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ECON20110 Fall 2013 - Lecture 14: Imperfect Competition — Transcript

by Glen Weyl · 10,476 words · 1,573 segments · language en · Watch on YouTube

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0:01so um that would then give us that P
0:04Prime is equal to -1 Q ^2 and therefore
0:09marginal revenue would be equal
0:11to
0:13uh
0:15the it would be equal to
0:19P plus
0:23Qi uh time P Prime which is 1/ Q ^2 and
0:27that becomes Q over
0:32q^2 uh minus uh Qi over Q ^2 which is
0:38equal to Q of netive I over Q ^2 right
0:42because p is equal to 1/ Q uh so p is
0:47also equal to Q over Q
0:49^2 okay so each firm is going to set um
0:56is going to set their marginal revenue
0:59equal to one
1:01one is their marginal
1:02cost and so that gives them that this is
1:07equal to 1 which is the same as Qi over
1:12Q ^2 is equal to 1 Q ^2 - 1 okay so now
1:17if we add this up over all of the
1:20firms
1:23um
1:25uh if we add this up over all of this
1:29firms does anyone want to say what we're
1:30going to
1:33get yeah so what you're going to do is
1:36you're going to put a sigma on
1:37everything so it's going to be Sigma and
1:40I'm going to say number of terms is n so
1:42that's Sigma up to n of Qi over q^2
1:46equals Sigma of 1 Q -1 y so just
1:50multiply everything by n on the right
1:52side yeah and on the left side Sigma Qi
1:55of n is just Q so that's going be one
1:57over Q because they cancel yeah
2:01absolutely so you're going to get 1 / Q
2:04is equal to n / Q - n which gives you
2:07the 1 is = n - n * Q or n * Q is = n - 1
2:15which is the same as Q is equal to n /
2:20nus1 okay so what that tells us is that
2:25as n grows large quantity is going to go
2:28to its efficient level which is quantity
2:32is equal to one why is that the
2:33efficient level because when price is
2:35equal to marginal cost which is equal to
2:37one quantity is equal to one and we'll
2:39talk more about that on Thursday and
2:43also notice that the per firm output is
2:46going to go to zero right because Qi is
2:49equal to capital Q Over N which is equal
2:51to N - 1/ n^2 which goes to zero right
2:55okay now when there are just two firms
2:57there's an easy way to represent this
2:59graphic in Ming how would we do
3:03that sorry what if we wanted to
3:06represent this equilibrium graphically
3:08how would we do that um if there were
3:10just two firms wouldn't you just add the
3:13two things
3:16horizontally uh add what two things
3:20horizontally um if we wanted to
3:23represent like um in particular like
3:26what is what like if we want to find an
3:28equilibrium we need it to be the case
3:30that every firm does the optimal thing
3:33given what the other firm is doing and
3:35how yeah so how would we represent that
3:40[Music]
3:45graphically so we had the demand
3:47function is fixed right so then and
3:49since we assuming that um we assuming
3:51that all the CL functions of all the
3:53firms are same right so they symmetric y
3:56so wouldn't it just be a shift of the
3:59cost
4:00yeah so the I don't want to rely on
4:03symmetry as much right now I just want
4:05to try as if this was a general thing to
4:08represent like what what does one firm
4:11do optimally when the okay do you
4:14remember the idea of reaction functions
4:16from the
4:18reading the best response function
4:20before hours I okay okay uh okay so that
4:25that that's fine so basically what we
4:26just do is we say what is my optimal
4:29thing given what what both of the firms
4:30are doing right so that's that I have Qi
4:37over Qi + qj^ 2 is equal to 1/ Qi + QJ
4:42which you can solve out and you get that
4:45Qi is equal to QJ plus
4:49this um or or this that's called the
4:52reaction functions of the firms so that
4:56says what's the optimal thing for me to
4:58do given what the other person is doing
5:00okay um and the intersection between
5:03these two things for the two firms is
5:04the
5:05equilibrium right so this says what
5:09is uh what is the optimal value of
5:13Qi uh sorry what is the optimal value of
5:18the uh J firms given what uh I is doing
5:24and here's the optimal value of uh I
5:28given what J is doing and the
5:30intersection point is the equilibrium
5:32and we can just check graphically for
5:34whether this is a stable equilibrium or
5:36not how do we do that well um if we were
5:41to increase what J was
5:43doing then I would want to do this right
5:47that would make J want to do this that
5:49would make I want to do this and we go
5:51back to the equilibrium on the other
5:53hand if we change it
5:54down uh if J is doing this then I wants
5:59to do this and J you see what I mean and
6:02if they crossed in the opposite
6:03direction we would know that the
6:04equilibrium was unstable now we can only
6:06do that with two firms but that gives us
6:09a way to check for stability graphically
6:12the same way we did in the supply and
6:13demand model and to make sure the
6:15comparative Statics will be reasonable
6:17as a result right by the correspondence
6:20principle okay yeah cross
6:25opposite okay so if these imagine that
6:27these were like for some reason reversed
6:30right and that this one was the optimal
6:32reaction of I given QJ and this was the
6:35optimal reaction of J given Qi right so
6:39then what would happen well if I were
6:42doing
6:43this then J would want to do this and
6:47then I would want to you see what I mean
6:49and that would not be
6:51stable uh yeah the slopes of these are
6:55those determined by
6:57the no they're determined by a whole
7:00bunch of stuff having to do with like
7:01the marginal revenue and how it change
7:03its curvature and so forth because it's
7:05like all about if they change their
7:07quantity how does that change what my
7:09marginal revenue curve looks like yeah
7:12so it has a lot to do with pass through
7:14actually so the the slope of this is one
7:17minus the quantity pass
7:20through okay so um in fact I think we'll
7:25go through that a little bit later um
7:31uh
7:32so um the St stackelberg argued that it
7:37wasn't reasonable that both firms would
7:40take their the other firm's quantities
7:42as given it might be that there's one
7:44firm which believes that if it makes a
7:47change the other firm will be forced to
7:50react to that um and therefore uh and
7:54they might be able to do that by
7:55committing to an advertisement about the
7:58level of quanti that they're going to
8:00sell or building a certain amount of
8:01factories or something like that and
8:05um uh as a result this is going to
8:09create a different incentive and philli
8:11what what incentive is that going to
8:12create for the first firm the first firm
8:15is going to commit to grabbing a large
8:17share of the market to deter to grab as
8:20much of the profit as it can yeah so uh
8:25it seems like that but is that true in
8:26this picture
8:30so imagine that I'm
8:32firm uh
8:34I and I uh increase my quantity in order
8:40to try to grab more share of the market
8:43right that would mean I go up what's
8:46that going to do that's going to
8:46increase the amount that J is producing
8:49and that doesn't allow me to grab part
8:50of the market so I know that that's the
8:53classic story and the one that they told
8:55in your book but it's not true in this
8:57particular case right so can you think
8:59of a more General expression of that
9:01idea well basically firm I is going to
9:06think of what the other firm is going to
9:08do graph out its best response function
9:11and then uh with that reply in mind
9:14optimize yeah so that that's right in in
9:17particular what they're going to do is
9:19try to take whatever action will get the
9:21other firm to reduce the quantity that
9:22it's
9:23producing right because they want the
9:26other firm to produce less because that
9:28allows them to get more profit right so
9:31in this case actually they're going to
9:33produce not more but less in order to
9:36try to get the other person to produce
9:38less I mean that's a particularity of
9:40the constant elasticity demand but in
9:42that case they're actually going to do
9:44the opposite of what you were saying
9:45yeah Evan so if the goal is to increase
9:47market share then why are they not it's
9:49not to increase market share it's to
9:50reduce the quantity of the other firm
9:53and to increase your quantity I mean
9:55that does imply an increase in your
9:57market share but it's not like you're
9:58exclusively interested in market share
10:00you also overall want to reduce the
10:02quantity towards Monopoly levels okay so
10:04I guess so that's kind of my question
10:06was why are they not just interested in
10:08making sure that they're at a point
10:09where they're where their um quantity is
10:11just growing faster than everyone else's
10:13because they Al also want to reduce the
10:15aggregate quantity towards the Monopoly
10:17level oh okay okay right because the
10:19aggregate quantity is too
10:21high and that's the reason why they
10:25might want to reduce their quantity
10:27relative to what they would do in a
10:28Corno equilibrium in order to
10:29incentivize the other firm to reduce
10:31their quantity if you have these upward
10:33sloping reaction functions now Philip
10:35was thinking about a case where we have
10:36downward sloping reaction functions in
10:38which case he's right but that's not
10:40generally the case okay so um the
10:46follower is basically just like a
10:49monopolist on the residual demand and
10:52therefore the follower's reaction
10:54function is going to uh just follow from
10:57whatever the leader uh does
10:59whereas the leader is going to take into
11:01account the reactions of the follower
11:04and wants to try to induce the follower
11:05to reduce their quantity um because this
11:09leaves more demand available for the
11:11leader to serve now
11:14uh uh Adam when just re re uh phrasing
11:19the discussion we just had when is is
11:21that going to induce the leader to the
11:22chart to produce more and when is it
11:24going to induce the leader to produce
11:27less um well in that case it was it
11:30would induce the lader to produce less
11:32yes why
11:36um does that to do with the elasticity
11:39or well you don't even need to go that
11:40fundamental just what like what was it
11:43about the way that the follower reacted
11:46that induced them that made them want to
11:48produce
11:48less well
11:51as as the leader produced less a follow
11:54produced less exactly yeah so that's
11:57called strategic complimentarity
12:00so things are called strategic
12:01complement if when one person does more
12:04of something the other person wants to
12:05do more of it they're called strategic
12:06substitutes when one person does more of
12:08something the other want to do wants to
12:10do less of it and this is driven by the
12:12pass through rate so they are
12:14substitutes of the pass through rate is
12:15less than one and their complements of
12:17the pass through is greater than one and
12:19we know that under constant elasticity
12:21the pass through is always greater than
12:22one and that's the reason why you got
12:24this result there whereas under linear
12:26demand which is the case considered in
12:28your book I think Philip you get
12:30strategic substitutes because the pass
12:32through is less than one and that's why
12:34you get this effect yes why does pass
12:36through
12:38conceptually complt versus substitutes
12:40because um okay remember that the pass
12:44through is the same as the quantity pass
12:45through right so the like if I pass
12:48through a lot of an increase in cost
12:49then when there's more competition I'll
12:51pass that through into a greater
12:52increase in quantity right now uh when
12:57the leader increases his quantity if the
13:01total in quantity increases more than
13:03one for one that means that the follower
13:05must have increased his quantity if it
13:06increases less than one for one that
13:08means that he must have decreased his
13:10quantity right does that make sense yeah
13:13which one was uh strategic complement
13:15again which one was substitute strategic
13:17complement is when pass through is
13:19greater than one strategic substitutes
13:22is when it's less than one um could you
13:24which one was it relative to the
13:26reaction functions okay when the
13:27reaction functions slope upward that
13:29that's complement because that means
13:30when one person does more the other
13:31person does more when they slope
13:33downward that's strategic
13:38substitutes it's strategically
13:41neutral so that happens when you have
13:43exponential
13:44demand or logarithmic demand in the
13:46inverse demand function so our simple
13:49example of CES had pass through greater
13:51than one and that's the reason that it
13:53had strategic compliments
13:55yeah that mean that the AC One affect
13:58the
14:00exactly and therefore the Corno
14:03equilibrium quantity is the same
14:05quantity that you would choose if you
14:06were the
14:09leader okay so let's um solve this all
14:14out uh in our case so let's try to find
14:18this stackelberg
14:20equilibrium okay so the quantity of the
14:22second firm we know from the reaction
14:24function is equal to the quantity of the
14:26first firm time the square < TK of 2 + 1
14:29over the quantity of the first firm
14:30minus
14:31one that also says the total quantity is
14:35equal to this function of the quantity
14:38of the first firm because if we just add
14:40back in the quantity of the first firm
14:42that cancels out that negative 1 there
14:45so what is the first firm's profits
14:47going to be then
14:48Barett
14:50uh so uh price is equal to 1 q y and
14:56then you multip by q y
15:01um so that gives something pretty simple
15:03one sorry so you're going to do one over
15:07this and then multiply by the quantity
15:09produced by the first firm so what will
15:11you get q1
15:17over that but what is just okay so you
15:20get one over 1 yeah exactly so it looked
15:23ugly but it's not too ugly actually uh
15:26so that gives you the uh
15:29okay so price is equal to
15:31this
15:38um sorry what's
15:42going price equals
15:48that are you assuming cost is equal to
15:51one now oh yeah sorry cost is equal to
15:52one so this is
15:55profits uh so I sorry what you gave is
15:57revenue of our
16:00uh and then uh we need to solve this so
16:04that gives this here and we need to
16:06solve that out for the optimal
16:09quantity
16:11um and uh Florence could you come up to
16:15the board and solve for the optimal
16:16quantity for firm one
16:26there uh let's see there's an eraser
16:29here if you want
16:47that okay so we have
16:52uh wait that's profit right yeah that 1
16:56over the square Ro TK of 1 plus 1/ q1
17:00minus q1 is
17:06profit probably don't call that P
17:08because that's price call it Pi that's
17:10what we usually call
17:18profit
17:2021 and we need to set
17:25um so we maximizes yeah when this is
17:28they derivative is zero so um
17:50[Applause]
18:28um I think it's this yeah that that
18:30looks good so we set this to zero so we
18:33get
18:34[Music]
18:46[Music]
18:48this uh
19:15one thing you might want to do is try
19:17bringing this inside of there yeah and
19:19then and then putting everything to the
19:212/3
19:26power um
19:48okay sorry I'm kind of just blinding no
19:50no you're doing pretty well it's not
19:52it's not
19:54easy so 2 * what is equal to
20:00uh okay here's another way of doing it
20:03try bring this has a negative right so
20:06you can think of it as being down in the
20:08bottom right to the three halves right
20:12yeah multiplied by that and what when
20:16you multiply two gives you three
20:21halves three exactly so you're going to
20:25have to put this in there with um
20:30with a uh 4/3 power right so it
20:36be
20:49this great and now
21:17yes there's no
21:20negative but um yep now you're very
21:24close
21:47great okay so this actually can't be
21:50solved analytically from the point that
21:51she's gotten it too uh but uh here's
21:55where she got um
21:59and Mathematica if you plug this in uh
22:02very nicely done Florence uh gives us q1
22:06is equal to .1 which is way way way
22:10below 0.5 which we got before right so
22:13this strategic incentive led the firm to
22:16dramatically reduce the quantity that it
22:18was producing because there was such a
22:20strong upward slope to that uh to that
22:26uh best response function we saw
22:29right on the other hand with linear
22:31demand you'd increase your quantity
22:33right so the issue of strategic
22:35substitutes versus complements and
22:36therefore have passed through is really
22:38crucial here to how firms want to choose
22:40their uh quantity okay yeah in that
22:44formula shouldn't two be raised to the
22:45power of yeah that's probably
22:48true uh I don't know how much that
22:51affected my mathematical calculation or
22:53not someone else can go and verify it if
22:55they want to can you post mathematic
22:58uh I don't think I have it uh I might
23:00have it I'm not
23:04sure yeah so Florence has got it right
23:07and I've got it not perfectly right
23:10unfortunately
23:13um uh
23:18yeah so um there's a few things to
23:22notice um so even with many firms prices
23:26are still above cost though on Thursday
23:29will show that they gradually fall
23:31towards cost um the prices are going to
23:34be between the prices under Monopoly in
23:36perfect
23:38competition and uh one of the most
23:41interesting results comes from asymmetry
23:43so imagine that firms had different
23:46costs um then the lowest cost firm is
23:49going to have to be producing more
23:51because the price is constant they have
23:53a larger markup and the markup that they
23:55have is equal to their quantity times
23:57the derivative of the negative quantity
23:59times the derivative of price so the
24:01bigger their quantity is the bigger
24:02their markup is and therefore the firm
24:05with lower cost will have to be
24:06producing more in order to um uh have
24:10the uh the same
24:13price but of course the higher cost firm
24:16is still going to produce some which is
24:18inefficient when we have linear cost
24:20right so Monopoly will always be you
24:24know they might uh charge to high of a
24:26price but whatever they're producing
24:27they'll produce efficiently competition
24:30always produces efficiently but olop may
24:32it misallocate production to inefficient
24:37firms okay so in this more General
24:39isometric case we can still add things
24:42up and we get the total quantity times
24:44the slope of Price Plus n * P of
24:48Q uh is equal to the sum of the costs so
24:52if we then divide by n we get the
24:54average quantity times the derivative of
24:56price uh Plus price is equal to the
25:00average cost and so what that tells us
25:02is that the pass through of any firm's
25:05increase in cost is like increasing the
25:08average cost in the industry by
25:111/n so it's sort of just the sum it's
25:14the average cost only that matters of
25:17the
25:19firms
25:20um and as we'll see some models that
25:23we'll talk about later where a tiny
25:27change in one firm's costs can have a
25:29really big impact here that's not true
25:31at all all the firm's cost changes have
25:34the same uh one over n impact even if
25:37firms are
25:38heterogeneous okay so what the
25:41situations we've been studying so far
25:43yeah Christian so since we're the costs
25:46don't really seem to matter as much so
25:48we're talking about like the stackelberg
25:50leader thing like that doesn't depend on
25:52like who can produce the cheapest at all
25:55it kind of depends on like who's first
25:56who's the most yeah well it's a it's a
25:58strategic assumption basically yeah so
26:02what we've been studying so far is
26:04usually called a game this is a
26:06strategic situation where a small number
26:08of people make a choice here either
26:10prices or quantities or quality or
26:12something like that um but more broadly
26:15it can be anything it could be who to
26:17date where to eat Etc uh and the
26:20participants payoffs depend on all
26:22players actions my profit depends on
26:24your
26:25quantity and the players take their
26:28action
26:29simultaneously as in Corno uh that is
26:33called a normal form game on the other
26:36hand if one player takes an action then
26:38another player takes an action that's
26:40called an extensive form game and that's
26:42what stackelberg is so for example chess
26:45is a uh is a um extensive form game well
26:52uh you know rock paper scissors is a
26:54normal form
26:56game and like like competitive
26:58equilibrium we need some notion of what
27:00it means to be a solution under perfect
27:03competition this was when Supply equals
27:04demand here it's not exactly obvious
27:07what's analogous and the most famous
27:09concept is a general version of what
27:11we've been studying so far which was
27:13invented by John
27:15Nash um and uh the two most famous
27:21solution Concepts in this area
27:23correspond exactly to the two games
27:25we've been talking about so Nash
27:27equilibrium corresponds to how we sered
27:30solve Corno it's where every player
27:32takes his given the strategy of the
27:33other players and chooses an optimal
27:36strategy given this and the equilibrium
27:39is therefore the intersection or the
27:41generalized intersection when there are
27:43more than two players of the reaction
27:45curves the second is the subgame perfect
27:48equilibrium which corresponds to the
27:50stackelberg model where one player acts
27:52first and the other takes their actions
27:54as given like in chess there would be a
27:56series of actions but at each stage
27:58would take everything that's happened in
27:59the past as
28:00given okay and these are usually solved
28:03via backwards induction rather than uh
28:07than the intersection of reaction curves
28:09backwards induction is you look at the
28:11last stage of the game and everything
28:13everyone could do you say what's the
28:14optimal thing for them to do at that
28:16stage then you ask what's everyone's
28:18best thing to do anticipating all the
28:20things that people will do in reaction
28:21to that and you go backwards from there
28:23and the reason that we can't solve chess
28:26perfectly why there aren't perfect ways
28:28to play it is just too hard to look at
28:30all possible outcomes and Trace them
28:33backwards uh but in fact backwards
28:36induction is precisely what all most of
28:38the best computer algorithms playing
28:40chess to at least in some part they look
28:42at potential things that could happen
28:44they assign points to those and then
28:46they trace backwards what people are
28:48going to do to maximize those points and
28:50so
28:51forth okay yeah
28:55reishi does that mean like you start
28:57with whichever move gets transed or
29:01whichever okay so that is something that
29:05you could do uh but the problem is
29:08that's like there's just too many things
29:10from that point so what these things
29:12usually will do is they'll take like the
29:13current state of play and they'll go
29:15about like 50 moves deep okay or maybe
29:18not 50 that could be too many but maybe
29:20they'll go like 20 moves or 10 moves
29:22deep and they'll look at all possible
29:24outcomes that could occur through any
29:26set of strategies they'll assign points
29:28to all of those and then they'll
29:30backwards and duct up from
29:33there okay so if we have this broad uh
29:38concept the key question is what are the
29:41strategies of players what do they take
29:44as given that other people are doing
29:47when uh they take their action now we
29:50assumed that um strategies were
29:53quantities right but there's no reason
29:56that they have to be quantities right
29:58um you know do we think that companies
30:00when they're choosing how much to
30:02produce take is given the quantity that
30:04other companies uh are producing why
30:07shouldn't they take as given the prices
30:10that other firms are producing I um Mike
30:15fosco can you see what difference that
30:17that would make if everyone took his
30:19given the prices that other exality to a
30:23real one cuz you have to change the
30:24quantity if you take the price that's
30:26fix yeah EX exactly so
30:29and what what would that do to how firms
30:32behave
30:35um they
30:37would change their quantity
30:40or try to go they would try
30:44to find prices that would
30:48or
30:49change oh I mean cut down their price so
30:52that they take all the competition from
30:54other firms yeah it's going to lead the
30:56firms to behave more aggressively than
30:58before so in particular let's imagine
31:00there's several firms with the same
31:02constant marginal cost and each of these
31:04firms takes its price of its Rivals as
31:06given Joan can you see what the
31:08equilibrium has to be among the firms um
31:12they take all the prices as given of the
31:14other firms is given yeah um I know that
31:18it's supposed to be just C why can you
31:21can you give an argument for why
31:37imagine that it were something above
31:38C so first of all it can't be anything
31:41below C right because then people would
31:42be taking losses right what what if we
31:44were anything above C what what would
31:46one firm want to do the other firms
31:48would under them why because they could
31:52that and they would gain all the yeah
31:54with just a tiny loss in price right so
32:01exactly so this leads to What's called
32:03the betrand and Edgeworth Paradox that
32:06with even two firms prices exactly equal
32:09to cost right and this seems a little
32:12bit implausible right because it
32:15requires that if I undercut the other
32:17firm even by a tiny amount I take all of
32:20the business away from them right um and
32:24you know Mor what are some of the
32:26reasons you think this might not happen
32:28in the real world um there like costs of
32:31like comparing the two products yeah
32:33that's a good reason that's called
32:35search yeah um can you think of other
32:38reasons maybe there's like consumer
32:39loyalty to a specific company yeah they
32:42might not view the two different
32:43products as completely identical with
32:44one another right
32:48um and
32:52uh both of these two forces can be
32:54captured in a model where my quantity
32:57depends on all of the prices but not
32:59necessarily in this particular way that
33:01if I just go a little bit below them I
33:03get all the market but it's just in some
33:04smooth way my quantity is a function of
33:07all the prices and each monopolist each
33:10firm is effectively a monopolist but
33:12only on their own product not on all the
33:14products in the market and the other
33:16products are substitutes in the sense
33:17that if the prices on the other products
33:19rise then the quantities of this firm
33:22will rise and that's the definition of
33:24being
33:26substitutes okay now now this is a very
33:28broad model and you could either choose
33:31the prices to be the strategies as we
33:33were just doing or the quantities to be
33:35the strategies but the most common way
33:37people do this is they do what's called
33:39nashan prices or ber trand uh
33:42differentiated products so this model is
33:44often called differentiated products
33:45ntion and prices yeah so when you write
33:48the quantity for firm i y why is it not
33:51Q minus I and why is pi inside that
33:55function because my Quant the amount
33:58that I sell depends on my price but it
34:00also depends on the prices of all the
34:01other firms you're not EV so so you're
34:05evaluating
34:06it so you're trying to evaluate it
34:09including your price well because if
34:11they raise their price then I'm going to
34:13get more business if they lower their
34:14price I'll get Less business
34:18right that was sort of the argument that
34:20Mory was giving
34:22right uh yeah could it be that um if you
34:27lower the price in the long term you'd
34:29like accumulate more market
34:31share uh because like consumers are able
34:35to like recognize that your price is
34:38lower over over time yeah so that's
34:39basically what this captures right is
34:41that like if my price is lower I'll get
34:43more business but in the long term
34:46wouldn't that be more like uh pronounced
34:50yeah well so we know that in general
34:51elasticities tend to be larger in the
34:54long term than in the short term uh in
34:56many cases though not always like an
34:59example where they would definitely be
35:00higher in the short term than in the
35:01long term is like if one company just
35:04has a sale this week everyone might go
35:06visit them that week and another company
35:09the week when that other company is a
35:11sale but if they lower their price over
35:12the long term you might not want to get
35:13all your stuff from that one company
35:15right
35:17so okay so we didn't actually do the
35:21hotelling model I'm realizing so we're
35:23just going to go through that and do
35:25that now Okay so simplest model is the
35:29hoteling
35:30model um this is one let me see if I
35:33have a picture of this no I don't uh
35:36imagine that there's like a
35:38line right and two firms are at
35:42different positions along this hotelling
35:45line and um customers find it costly to
35:50travel so people live at different
35:53positions and the firms are at two
35:55different positions and so the firms are
35:57not identical you like the product that
35:59you live closer to and you dislike the
36:01product that you live farther
36:03from um so then a consumer living at
36:06point
36:07x um in particular imagine that the
36:11firms are at the two ends of this line
36:14right so a consumer living at point x
36:16can either pay a t * X to go to the firm
36:20that's at zero and the price of zero or
36:23they can pay T * 1 - x to go to the firm
36:27that's at one and play their price
36:31P1 okay so um Ming what is going to be
36:36the value of x such that the consumer is
36:39just indifferent between uh the two
36:44firms yeah
37:09essentially what I do is just SOL X
37:10right yeah using the inquality you you
37:13using the equality right because if
37:16you're indifferent then you're then you
37:18don't care the way
37:21exactly okay my bra
37:29doing yeah yeah that's to be great
37:31thought be my
37:58[Music]
38:22uh you have a double negative so it
38:24needs to be a positive so it's 2 TX
38:26right
38:52you lost a
38:55t wait no yeah
39:02oops and
39:05then nicely done Ming yep
39:10great
39:12um okay so thus if okay so what does
39:17this tell us this says that when the
39:19prices are equal to this everyone to the
39:22left of this point is going to be buying
39:24from zero and everyone to the right of
39:26this point is going to be buying from
39:28one right so if we have uniform
39:30distribution of people the number of
39:32people buying from one is just the
39:35number is just X right because everyone
39:38to the left of X buys from one and so
39:41their quantity is P1 minus P0 plus T
39:44over 2T so this gives us just linear
39:47Demand right uh between the two
39:51firms um and what is going to be the
39:54optimal price myy when the cost is equal
39:56to zero
39:58when the cost isal Z so
40:01you so what would be from one uh sorry
40:05this is firm Zero's optimal
40:07quantity uh quantity sorry not firm one
40:11and I got two and this is all messed up
40:13so this should be q0 of p 0
40:17P1 what's firm Zero's optimal uh optimal
40:23price going to
40:25be um
40:28so would you try to maximize quantity
40:30here you're going to maximize profit
40:33right yeah and do you remember how you
40:35price if you're a monopolist against a
40:37linear
40:39demand
40:43um
40:45no well I mean you can also try to solve
40:48it out but there's a there's a trick is
40:50is the trick from the maximum price
40:53exactly so so with a little assist from
40:55Ming can you can you figure out what
40:57that means here so you go half from the
40:59maximum price that would kill all demand
41:02oh okay
41:04um so you set quantity equal to
41:08zero no you go halfway to the price that
41:12would kill all Demand right so what
41:14what's the price here that would lead
41:16you to have no demand if you what would
41:18p 0 have to be for you to have no demand
41:21um it would
41:24be p1- t P1 plus T right plus T sorry
41:29yeah yeah so then what what's the price
41:31you going to charge P1 plus T 2 exactly
41:37exactly okay
41:42um so if p 0 is equal to P1 + t/ 2 what
41:49is
41:50P1 uh going to be equal to um philli um
41:55by symmetry is just going to be p plus
41:59exactly and so what's then going to be
42:01the equilibrium value of both prices
42:04Phil well by symmetry there's going to
42:07be a symmetric equilibrium so you get p
42:10= p + t/ 2 then it's adding P
42:16subtracting p/ 2 from both sides p/ 2 =
42:20t/2 so tals T right
42:25exactly nicely done
42:28um How about if both firms had a
42:31positive cost myy what would be the
42:33equilibrium
42:39then do you remember what the pass
42:41through is under linear demand would be
42:43a half right okay right so this is just
42:47going to be equal to this whole thing
42:49plus
42:50what plus cost divided by two yeah right
42:55and so that's just going to add on like
42:57P like C is going to do yeah and and
43:01like T did and so what would the
43:03equilibrium here
43:04be um it would be t plus C
43:11exactly
43:13okay so overall there's a pass through
43:15of one and the reason is that no
43:17consumers would exit the
43:20market and as a result of that like you
43:23know an increase in cost just gets past
43:25one for one under price because there's
43:26no no like exiting of consumers out of
43:28the
43:29market okay now this is just one example
43:33but in general you could solve this
43:34using reaction
43:36functions and um the same uh basic
43:40principles that apply to Monopoly are
43:43going to apply to um are going to apply
43:48more generally to this differentiated
43:51products Nash and prices model so uh
43:54Rishi what's going to be the elas it of
43:57your demand holding fixed the prices of
44:00all other
44:02firms
44:05um this is sort of the elasticity of the
44:08demand facing this monopolis right
44:09because he's taking all the other prices
44:11it's given and then he's going to charge
44:13along this sort of residual demand curve
44:15which holds fixed the prices of all the
44:16other
44:22firms you take
44:34the the elasticity generally would
44:38be the
44:40quantity the derivative the quantity
44:43yeah with respect to the price right and
44:46then what do you do to turn it into an
44:49elasticity
44:50percent you you multiply it by the price
44:53and divide it by the quantity right and
44:55then but if I I want to hold fixed all
44:57the other firm's prices then what type
44:59of derivative do I
45:01take
45:04um okay when I take the derivative of
45:08one thing holding fixed other things
45:11have you taken multivar yet uh no okay
45:15so there's like the notion of a partial
45:16derivative right which is the partial
45:20derivative of quantity with respect to
45:21price and then we take a negative and
45:24you multiply that by Price divided by
45:26quantity right that's the part that's
45:29the residual the partial elasticity in
45:32some sense right and then firms are just
45:34going to price according to the mark
45:36learner rule that the relative markup is
45:38equal the inverse of the residual
45:41elasticity
45:42now now of course there's nothing
45:45specific to this about prices being
45:47strategies we could also Define the
45:49residual elasticity holding fixed other
45:51firms quantities or anything else right
45:55you just have to hold fixed something
45:57for the other firm we could also hold
46:00fix the other firm's prices and derive
46:02my optimal
46:03quantity using the inverse demand
46:05holding fixed everybody's prices right
46:10um but this basic model where we hold
46:13fixed other firms prices is used
46:14extremely broadly in industrial
46:16economics and we'll use this to talk
46:18about uh lots of things in competition
46:21policy during the next
46:22lecture now ol theopolis create
46:26externalities for each other and how do
46:28they do that Joan what are the types of
46:30externalities that oligopolists create
46:31on each
46:32other um they can either benefit each
46:35other by kind Str strategizing so that
46:44UMES
46:46to be position where they can all have
46:51or sure sure but I'm just saying
46:53forgetting about any strategies they do
46:55together what are the what are the
46:58externalities that one oligopolist
47:00creates on the other by changing their
47:03strategy um it basically affects the
47:08ability for other firms
47:16to uh yeah and and and how does it do
47:22that
47:24by Yeah by changing the prices or the
47:26Quant ities right so firms
47:31um when they change their strategies
47:34aect other firms the terms that other
47:37firms get in markets either the
47:38quantities that they have or the prices
47:40that they're getting now those
47:42externalities under Corno are purely
47:45pecuniary and Rishi why is that the case
47:48well because any any reduction in price
47:53um or reduction would uh is reflected um
47:58in like in another
48:00firm's uh in another firm's production
48:03right so well what are the definition
48:06what's the definition of a pecuniary
48:07externality well any
48:10um the effects between things are the
48:14price system it's purely driven through
48:15prices right and in the cor no model
48:18what adjusts when I change my quantity
48:20and what do I hold fixed when you adjust
48:23your quantity price adjusts an addition
48:26and uh when and what you're holding fix
48:28is the the what everybody else's qu
48:31exactly so all effects that I have on
48:34other
48:35firms it come through prices in the
48:37Corno model that's
48:39right
48:41um and therefore all externalities are
48:44purely pecuniary right um on the other
48:48hand under differentiated products
48:50Nation prices all your externalities are
48:52purely real and Mike fosco why is that
48:55the case uh because you take given the
48:57prices of as yeah given so then they
49:00have to change quantities exactly and
49:02all and changes driven through
49:03quantities are real changes
49:06right
49:08um so this implies that quantities are
49:11always going to be two low under Corno
49:14why is that because when the firm
49:16increases its quantities it has purely
49:19pecuniary externalities on all the firms
49:21and it is a direct positive externality
49:24from increasing its quantity on the
49:25consumers and that means it's going to
49:26choose too low of a quantity right but
49:30um D does
49:34uh does the uh do firms under Bertrand
49:40necessarily um charge to have too low of
49:44a
49:45quantity you have no idea
49:48yeah okay anyone else want to try taking
49:51that on uh yeah Mike uh would prices be
49:55higher uh
49:59okay so we said that quantity is always
50:01too low under Corno does quantity need
50:05to be too low under Bertrand for all
50:07firms oh sorry
50:10uh no because you've made assumptions
50:14about other firms quantities that
50:22you I'm actually not sure I thought the
50:24question is this Agate quantities or
50:25quantities for each individual firm this
50:28is for one individual firm what do you
50:31think of so we actually talked about how
50:33this can actually result in the in um
50:36firms with high marginal costs actually
50:38producing which is not what we would
50:41want that's too high yeah so you can
50:42have situations where it's too high well
50:44in particularly lowquality
50:46firms
50:48um so imagine that there are two firms
50:52one firm produces a high quality product
50:54that has a really big markup another
50:56firm firm produces a lowquality product
50:58that has a really low
50:59markup now and imagine these are
51:02substitutes for one another you can
51:03either buy the high quality product for
51:04a high price or the lowquality product
51:06for a low price actually it could be
51:09beneficial If the lowquality product
51:11were to raise its price because that
51:12would drive more people to buy the high
51:14quality product that might actually be
51:15socially
51:18beneficial because it might be that
51:20people are buying the cheap product
51:22because the markup is so high on the
51:23high high quality product right so
51:26actually under Nash and prices you could
51:29have two high quantities for some firms
51:33because of the real externality they
51:35have by stealing business from the
51:37higher quality
51:38firm okay regardless of the social
51:41benefits and costs firms can benefit
51:44from internalizing these types of
51:46externalities because goods are
51:48substitutes one firm's lowering its
51:50quantity or raising its price will
51:52benefit its competitor and in fact this
51:55is how we Define firms being substitutes
51:57right and when firms act to internalize
52:00these externalities across firms what do
52:02we say that they're doing uh Julian um
52:05they're merging yeah yeah or when
52:10they're not doing it legally what would
52:11you call it um cluding exactly or
52:14forming a cartel right um and my
52:18favorite phrase for this is a very
52:19old-fashioned one combinations in the
52:22Restraint of trade uh and these have
52:25been denounced by economists ever since
52:27Adam Smith So Adam Smith said that
52:29people who are in the same industry as
52:30one another rarely meet on friendly
52:32terms unless it's in a conspiracy
52:34against the public interest and uh this
52:37was made illegal under the Sherman uh
52:41Antitrust Act so um the reason that the
52:45shman Antitrust Act got passed was
52:47because people were really concerned
52:49about the power of these uh combinations
52:51in the Restraint of trade and U mck
52:54raking journalists during the
52:55Progressive Era made a lot of hey about
52:57this and in particularly they created
53:00cartoons like this showing the power
53:02that these uh combined firms would have
53:05had and in fact that's why I have that
53:07octopus in my office that maybe some of
53:09you guys have seen during office hours
53:11is to represent the this uh this picture
53:15that I often show students uh this was
53:17of Standard Oil which as you know had an
53:20important role in the founding of this
53:22University
53:24um so uh Once Upon a Time cartel
53:28agreements were legally
53:31enforcable in fact that was true in the
53:33United States prior to the Sherman Act
53:35and in Continental Europe prior to the
53:37EU
53:38reforms uh and it's hardly even illegal
53:41in many developing countries like Peru
53:44Britain in Britain it was banned all the
53:45way back to the 18th century um and uh
53:51in the United States
53:53nowadays uh the US government is
53:55probably the lead in antitrust
53:57anti-cartel enforcer in the world um
54:01explicit agreements between firms about
54:04prices or services are now
54:07illegal uh yeah why are sports cartels
54:11then uh something that we see in the
54:13United States what's a sports
54:15CTO like the NFL or the NBA NCA they
54:19have exemptions from the antitrust
54:22laws why uh good question I don't know I
54:26mean
54:26it's the idea is that there's do you
54:29really want the usfl to come back I I
54:32don't even know if sports are socially
54:35valuable well I mean the idea is that
54:38there's some that you need to do to
54:40manage competition so that fir like
54:43because what makes it fun is that it's
54:46competitive and so that's I think the
54:48idea behind the antitrust exemption yeah
54:49Tanner I mean it goes back to the 1920s
54:53suem Court baseball Court to uh these
54:56the players wanted higher salaries so
54:58they were going know form their own
54:59League yeah and the uh they sued for
55:01antitrust and back then you know this
55:04very Pro bus anti workers yeah so with
55:08the own and basball still anti trust
55:10exception yeah yeah that's a that's a
55:14good point I mean I think that the
55:15reason why this is maintained is that
55:17people are afraid that if you just allow
55:18people to completely freely compete that
55:20someone like the Yankees would like end
55:22up with all the money and then it would
55:23no longer be fun to watch uh
55:25professional sport reports isn't that
55:27happens in Europe yes it's completely
55:31free yeah so I mean I'm not sure that
55:35whether this is a good or a bad policy
55:37but it it is it is the policy um okay so
55:43even it's even can be illegal if you
55:46don't make an explicit agreement if we
55:48you think that the firms are somehow
55:50taking into account the good of the
55:52other firm implicitly or tacitly but
55:55this is much harder to prove and
55:57therefore much less enforced against and
56:00there are both criminal uh penalties
56:03such as jail time and civil penalties uh
56:07for collusion and in particular the
56:09Civil penalties because um it's not uh
56:14easy to catch this sort of thing are
56:17usually three times the damages to
56:19Consumers because it's assumed and this
56:21is completely arbitrary but it's assumed
56:24that you only catch about one in thir in
56:26every three cartels yeah mention the USF
56:30earlier the famous story of that is they
56:32won the antitrust case but the D $1 so
56:36they were treble to $3 I see they Donald
56:39that's funny I didn't know about that I
56:41think he still has he founded the usfl
56:43he at that time this us Football League
56:45he was in control of it he had bom the
56:47teams and was like the one this is like
56:48was a competitor to the NFL that
56:51complet they they played football in the
56:53spring and beginning of the summer it
56:55was like the it they Americans Americans
56:59needed more football I yeah have there I
57:03I know you had one old paper that
57:05suggested that you from um what was his
57:08name in the readings Stigler Stigler
57:11we're about to talk through all that
57:13yeah that estimated the probability of
57:14detection Mr Been recent stuff or is
57:16that what you're going to talk about uh
57:18no I'm not going to talk about any of
57:19the empirical work on this stuff but
57:22yeah
57:23um Okay so I don't actually know what
57:27the most recent estimates of the
57:28probability detections are I haven't
57:30followed the literature that much um
57:32okay so there's many practical
57:34challenges as a result of it being
57:36illegal to running a cartel these days
57:39uh collusion is often difficult and
57:41therefore only possible in very limited
57:43settings and the basic problem is that a
57:45cartel benefits all of its members but
57:49each firm is going to have an incentive
57:51to portray that cartel uh and Barett why
57:55is that the case
57:57uh is it could be like
57:59a prisoners dilemma sort of thing where
58:03you could lower the price and
58:07benefit
58:09so uh is he interest to do that even if
58:12it's in fact that's exactly what an
58:14externality means right an externality
58:17means that unless something's forcing me
58:20to do it I'm not going to take that
58:21thing into account right um and each
58:26firm will benefit by decreasing their
58:28price or increasing their quantity which
58:30would hurt other firms but would benefit
58:32them by taking business away from their
58:34Rivals right um and in fact the more
58:37ambitious a cartel is the less stable
58:40it's going to be the harder it is going
58:42to be to maintain that cartel Rishi why
58:44is that true well if each person in the
58:47cartel is more ambitious by ambitious I
58:49mean it's like they're earning more
58:51profits right if it tries to elevate
58:53things higher above what you would get
58:54in an oligopolistic cut by one cut by L
59:01and so you can steal the profits but
59:04without having to undercut like an
59:05enormous amount
59:07of yeah in particular when there's a lot
59:10of profits on the table you have more
59:11incentive to steal a lot of them right
59:15um okay whereas near the competitive
59:17level you hardly gain any profits by
59:19undercutting so the extent of collusion
59:22therefore is sort of determined by the
59:24ability to deter cheating
59:26and as a result every cartel if it wants
59:29to actually achieve much in terms of
59:30collusion needs to create Expectations
59:32by other cartel members that they will
59:34punish uh deviations right and policy on
59:39the other hand tries to make this
59:41difficult right so the goal of the
59:42cartel is to ensure that there exists
59:45these credible punishments of cheaters
59:47whereas the goal of the agency is to
59:48catch the cartel and prevent them from
59:50creating an expectation of credible
59:53punishments and stigler's uh theory is
59:57basically about this multi-level Cad and
59:59mouse game where the cartel is trying to
1:00:00catch cheaters and the government is
1:00:02trying to catch the cartel and stop them
1:00:04from catching their cheaters so that the
1:00:06cartel will fall apart yeah philli do
1:00:08you know exactly what mechanism OPC
1:00:13uses uh yeah so I think OPEC uh punishes
1:00:17cheaters by flooding the market with oil
1:00:20they the the members agree that if one
1:00:23person defects it all other members will
1:00:24flood the market with oil
1:00:26and that's actually happened at some
1:00:27points during opec's operation when one
1:00:31member was misbehaving for example when
1:00:33Iran during the 1980s tried to produce
1:00:36more oil because they were in war with
1:00:37Iraq all the other members uh flooded
1:00:40the market with oil and made it uh very
1:00:44um hard for Iran to earn any Revenue as
1:00:46a
1:00:47result H yeah uh Christian I know I
1:00:50guess that's happened but like is that
1:00:51still a credible threat like I don't
1:00:54know it seems difficult for me to
1:00:55imagine all the other countries just
1:00:57wanting to float the markets it seems
1:00:58like it hurt them a lot too yeah I mean
1:01:01they might not have to do it for that
1:01:02long if it hurt Iran for a while I mean
1:01:04that's the idea is like you do that for
1:01:06a while and then you go back to the equ
1:01:08other
1:01:10equilibrium yeah or or another thing
1:01:13that you can do that's more efficient is
1:01:15you can say we're going to flood the
1:01:16market with
1:01:17oil unless you start agreeing to a new
1:01:20agreement where you make up for your
1:01:23past misbehavior by having a lower
1:01:25Market sh so that's a more efficient way
1:01:27of doing it yeah Tanner since obviously
1:01:30is business even though they're cartel
1:01:32and most governs CRA down to cartels is
1:01:34there are there any mechanism for
1:01:35dealing with the fundamental problem is
1:01:37international there's no International
1:01:39antitrust authorities and this is a huge
1:01:41problem so like in the US like OPEC is
1:01:44one case of this but if you're a little
1:01:47country like Peru and there's like
1:01:49companies serving all of Latin America
1:01:51and they merge like what country goes
1:01:53after them it's a big problem right so
1:01:56for the US it's less of a problem
1:01:57because we're such a big Market that we
1:01:58have like power to like stop these sorts
1:02:00of things but as small countries don't
1:02:03and for them International antitrust
1:02:05enforcement is really important and
1:02:06doesn't exist
1:02:08so okay in order to deter cheating uh
1:02:12what does a cartel need to do uh
1:02:17Christian
1:02:19um I mean I would say you have to have
1:02:22the credible punishment right yeah what
1:02:25else do you need to do so you need to be
1:02:27able to detect if someone is cheating
1:02:29exactly um and you need to be able to
1:02:31enforce that punishment but outside the
1:02:34law exactly um so you need to be able to
1:02:39first of all you have to even determine
1:02:40what the optimal agreement is Right
1:02:42which is a problem because as we know
1:02:44from externalities there's usually
1:02:45diffuse information about what the right
1:02:47level of something is to do right and
1:02:50it's further that sort of communication
1:02:51that's necessary to achieve that is
1:02:53further hindered it was already really
1:02:55problematic even if if you can do it
1:02:56legally and if you can't do it legally
1:02:57then it gets really hard right you have
1:03:00to have a clear sense of what does and
1:03:01does not constitute cheating because um
1:03:05and this is a real problem because you
1:03:07want to give firms some flexibility I
1:03:08mean if they suddenly get an opportunity
1:03:11to make a bunch of profits but there's
1:03:13you know some great sales opportunity
1:03:15that's only available to them or they
1:03:17get a reduction in cost all of a sudden
1:03:19you want them to be able to expand their
1:03:20quantity but if you allow them to freely
1:03:22do that then it gives them a free ride
1:03:24to cheat so so that's a a problem right
1:03:29you have to be able to detect cheating
1:03:31from background noise right because
1:03:33there are many things where the firm
1:03:35didn't do anything at all but they just
1:03:37through a no fault of their own ended up
1:03:40uh getting more profits and you don't
1:03:43want to punish that because then you'll
1:03:45get into a price War over nothing right
1:03:48um you have to have a coste effective
1:03:50means of punishment so as we were
1:03:52talking about if it's not going to be
1:03:54credible if it's going to hurt everybody
1:03:56right so these like market share type
1:03:57things are going to be better because
1:03:59they're going to be closer to like
1:04:00taxing one firm and redistributing to
1:04:02the other because uh as we um uh talked
1:04:07about when we talked about crime you
1:04:09want to deter things at the lowest cost
1:04:12possible right um and you have to be
1:04:14able to do this quickly because
1:04:15otherwise the firms are going to say hey
1:04:17they're not going to punish me anytime
1:04:18soon might as well just cheat and make a
1:04:20lot of profits in the interim and maybe
1:04:22they'll eventually get around to
1:04:23punishing me but who cares at that point
1:04:25right
1:04:26so stigler's theory was based on factors
1:04:30that help the firms achieve or limit
1:04:33their ability to achieve these things so
1:04:34Andrew what were some of the factors
1:04:37that uh Stigler highlighted um so the
1:04:40large heterogeneous buyers as opposed to
1:04:43Sol
1:04:45iters make it easier to or harder to
1:04:49track um
1:04:52then um like growing demands versus
1:04:56demand demand more to go and get you can
1:05:00while you can
1:05:02to yeah and that makes it harder to
1:05:03sustain collusion right yeah so he
1:05:06emphasized that if you had as Andrew
1:05:09said if you had large or heterogeneous
1:05:10buyers then it's going to be really hard
1:05:12to like parcel up the market so for
1:05:14example in
1:05:16Peru uh the government was accused of
1:05:19facilitating collusion in an auction by
1:05:22dividing the country up into three
1:05:24segments when there were three produc
1:05:25users of the product so each could take
1:05:27one whereas if you had only one thing
1:05:30that you were bidding for then the
1:05:32companies would find it really hard to
1:05:33collude because one would be the winner
1:05:35and the others would have to be losers
1:05:37right uh also large buyers can possibly
1:05:40try to break up the cartel if they
1:05:42realize it's going on try to play the
1:05:44guys against each other whereas if
1:05:45there's small homogeneous buyers they're
1:05:47going to have really hard time
1:05:48coordinating themselves to fight back
1:05:51against the cartel and it will be really
1:05:52easy to chop things up finally to fit
1:05:54all the things
1:05:56heterogeneity of the products and the
1:05:58firms makes it harder to collude because
1:06:00it's because there's all these different
1:06:02guys are going to have different
1:06:03information about exactly what they're
1:06:04producing and it's going to be hard to
1:06:06come up with like an equitable agreement
1:06:08that everyone is on board with without a
1:06:10lot of
1:06:11communication price transparency if it's
1:06:14clear what prices firms are charging
1:06:15it'll be easier for them to collude
1:06:17right but if prices are opaque it will
1:06:21be harder for them to collude because it
1:06:23will be harder to know when one firm has
1:06:25has defected they might offer say secret
1:06:28discounts to one of their customers uh
1:06:30and the other firms might not be able to
1:06:32figure that out in Industry um and by
1:06:36the way this is one reason why the
1:06:38antitrust authorities are often
1:06:39concerned about industry associations
1:06:42that like collect data about the
1:06:44industry because it might make it easier
1:06:46to collude Industry
1:06:48concentration uh helps reduce the
1:06:51tracking problem uh because there aren't
1:06:54as many people to keep track of and one
1:06:56firm won't have a temptation to like
1:06:58break out from being this little firm
1:07:00and grab the whole Market because
1:07:01they'll all have a stake in the market
1:07:03doing well the more demand fluctuates
1:07:05around the harder it's going to be to
1:07:07figure out what's cheating and what's
1:07:09just natural
1:07:10fluctuations um the frequency of
1:07:13interaction makes it easier for firms to
1:07:16detect uh uh things sooner so like the
1:07:20more like if we were in bidding the more
1:07:23often we have uh bids the easier it is
1:07:26to be to is going to be to keep track of
1:07:28things or if sales figures come out
1:07:30frequently whereas if we only learn
1:07:32about things with a long delay then
1:07:34firms will have an incentive to undercut
1:07:36the collusive agreement and um while
1:07:39they can uh and um won't be too worried
1:07:44about punishment by other firms growing
1:07:47demand helps uh as Andrew said and
1:07:51declining demand hurts because if demand
1:07:52is declining you want to grab everything
1:07:54you can now
1:07:55which will break collusion uh rather
1:07:58than worrying about the fact that you
1:08:00might get punished in the
1:08:02future okay so all of these factors
1:08:06determine the extent to which firms are
1:08:09going to be able to deter uh their
1:08:12members from uh cartels will be able to
1:08:16deter their members from colluding and
1:08:18most of that deterrence happens through
1:08:19some form of a price War right where as
1:08:23I said you might flood the market or
1:08:25otherwise really reduce prices in order
1:08:26to try to hurt the other firms so one
1:08:29simple way to summarize this is firms
1:08:31conjectures about if they take some
1:08:34action what how the other firms will
1:08:36respond right
1:08:39um and uh exactly what firm's
1:08:43conjectures will be of course depends on
1:08:46stigler's factors if I expand my
1:08:48quantity do I think the other firms will
1:08:49punish me by expanding their quantities
1:08:52or you know be nice and actually reduce
1:08:54their quantities in which case that's
1:08:55going to encourage me to be more
1:08:57aggressive right so this is uh a model
1:09:01that incorporates this explicitly is
1:09:03called the conjectural variations model
1:09:05and these usually use some parameter of
1:09:09uh how much I conjecture other firms
1:09:12will change their price when I change
1:09:13mine um to try to capture the extent to
1:09:16which firms uh anticipate being punished
1:09:20right um and the conjectural variations
1:09:25uh is sort of a broad framework that
1:09:26incorporates all of the theories because
1:09:29you can Nest Bertrand Corno and all
1:09:32these forms of collusion into just
1:09:34different conjectures about what the
1:09:35other firms will
1:09:38do okay so
1:09:41um the uh We've now seen a bunch of
1:09:45different sources of firms Market power
1:09:49in Coro Market power comes out of having
1:09:51few firms when they're differentiated
1:09:53products it comes out of the fact that
1:09:55prices will be above cost to the extent
1:09:57that people have this Transportation
1:09:59cost that they view the other products
1:10:01as different right we saw that as
1:10:03Transportation costs went up firms
1:10:05prices went up also if we have search
1:10:08frictions uh it can also happen if firms
1:10:10have heterogeneous costs all of these
1:10:12things can be sources of Market power um
1:10:16and Market power can be particularly
1:10:18severe if there are complementarities
1:10:20between monopolized products as we'll
1:10:22talk about in lecture uh 16
1:10:26um and but for welfare and incidence
1:10:31it's going to be the level rather than
1:10:33the particular source of Market power
1:10:35that uh is going to be important and a
1:10:38way to summarize the degree of Market
1:10:39power is the degree to which pecuniary
1:10:43versus real effects are
1:10:45internalized so uh let's consider this
1:10:48in the case of um symmetric firms uh
1:10:53we'll talk we won't get to talk about
1:10:55asymmetric firms but the analysis is
1:10:57pretty
1:10:58similar um when a firm changes any
1:11:02strategy that it has this has basically
1:11:04two effects on profits in the industry
1:11:08uh one that's uh basically they
1:11:12correspond to two different types of uh
1:11:14sort of externalities or effects that we
1:11:16generally talk about Philip what what
1:11:18are those two effects um if
1:11:22it look uh if it assumes that the other
1:11:25firms of going to just fix a quantity if
1:11:28it lowers a price then it's going to cre
1:11:31a pecuniary externality May transferring
1:11:33from the the consumer uh if
1:11:38it and by raising it a quantity and uh
1:11:41taking market share that's a real
1:11:44externality on the other firm because
1:11:46it's taking uh profitable units yeah so
1:11:50we can actually just like put all those
1:11:51things together into a set of real
1:11:54effects that the firm has and a set of
1:11:56pecuniary effects right the real effects
1:11:58that it has are the changes in its
1:12:00quantities times the markup so the
1:12:03changes in all any industry
1:12:06quantities multiplied by the markup
1:12:08right those aren't mediated through
1:12:09prices so they're real effects on the
1:12:12other hand it can have pecuniary effects
1:12:15of changing
1:12:16prices uh and then that will be
1:12:19multiplied by the quantities right so
1:12:20the two effects that you can have on the
1:12:22industry are changing quantities
1:12:24multiplied by markup
1:12:25and changing prices multiplied by
1:12:29quantities um and I'm out of time so I'm
1:12:32going to come back and finish this up uh
1:12:34at the start of the next uh lecture

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