but on the other hand it
38:56might be more efficient then completely
38:58Banning that activity so you might want
38:59to tax advertising but you wouldn't want
39:01to eliminate it
39:03entirely um yeah Christian so would that
39:05be a real externality of advertising
39:08yeah can you it's real because it affect
39:13it hurts the consumers but doesn't
39:15benefit anyone other than the firm and
39:17so the firm's the one
39:22doing okay um so as a result we can
39:27measure
39:28the dead weight loss using the standard
39:30dead weight loss triangle the only
39:32difference is now the size of this
39:34triangle is determined by the Monopoly
39:36Optimum and in particular it has a
39:38particular relationship to Monopoly
39:40profits that we'll explore in a minute
39:42and this is the triangle bounded by the
39:44supply curve the demand curve and the
39:45equilibrium quantity now we can measure
39:48Monopoly profits graphically in two ways
39:51one is the area between the equilibrium
39:53price and marginal cost or the area
39:56between marginal revenue and marginal
39:58cost so let me show you that so the area
40:02between price so if this is the marginal
40:05cost curve and this is the marginal
40:08revenue curve here is the price and
40:12profits are either the area between this
40:14price and marginal cost C plus d or the
40:17area between uh marginal revenue and
40:20marginal cost which is a plus c and you
40:23notice by similar triangles these are
40:24the same areas wait which which what
40:27what what each l so this is the demand
40:30this is the marginal revenue this is the
40:32marginal cost so this is the optimal
40:35quantity and the optimal price so here's
40:38profit the area between price and
40:40marginal cost or profit the area between
40:43marginal revenue and marginal cost and
40:45they're the same by similar
40:48triangles we can also measure consumer
40:50surplus is either the demand between the
40:53area between demand and price that's the
40:55way we usually measure it that's a plus
40:57be up here right but you can also
41:00measure it as the area between demand
41:02and the marginal revenue curve because
41:04remember that the difference between de
41:06uh demanded marginal revenue is the uh
41:08marginal surplus of those consumers so
41:11it's the area B plus d which Again by
41:13similar triangles is the same as the
41:15area a plus
41:17b
41:19okay
41:22um so
41:26um the dead weight loss
41:29triangle is
41:31e the area over here because this would
41:35have been the efficient quantity and
41:37here's all the loss in willingness to
41:39pay minus marginal cost that occurs
41:41between
41:42those
41:44okay now um Alfred Marshall who is uh
41:48not only one of the you know most famous
41:51economists of all time but also was um
41:57sort of the founder of price Theory
41:59which is the school of Economics that
42:01The Chicago School uh is so into um said
42:06that you can think about almost
42:08everything in economics in terms of tax
42:11incidents and you probably learned in
42:13both your basic courses and probably
42:14last term the basic principles of tax
42:17incidence for uh perfect competition and
42:20use those to think about all sorts of
42:22different types of interventions uh that
42:25happened in markets
42:28now most of what's different under
42:30Monopoly remember that Monopoly models
42:32are really only useful for thinking
42:33about interventions that occur directly
42:35through the actions of that firm and so
42:38if we just think about the incidence of
42:40changes to that firm we can think about
42:42most interventions that are relevant to
42:44Monopoly so I want to give a brief recap
42:47of compet perfectly competitive
42:48incidents and then I want to contrast
42:50that to
42:51monopo and um Evan could you tell us
42:55some of the principles of incidence
42:57under perfect
42:59competition um
43:03princip incidence of
43:15taxes can't remember
43:17it um anybody else want to yeah Phil um
43:22in the short run uh because
43:28well in the long run the incidence is
43:30purely on consumers because a firms need
43:35to enter and exit to maintain zero
43:38profits in equilibrium well if in the
43:40long run the demand the supply curve is
43:42extremely elastic and the demand curve
43:44is not so elastic but yeah um yeah
43:48assuming assuming infinite using that a
43:52standard
43:53elasticity yeah but I mean even more
43:56basic than than that
43:58uh tavish whoever has the more
44:02elastic
44:05supp yeah that's the most that's one of
44:07the most basic principles so the most
44:09basic principle is that the physical
44:11incidents who literally pays the tax is
44:14irrelevant to who actually Bears the
44:17burden of the tax because if we charge
44:20tax on the consumers the price of the
44:22good will fall if we charge tax on the
44:25producers the price of the good will R
44:27in response to that most likely right
44:30and um therefore we can always treat the
44:33tax as if it's directly paid by the
44:35producers and then just study how it
44:37gets passed through to Consumers and I'm
44:40going to call that rate of pass through
44:41the rate at which the price increases
44:42when the tax increases uh
44:45dpdt uh the pass through rate
44:48row so then the fraction of the tax that
44:54ends up getting paid by the
44:55consumers uh is going to be equal to the
44:58pass through rate and the fraction
44:59that's paid by the producers is 1 minus
45:01the pass through rate right and all of
45:05the tax is borne by one side or the
45:07other right if we have put in a small
45:10tax all of that tax is born either by
45:13the consumers or the producers so if we
45:16want to call the incidence the ratio of
45:18the amount borne by the consumers to the
45:20amount born by the producers that will
45:22be row over 1 minus
45:24row okay so the second principle and
45:27this is what tavish was getting at is
45:30that the inelastic side of the market
45:32Bears the um tax uh in particular the
45:36pass through rate is equal to 1 over 1
45:38plus the elasticity of demand over the
45:40elasticity of supply and Tanner could
45:44you derive that
45:46formula you'll probably want to do it on
45:48the board yeah sure
46:09can I ER yeah please uh there's there's
46:11a eraser if you want it where's
46:23that so I'm driving the uh the price one
46:26over 1 plus the man Supply right yeah
46:34okay it's the pass through is equal to
46:36one oh pass yeah yeah sorry so to derive
46:39the pass through rate remember you need
46:41to do a comparative static it's how does
46:43the price change when the tax changes
46:45right so what's the equilibrium
46:47conditions in the market
46:50um just it's demand equals Supply right
46:54but remember that the producer doesn't
46:56get the full price he only gets the
46:57price minus the tax so how would you set
46:59up the equilibrium conditions for
47:02that let's see
47:20so we want to find the change in price
47:23as the as the tax the change change in
47:25price of the tax happens yeah so what's
47:27the first just write down the
47:29equilibrium condition so demand is a
47:32function of
47:41price just D of P right that's just a
47:43function D of P or D of P like demand of
47:49price is equal to the supply is a
47:51function of price minus the tax right
47:56right yeah okay so now how would you
47:59figure out how the price changes with
48:01respect to the
48:02tax uh take size
48:13yeah so by the implicit function theorem
48:15you have to put dpdt here and you have
48:18to put dpdt minus1 there
48:28yeah you heard parentheses I know okay
48:32so now you need to solve for dpdt which
48:33is the pass through r
49:22good
49:29you can drop the arguments inside of
49:30those things it'll make your life
49:37easier right okay and then try dividing
49:41through both the top and the Bottom by S
49:45Prime by S Prime
49:54yeah no don't don't divide both sides
49:58just divide the top and the bottom of
49:59this expression
50:07by yeah D Prime over S
50:11Prime yeah you go to a negative there
50:14this but and put a negative in Fr of
50:17this
50:18yeah
50:20um yeah and then note that D Prime over
50:25S Prime is equal to the e of demand over
50:27the elasticity of supply because both
50:29have the same price and the same
50:31quantity right at equilibrium and so
50:35that's how you get this
50:37formula heroic job Tanner thank you um
50:41okay so just to give you an intuitive
50:43sense for this suppose that um the
50:47demand curve is totally inelastic and
50:49the supply curve is somewhat elastic
50:51then look the consumers are going to
50:53Bear all of the tax if we put the tax on
50:56the price price Rises exactly by the
50:57amount of the tax and the consumers bear
51:00it
51:01all um on the other hand if the supply
51:05is perfectly elastic and then when the
51:09um demand is perfectly elastic then when
51:12the supply uh when the tax Rises the um
51:17price is going
51:19to
51:21uh then the price is going to stay the
51:24same and the amount received by the the
51:26firm is going to fall by exactly the
51:28amount of the tax and therefore the firm
51:30will bear all the incidents right now
51:33more generally if both are elastic it
51:36depends on the relative elasticity of
51:38the two curves um as shown here
51:43okay now if we keep raising the tax on a
51:46market if we start with a small amount
51:49and we raise it f higher and higher at
51:51some point we're going to reach a tax
51:53that's so high that no one's willing to
51:55buy the product at all anymore more
51:57right and we can work backwards from
51:59that point to determine the total amount
52:01of consumer surplus right so because
52:04once we reach a tax of T there's no
52:06consumer surplus the consumer surplus is
52:09just going to be the integral of the
52:11pass through rate times the quantity
52:13because that's how much the consumers
52:15lose every time we raise the price by a
52:17little by the tax by a little bit and
52:20the producer Surplus is going to be the
52:22integral of one minus the pass through
52:24rate times the quantity so if we then
52:26let the average pass through rate be the
52:28quantity weighted average of pass
52:30through between a tax of zero and the
52:34maximum tax then the global incidence
52:38the ratio of total consumer to Total
52:40producer Surplus is the ratio of the
52:42average pass through over one minus the
52:44average pass through right so you know
52:49often when you say the consumer Bears
52:51the weight of a tax you want to think oh
52:55poor consumer he has to pay all the tax
52:58but in reality the only reason the
52:59consumer is bearing the weight of the
53:00tax is that the consumer is the one who
53:02benefits from the market existing in the
53:04first place right the person who Bears
53:07the tax is the person who benefits from
53:08the market being there right um so the
53:14global ratio of consumer to producer
53:16Surplus is just the uh quantity weighted
53:21average of the ratio that happens for a
53:24small change in the tax rate
53:28so the inelastic side is the one that
53:30benefits from the market existing
53:32they're the ones who really need it to
53:33be there whereas the elastic side
53:35doesn't care whether the Market's there
53:37or not they're H just as happy either
53:38way
53:43okay now um under Monopoly there's going
53:47to be a fundamentally uh there incidence
53:51is going to be fundamentally different
53:52in a couple of ways so it's still going
53:55to be the case that physical and
53:58economic incidents are independent of
54:00one another um because it doesn't matter
54:03whether you tax the consumer or the
54:05producer but now rather than the tax
54:07being split between the two sides
54:10there's actually going to be an excess
54:12burden because too little of the good is
54:14already being produced there's going to
54:17be more loss to the firm and the
54:20consumer than is uh the revenue that the
54:23government
54:24gets um
54:27in particular The Firm chooses its
54:30quantity so as to maximize prices and
54:33its profits are given by this formula so
54:36what is going to be the loss to the firm
54:38when the taxes increase by a little bit
54:41uh reishi and you can use the envelope
54:43theorem uh see if you can use the no no
54:46don't look uh see if you can use the
54:48envelope theorem to figure out really
54:51simply uh what the effect of a change in
54:53the tax is on the firm's profits in this
54:57okay
55:03um remember the quantity is being chosen
55:06optimally right
55:11right the tax changes by a very small
55:15amount
55:18the quantity
55:21also the quty also Chang
55:23by that's true but it's not enough what
55:28does the envelope theorem tell us to
55:30do to differentiate with respect respect
55:37Quan yeah it says that we can hold fixed
55:41anything that's being
55:42optimized right when we take the
55:44derivative of the thing that it's
55:46optimizing right so here what that what
55:48would that tell us the effect of the tax
55:50on profits is um you can hold profits
55:55you can hold quantity
55:56that's the thing you're choosing to
55:59optim
56:01so would it just
56:05be quantity F would just be the um the
56:10Der with respect
56:15to T directly right so just be um
56:21negative uh just Q minus just negative
56:26Q yeah so the monopolist because he
56:29chooses his quantity to maximize profits
56:33um Bears the full burden of the
56:38tax he gets exactly negative Q that's
56:41the full amount of Revenue raised right
56:43and he Bears all of that directly right
56:47but the consumer still loses the pass
56:51through rate times the quantity right
56:53because if this price Rises he's worse
56:55off and it will will typically rise
56:57right so the excess burden then is row *
57:02Q so everything the burden is fully
57:05borne by the monopolist and then it's
57:07additionally borne as excess burden by
57:09the
57:10consumer therefore the incidence the
57:12ratio of how much the consumer loses to
57:14how much the firm loses is the pass
57:16through rate divided by one or just the
57:18pass through rate right and again we can
57:20integrate this up as before to get the
57:22ratio of consumer to producer Surplus is
57:24the average pass through rate
57:28okay so just to see how this works
57:31here's a monopolist here's his marginal
57:33cost imagine now we shift up his
57:34marginal cost with a
57:36tax how much does he lose in profits
57:39well profits is the area between
57:40marginal revenue and marginal cost and
57:44that's Fallen by the quantity multiplied
57:47by the change right now there's a little
57:51extra triangle here but that's very
57:53small that's second order
57:56okay so um under uh under Monopoly the
58:03logic of incidence is therefore
58:05different in two ways so one is that
58:07there's this extra dead weight loss so
58:09that the incidence is not just split but
58:11there's this excess burden and the
58:13second thing is that the marginal
58:15revenue curve and not just the demand
58:17curve will help determine the pass
58:19through rate so now I want to consider
58:22uh P the pass through rate so Tanner
58:25very nice nicely derived from us for us
58:27the pass through rate under perfect
58:29competition let's do the same thing for
58:31Monopoly right for Monopoly marginal
58:33revenue is equal to marginal cost which
58:35also includes the tax so implicitly
58:38differentiating we get that marginal
58:39revenue Prime multiplied by the
58:42derivative of quantity with respect to
58:43the tax is equal to marginal cost Prime
58:46Times the derivative of quantity with
58:47respect to the tax plus
58:51one um and the derivative of quantity
58:55with respect to the tax is therefore
58:57equal to one over the derivative of
58:59marginal revenue minus the derivative of
59:01marginal
59:04cost um now how much does that lead to a
59:07change in price well how much does price
59:10change when quantity changes well it's
59:11just the derivative of price with
59:13respect to quantity and so the passive
59:15rate is p Prime over Mr Prime minus MC
59:19Prime now remember that Mr is equal to p
59:22+ P Prime * Q so if we let the marginal
59:26Surplus as we were talking about before
59:28equal to P Prime *
59:31q and we identify the marginal cost
59:34curve remember that the supply curve is
59:36just the inverse of the marginal cost
59:37curve so we can identify the supply
59:39curve with marginal cost
59:41curve then marginal cost Prime is equal
59:44to P over Q * the elasticity of supply
59:49just by the same logic we did to derive
59:52the elasticity of uh demand in the
59:55learner index before and P Prime is
59:57equal to P Q * elasticity of demand then
1:00:01we can replace all these terms with
1:00:03these
1:00:04here and we can divide through to give
1:00:07that the pass through rate is equal to 1
1:00:09over 1 plus the elasticity of demand
1:00:12minus one / the elasticity of supply
1:00:15Plus the one over the elasticity of the
1:00:17marginal Surplus function now this is
1:00:20basically similar to what we saw before
1:00:22right there's still 1 plus the
1:00:24elasticity of demand divided by the El
1:00:25elasticity of supply there's a negative
1:00:27one in here which is not all that
1:00:29important but the key new term is the
1:00:32one over the elasticity of the marginal
1:00:34Surplus
1:00:36function so the question is how should
1:00:38we interpret this elasticity of the
1:00:40marginal Surplus function Kim do you
1:00:42have any thoughts about
1:00:46that
1:00:49yeah anybody else like we we saw how the
1:00:53marginal Surplus function was behaving
1:00:55before
1:00:56right it was that area between the
1:00:58demand and the marginal revenue and we
1:01:00saw that it was doing different things
1:01:02depending on the demand curve that we
1:01:04looked
1:01:17at well so the El one over the
1:01:20elasticity of the marginal Surplus
1:01:23measures the curvature of
1:01:27demand it's going to be greater than one
1:01:32for concave demand how do we know that
1:01:34well remember as quantity was increasing
1:01:36that thing that that distance was
1:01:38increasing more than one for one when
1:01:41you had concave demand it wasn't just
1:01:43linearly increasing it was increasing at
1:01:46an increasing rate so that means it had
1:01:47an elasticity greater than one with
1:01:49linear demand it was increasing at a
1:01:51constant rate so that means it had an
1:01:53elasticity of one
1:01:55and for negative exponential demand it
1:01:57was completely constant so that mean it
1:01:59had zero elasticity right for log convex
1:02:03demands like the um the
1:02:07marginal uh like the constant elasticity
1:02:10demand it was it was actually decreasing
1:02:12and that means it has a negative
1:02:13elasticity right and if this is negative
1:02:17enough then the passor rate can even be
1:02:20infinite uh how do we know that well
1:02:23remember that in the inov at all example
1:02:27right we had that ironing line so that a
1:02:28small increase in marginal cost could
1:02:30lead to a discontinuous increase in
1:02:32price that's an infinite pass through
1:02:34rate and that came from the fact that
1:02:35that marginal Surplus was
1:02:38shrinking uh very quickly as the
1:02:42quantity was increasing right so in
1:02:46addition to the
1:02:48elasticities uh of demand and Supply we
1:02:51now are going to care about the
1:02:52curvature of demand as well
1:02:56um in particular when demand is concave
1:02:59when it's negatively curved the
1:03:01elasticity of marginal Surplus is going
1:03:03to be positive um and that's going to
1:03:06tend to make the um uh the pass through
1:03:11lower and when the elasticity and when
1:03:14the demand curve is convex it's going to
1:03:16tend to make the pass through much
1:03:18higher um now uh what are some ways that
1:03:23we might think about circumstances in
1:03:25which the curvature of demand might be
1:03:28positive or negative uh Kim do you have
1:03:30thoughts about
1:03:48that
1:03:50okay um well you can think of this as
1:03:53how much of the valuation is out in the
1:03:55tail
1:03:56so if inelastic demand really means
1:03:58people have spread out valuations for
1:04:00the thing uh curvature is really a
1:04:04measure of something like curtosis it's
1:04:06like how much is out in the Tails and in
1:04:07fact you can relate this to our Notions
1:04:09of fat taals before anytime you have fat
1:04:12tails and the fatter tails you have the
1:04:14more uh negative is going to be one over
1:04:18the elasticity of marginal
1:04:20Surplus um in fact the elasticity
1:04:23marginal Surplus is equal to the
1:04:24negative of that parameter Alpha that we
1:04:27had before and so 1 over negative Alpha
1:04:32is equal to this and so as you get
1:04:34towards Zip's law for example this is
1:04:36going to get very very uh
1:04:40large um so
1:04:42income uh tends so when income generates
1:04:46values when there's Goods that are
1:04:47valued more by the rich than they are by
1:04:49others and the more that they're more
1:04:50valued by the rich the more that this is
1:04:53going to be large or if the if a good
1:04:55very Niche appeal then this is going to
1:04:58be uh very large so let me give you um a
1:05:03graphical illustration of this so here's
1:05:06a concave demand function and here's its
1:05:10marginal revenue curve which is
1:05:12diverging at an increasing rate from the
1:05:14demand curve that means that for a small
1:05:17increase in marginal cost the increase
1:05:20in price is going to be much smaller
1:05:21because we move more up the marginal
1:05:23revenue curve than we do up the demand
1:05:25curve
1:05:27on the other hand when we have a
1:05:28constant elasticity demand like this
1:05:31because these are converging a small
1:05:33increase in the marginal cost curve
1:05:35leads us to move farther along the
1:05:37marginal revenue sorry farther along the
1:05:39demand curve than it does along the
1:05:41marginal revenue curve and therefore
1:05:42leads to twice as large of an increase
1:05:44in price as it did um an increase
1:05:48in uh uh marginal cost similarly changes
1:05:54in the shape of the marginal cost cost
1:05:56function which effectively changed the
1:05:58elasticity of supply will affect this as
1:06:00well so if we have a upward sloping
1:06:03marginal cost curve which makes you know
1:06:05somewhat inelastic supply then an
1:06:08increase in marginal cost leads to a
1:06:11smaller move in the quantities and
1:06:12therefore a small change in price
1:06:14whereas if you have declining marginal
1:06:16costs as you often do in natural
1:06:18monopolies then an increase that's like
1:06:20a negative elasticity of supply then an
1:06:22increase in marginal cost leads to a
1:06:24bigger change in quantities and
1:06:25therefore a bigger change in
1:06:28price okay that's it for today

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