nm0785: on this i've printed it off in a machine which was a clever machine 
'cause it 'cause it's given you the the home page address on this thing as well 
okay so what i advise you to do is to go to the home page for this course to 
find it either straight from this address or just the department's home page my 
home page there's a link in there to this M-S-C labour market economics home 
page okay so let me so i thought this would be a non-paper course it's just all 
going to be an electronic course and then i thought well you can't not give 
handouts and when when people come round universities doing teaching quality 
assessments all they do is they er they don't look at films like this they er 
all they do is they er they go to filing cabinets and they flick through filing 
cabinets and they want to see lots of handouts okay so i've had to do a handout 
nm0785: now to some extent because i've just downloaded it all you know you n-, 
you now need not go and look at the home 
page 'cause you've got it all here but what i'm going to be tr-, what i'm going 
to be doing as i go through the course is sometimes i'll be saying i'm not 
going to cover this in the lectures it's and it might not be fully explained in 
the in the download of it because i've updated the home page so periodically i 
will be adding things to the and and updating the home page when i do that i 
will try and put within the home page er a recent edition blinking er icon that 
s-, that that warns you that there is something new that you might want to look 
at so it might be something that you want to keep up to date with to some 
extent and indeed this relates what i've just given you now relates to this 
first topic i'll say a few words in a minute about the course outline i'm going 
to go through in these five weeks but this relates just to this topic er over 
Christmas i spent a good fortnight of my time putting all this together on the 
home page which is a slightly tedious 
business er i haven't yet got round to putting all the material in for topic 
two but i will be doing that hopefully before next week er and for topics three 
four and five it m-, er as my time becomes more and more precious through term 
rather than through Christmas and New Year et cetera my ability to deliver on 
my promise to have everything on the home page might become less and less 
credible so er by topics three four and five finishing off the course it might 
simply say here's a link to a few of the things er but it's n-, might not be as 
complete as this but i intend it th-, i intend that it should be okay so that's 
all by way of of introduction er so let me turn now m-, to more somewhat more 
substantive matters albeit still by way of some introduction if you turn d-, in 
this handout to the third page of it that gives you the course outline and i've 
indicated here that we're going to be having five lecture topics now they might 
not correspond exactly because of my inability to time 
things perfectly to each of our five meetings in fact some of these topics in-, 
inherently are bigger than others so for example this lecture one material that 
i'm going to to motivate in a few minutes er is going to certainly run into 
next week and i'd suspect that it will probably run into the fu-, first full 
hour of next week trade and wages will then occupy the second part and maybe 
just kick into week three and as we go through the topics become a bit smaller 
so we'll catch up with ourselves hopefully and cover all this material the 
first four topics are all pretty much integrated around the central theme and 
the theme is what determines wages in labour markets especially labour markets 
where there was imperfect competition both on the labour market side in terms 
of the presence of trade unions or other forms of bargaining by workers and 
also imperfect competition on the product market side now that's a s-, a theme 
which has still has relatively 
little attention in the literature i i'll say a few more words about that in a 
minute so that's that's the main theme in a sense within that theme we say well 
this imperfect competition in the product market has an international 
competition element as well so product markets are typically internationally 
competed increasingly through globalization regionalizing of econ-, of of 
product markets er and through int-, in a European context through the 
increasing ec-, economic integration that we're seeing in a global sense but al-
, but er specifically not least after the er the Euro was introduced in a i-, 
in a European context and i want to address questions to do with how that 
international context of product markets especially that increasing integration 
of product markets in the international context how that impacts on labour 
markets er wage determination in particular and of course the endogeneity of 
that how those labour market institutions and labour 
market processes themselves shape the kind of influences that we'll expect to 
see from economic integration so much of that focus will be on a in a in a U-K 
European context but bearing in mind that there are analogies for f-, for North 
American labour markets er which we'll also be bearing in mind another aspect 
of that trade and wages literature of course is that that we we know that in 
the U-K and in the North America there have been tremendous growth in wage 
inequalities in in in the nineties perhaps starting earlier than that which in 
the wider European context has not seen the same impact er on wage inequality 
but there have been other impacts in terms of unemployment in the way that 
labour markets have adjusted and we want to address that question of to what 
extent have these changes in the labour market outcomes wage inequality and 
unemployment to what extent do those reflect the changing nature of trade that 
we're seeing in product markets or that they have 
other causes and that will be our our second topic the third a-, and we'll be 
mostly focusing now on things to do with empirical evidence in the third topic 
i'm going to say er let's look at some recent models of the economic theory of 
trade unions in the context of international competition but in which we also 
look explicitly at international trade in the theoretical models er lecture 
four then still has that same theme of thinking about er er wages and 
institutions like unions and and like imperfect competition and more explicitly 
says well are these things of unions are these institutions are they 
exogenously determined do we just say some labour markets are unionized let's 
think about the impact of that or shouldn't we have more of a r-, of a role in 
saying well what determines whether we'll observe different kinds of bargaining 
arrangements in different labour markets so we look there at union formation er 
in a eu-, in a U-K context we ought to look at the 
question of well this formation of unions this issue of whether unions are 
present or not isn't only to do with a supply side response by workers wanting 
to form unions but it might also depend on the attitudes of firms in whether 
they're prepared to accommodate unions and and in the U-K context that means 
looking at the issue of recognition the issue of whether firms recognize unions 
for the purposes of bargaining with them in the determination of wages and or 
other conditions that's very relevant as we as w-, at the moment because the 
new Labour government is proposing big changes in the way in which unions er 
can obtain recognition for the purposes of bargaining er in the U-, in the U-S 
for a long time there's been a long literature now on the fact that workers in 
the f-, er through organizing elections can er can have a legal right to have 
recognition by their by their employers in the U-K there haven't been there 
hasn't been that kind of legislative 
environment and that's what's being introduced so we'll look at the context for 
that in terms of the li-, er any literature on recognition and a related issue 
to that is what determines why individual members might want to join unions er 
to the extent that unions are a public good or or a collective good then 
there's a there's a dilemma for for economic theory to explain why unions form 
let let me make that a bit more concrete suppose we're we we are a workforce 
the the eight or nine people of us in this room are a workforce er then we can 
all agree that jointly we might want to get together and form some some kind of 
bargaining unit let's call it a union might not always be formalized through 
channels like unions in the belief that if all of us in this workforce are are 
a m-, are a part of this group then our collective bargaining power is greater 
than our individual bargaining powers depending upon the nature of the work we 
do perhaps but if that is 
the case then we can hope that by exerting that kind of bargaining power we can 
raise our wage if we're able to do that typically in labour markets any wage 
increase that we're able to bargain is then bai-, paid to all the members of 
that workforce not only to those people who have got themselves together er and 
and obtained through bargaining that wage so that generates a free rider 
problem for each and every one of us each one of us thinks well i'll let the 
other guys get together and spend their evenings and and their resources on 
forming this union and maybe also risking the wrath of employers depending on 
the attitude of of firms to unions and if they're successful in raising the 
wage i will then have a higher wage as well without incurring the costs so 
there's especially when there's a large workforce not when there's a small 
group like this perhaps but especially when there's a large workforce that kind 
of free rider incentive that kind of 
prisoner's dilemma problem can undermine the generation of u-, er of unions of 
bargaining groups and so we'll be looking at questions to the ex-, er about 
have y-, have economists in the literature adequately explained that kind of 
thing and that's particularly important in a context in which union membership 
in economies like the U-K and in Europe generally er have observed such 
dramatic changes in the in the kind of levels of membership U-K is not 
necessarily representative throughout Europe but in the U-K in nineteen-seventy-
nine something like fifty-five per cent of all workers were members of trade 
unions anyone know for the figure for nineteen-ninety where are we now nineteen-
ninety-nine roughly 
sm0786: thirty 
nm0785: yeah it's possibly even less than thirty per cent around twenty-five 
twenty-seven per cent that's a dramatic change that's happened in a number of 
European countries it's not happening in all European countries indeed there's 
a literature on the 
diversity and the causes of the diversity in union membership across European 
countries and not only the diversity in the level but the diversity in the 
pattern of change and that's something that we'll address in in topic four that 
then finishes the theme of of wages bargaining institutions imperfect 
competition er and in er and in some ways it it finishes the course and it 
might occupy all five of our meetings er but i'm wanting to have time to cover 
lecture five which if i find that our time is squeezed out by the other 
material becoming larger than than we in-, intend now i'll offer as a on a 
purely voluntary basis an additional lecture where i cover two other aspects er 
which are very relevant to current policies the first of those is what i call 
here er the analysis of monopsony er now the analysis of monopsony has A a very 
long tradition er and B a more recent tradition in terms of models of dynamic 
monopsony but i'm not concerned with either of those 
i'm concerned with the issue of explaining not levels of employment and wages 
but the number of hours that people work at the moment in the European Union 
and impacting perhaps exclusively on the U-K you may well be aware that there 
is an E-U directive on maximum hours legislation which proposes a maximum of 
forty-eight hours per week er as a as a required contractual maximum by firms 
on workers firms and workers will be entitled to negotiate voluntarily and 
jointly hours in excess of forty-eight hours but firms will not be legally 
allowed to require workers without that kind of bargaining or voluntary 
contracting er it will they will not be require able to require workers to work 
for more than forty-eight hours per week now in many European countries that's 
irrelevant 'cause no one works that or very very few workers work that number 
of hours per week but the U-K is an outlier at least in Europe for having a 
very large number of workers who are working very long 
hours and so i'm going to be concerned with addressing the question of why 
might workers be working very long hours and what might be the impacts of br-, 
introducing legislation on that and the context for examing that er examining 
those kind of issues will be er a comparison or a contrast of competitive 
models of labour markets with monopsonic models of labour markets in that 
context and and er underlining the emph-, the importance of that kind of issue 
in terms of that regulation of of eur-, of labour markets within Europe and 
impacting perhaps exclusively on the U-K at a time when other labour markets in 
Europe are bringing in national legislation to bring in maximum hours much less 
than that more like forty thirty-eight or even thirty-seven hours in the case 
of France Italy and Germany all through different methods some by being imposed 
by government some by being er voluntarily er negotiated through union and firm 
kind of arrangements er but at the same time as 
that's happening in the U-K we also know that the new Labour government is 
bringing in minimum wage legislation which is another kind of regulation on the 
labour market i'm interested in the combination of those two forces on on 
labour market outcomes in terms of wages hours worked and employment okay so 
that's one of the er two issues i want to cover in lecture five and the second 
issue i want to look at is more to do with er er it's a r-, er a rather 
narrowly U-K focus and it's geared around some work that i'm doing with Jeremy 
Smith in the department er in which we're looking at evidence on U-K students 
and addressing questions like er does your does A your degree performance but m-
, perhaps more importantly for our focus on this course do your earnings after 
graduation vary very much with the following kinds of characteristics firstly 
which university you went to so is there a big premium on going to some 
universities and not others secondly the subject you've taken 
is there a big premium for economics versus business studies or whatever er and 
thirdly perhaps more interestingly to what extent do your does your labour 
market outcome depend upon your personal characteristics er age and gender 
being er marital status being one set but others being er your schooling 
schooling information prior to university so does it depend on what kind of 
school you went to and are there big differences for example between private 
schools and state schools in your labour market outcomes even for those people 
who graduate does it also depend upon the degree class you obtain er and does 
it depend upon demographic characteristics or social background characteristics 
such as the occupational background of the f-, of the parental background from 
which you you come so that's one set of issues related to that issue is er how 
can we explain different performances in the labour market across different 
universities if we observe a big premium for 
going to Oxbridge rather than to other universities is that because of some 
kind of signalling in the labour market some kind of discrimination maybe in 
the labour market or is it to do with er different characteristics of those 
universities which can be explained which aren't some kind of residual to be 
attributed perhaps to discrimination okay so those are the things to do to do 
in lecture five okay so i've spent quite a bit of time motivating lectures two 
to four to five and had er s-, said very little about lecture one so now now 
let's get down to the business of looking at the material for lecture one so 
this material for lecture one and hopefully this is going to be a sufficiently 
large font size o-, our our heading our title is wages bargaining and product 
market competition with namex in the first part of er the academic year in this 
on this course in part one 
you have spent er one part of your course looking at wages and bargaining so i 
don't intend to replicate that kind of thing my focus will be more on saying 
well let's extend that analysis of wages and bargaining to a context in which 
product markets are not necessarily perfectly competitive nor necessarily 
monopolistic say a bit more about why i'm going to do that in a moment this m-, 
m-, material on lecture one is going to be split into two one-A looks at the 
theoretical motivation for wh-, why we might be interested in this theoretical 
issues and then part one-B we'll look at the empirical evidence on these kinds 
of issues that we're going to be motivating in this hour i'm going to be 
focusing exclusively on theoretical motivation sometime in the second hour i'll 
get round to empirical evidence is there a problem in terms of 
sm0787: yes 
nm0785: visibility or the handout 
sf0788: no 
sm0787: no it's er 
sf0788: it's different 
sm0787: 
it's a different it's a bit different 
nm0785: it's a bit a little different from this is that right er 
sf0789: it is different 
nm0785: i don't think it is we're doing lecture one product market influences 
sm0790: 
nm0785: er on wages okay 
sm0790: oh okay 
nm0785: different way of saying the same thing sure okay and then we're looking 
at the theoretical motivation sure er a general point we're a small group this 
must be interactive so do raise issues and that's why i was looking for the 
facial expressions okay i'm very keen to have this interactive and respon-, 
okay so raise an eyebrow at your peril 'cause i will ask you to say what the 
question is [laughter] 
om0791: may i raise a point 
nm0785: yeah of course 
om0791: er sorry is this weeks six to ten there is that 
nm0785: yep er that's weeks to s-, er six to ten of this course 
om0791: ah 
nm0785: er the students have already taken weeks 
one to five 
om0791: ah right 
nm0785: of the course sorry it doesn't relate to term time it's [laughter] it's 
a good point it it's 
om0791: no 
nm0785: potentially very confusing er okay er so in this issue of theoretical 
motivation er i'm going i'm ar-, i'm arguing that that there are two questions 
which are going to concern us for this part of the course and one question is 
what generates rents if we're looking at what determines wages and we're saying 
we're not just going to assume that wages are given by competitive levels but 
they might differ from competitive levels then we ha-, have to explain why 
there might be rents which enable workers to have wages in excess of 
competitive levels so the question i-, i-, w-, wh-, a question which is very 
important is what generates rents with namex in in the previous weeks of this 
course you'll have spent quite a bit of time looking at issues to do with rent 
sharing 'cause that's 
something which namex's done a lot of work on and and one of his assumptions is 
that there are rents and then a-, and he m-, and he demonstrates using a lot of 
evidence er about the existence of these rents and the and speculates what are 
the determinants of those rents so he's looked a lot at rent sharing i'm going 
to be initially asking the question well what does what generates those rents 
but primarily for us then to address the question of assuming those rents exist 
under what conditions are workers best able to capture a share of those rents 
'cause you can imagine situations in which firms are generating huge rents 
because of monopoly power but that same monopoly power or reasons associated 
with that monopoly power might give those firms a great bargaining power over 
workers and prevent those workers from ex-, ec-, from generating er a share of 
those rents from capturing a share 
of those rents okay indeed it might be the case that firms which are very 
powerful in their product markets also exert enormous m-, labour market power 
and com-, and er which enable them to pay wages below competitive levels so it 
it doesn't follow that just because rents exist workers are going to be 
capturing a share of them so we'll be er addressing the question of what ena-, 
under what conditions are workers best able to capture a share of any such 
rents which firms are are are are are are re-, are receiving so what are the re-
, sources of rents on the first of those two questions what are the sources of 
any such rents the most obvious starting point is to say that imperfect 
competition in the product market can generate rents two forms of product 
market imperfect competition would be monopoly and duopoly models of unions the 
economic theory of the trade union almost exclusively focuses on monopoly okay 
you will have looked at a number of of 
models where you s-, you say that there's a union downward sloping labour 
demand curve wages employment and maybe unions have got s-, er in a monopoly in 
a model unions are trying to er aim at this utility maximizing point with a 
wage in excess of some competitive wage and so they're extracting some rents in 
the form of wages being higher than they otherwise would be and those rents are 
pretty much assumed to come from monopoly power by firms or if not from that 
from a second source of p-, of rents and this is arguably even more common in 
the literature this this source being the diminishing marginal product of 
labour okay so i-, in models like that you've the argument goes that the firm's 
profits are equal to price which is parametric exogenously given at some 
competitive price level times output output being some function of labour 
inputs minus costs 
themselves some function of wages and so often the argument goes that the price 
is parametric price is exogenously given at some competitive price level and 
then what's enabling workers to have wages above a competitive level is that 
the production function exhimits exhibits diminishing marginal product of 
labour and that then is used to er to generate the result that wages set by 
unions or bargained between unions and firms might be greater than the 
competitive level now if you think about that model it's not very satisfying 
from an empirical point of view because if the product market is competitive 
then we're going to assume pretty much that at least even in the medium term 
but certainly in the long run firms are not going to be able to persist in 
paying wages above competitive levels okay so a much more satisfactory it seems 
to me motivation for the existence of rents being used to share is the 
existence of 
imperfect competition in the product market and monopoly is an extreme version 
of that which the literature has taken on board and has focused on when it's 
not adopted this kind of approach but of course we know that monopoly is a 
rather extreme form of market competition perhaps no more likely than perfect 
competition and it strikes me that oligopoly er i have in-, indicated here two 
firm oligopoly but perhaps m-, i should s-, more generally say oligopoly is a 
more likely context to explain the existence of rents being as we capture them 
so what i'm going to be wanting to do quite early on in i-, in this hour is 
look at extending the traditional model of union- firm bargaining to a context 
where there's oligopoly and and a reason for doing that is because that forces 
us to look to think more seriously and more formally about interaction between 
labour markets and product markets which these kind of models ignore because if 
we're dealing either with perfect competition where price is 
parametric or with monopoly unless we're thinking about entry deterrents then 
there there's no strategic behaviour going on in the product market and perfect 
competition there's no strategic behaviour because you are a such a small part 
of the big product market you needn't think about the impact of your behaviour 
on other firms and if you're a monopolist there are no other firms so again 
there's no strategic behaviour so those two traditional approaches free us from 
the requirement to or more critically don't encourage us to think more formally 
about the importance what will be in the real world the important interactions 
between labour markets and product market outcomes in terms of strategic 
behaviour let me give you a more concrete example on all of that if we are a 
workforce if we are a unionized workforce and we are determining what wage to 
set do we merely think in terms of the wage and employment combinations in some 
way abstracted from the the 
wider world outside us or do we recognize that the higher is our wage the less 
potentially at least the the the er potentially at least the higher is our wage 
the less competitive will be the product market position of our firm in its 
product market decision making so we perhaps ought to be aware as a union of 
the dangers of setting a high wage er in terms of the impact that that will 
have on the product market competition er competitiveness of the firm that 
we're bargaining with er and so there are strategic behaviours that we should 
consider and that's what we'll analyse in a few moments er course other f-, 
other forms er of the generation of rents would include imperfect competition 
in the labour market rather than the product market okay so it might be for 
example that firms have monopoly power which is generat-, monopsony power which 
is generating rents for them and there is an increasing literature on monopsony 
power or other v-, 
other forms of imperfect competition in the labour market might you might 
interpret efficiency wage models and even insider-outsider models in terms of 
imperfectly competitive labour markets okay and see those as forms of of rent 
generation but i'm going to pretty much exclusively concentrate on this issue 
of oligopoly so what i want to do er within this theoretical motivation is look 
at actually three models of union-firm bargaining in a wider context of 
imperfect competition in the product market in order for us to get some feel 
for the kind of important issues that are that are going on there so let's look 
at the three models the first of and i label the models one-one-one one-one-two 
and one-one-three er and the first two of these are closely related to a paper 
published by Steve Dowrick in the Economic Journal of nineteen-eighty-nine okay 
so let's think first about er th-, the model one and model one is 
sketched on the home page a copy of which you've got er if you click on your 
handouts which means in this context scanning just a few pages you'll find 
something called model one- point-one- point-one and i will just er go through 
the key points of that on the board and it will be easier once i discover where 
the board rubber is 
nm0785: so thinking about this first model okay we're going to er make a number 
of simplifying assumptions the first one will be that product demand is linear 
so you'll er so we'll write product demand of some linear er indirect demand 
function where X is market outputs of a homogeneous commodity in model two 
we'll look at differentiated commodities and see that that adds something to 
our analysis informs our analysis but for now assume a homogeneous commodity X 
er is the quantity of that and that is being supplied by N firms we're dealing 
initially with an N 
firm oligopoly so the market output X is the sum of the outputs of all the 
individual firms which we'll label I I going from one to N we'll assume a 
constant marginal product of labour and we'll take that as our numeraire in 
other words marginal product of labour is equal to one the reason for doing 
that it simplifies things very nicely we can just label outputs and employment 
as the same thing it means output is e-, equals employment one unit one unit of 
labour generates one unit of output we could easily ec-, generate out from that 
it wouldn't it doesn't change things too much so long as we keep the assumption 
of constant marginal product of labour we're going to assume a two stage game 
in which in stage one each union and firm pair 'cause we assume that each one 
of these N firms is bar-, i-, i-, confronts a local union so we're going to 
have decentralized bargaining between each union and firm pair we'll 
call it a union-firm bargaining pair so each union-firm bargaining pair sets 
the wage in that in that for that pair so W-I for f-, p-, pair I as a resul-, 
as a as a result of bargaining bargaining being described in the in a 
traditional right to manage model okay so that there there's bargaining going 
on over the wage but the firm is then going to be at some point it'll actually 
be in stage two is going to be setting employment autonomously in other words 
the union has no influence over employment in this model when each union-firm 
pair sets its wage W-I it it takes as given in a kind of Cournot way Cournot-
Nash way it takes as given any wage set in any other union-firm bargaining pair 
so it doesn't take on board in a kind i-, in er in any kind of Stackelberg way 
the er the choice being made by others the impact of its choice on others okay 
in in er we we can exten-, we can easily extend that in fact i might as i'm 
doing this 
extend that er okay so let's let me write that down in that way if each firm is 
spending let's let's say that more generally actually the Cournot-Nash 
assumption of course is a w-, a specific form where you assume that your action 
doesn't affect the actions of others you take the actions of others as given 
more generally we could use a conjectural variation approach which many people 
don't like and if you don't then just set the l-, conjectural variation 
parameter equal to zero and assume you're dealing with a Cournot model the con-,
a conjectural variation pr-, approach would say that when we're setting as a 
union-firm pair when we're setting our wage er we allow for the possibility 
that the choice of our wage influences the wage choice of the other union-firm 
pairs according to some conjecture captured by the conjectural variation if 
that parameter is zero it means you assume that your wage doesn't affect the 
others 
and that's like adopting a kind of best reply approach a Cournot approach where 
you just reply to if there's a choice in yours not taking into account how your 
wage impacts on the others 
sm0792: in the model which this kind of er game result just in the symmetries 
in in which er the two different are way 
nm0785: okay what i'm going to be assuming for these purposes er is that all of 
these union-firm pairs are identical that's is that the part of the point 
you're making that we that they're s-, that so the equilibrium we're going to 
generate will be a symmetric equilibrium and indeed at one point in the 
analysis we're going to use that to simplify the the solution to the problem 
but we're not going to be imposing it on the problem from the beginning 
sm0792: 
nm0785: we er er in er it's a good point i'll bear it in mind as i'm going 
through the model to try and explain what i mean by that er so the result will 
be one in which er we get symmetry but we can't impose right from the beginning 
the knowledge that in a symmetric 
equilibrium wage will be the same just as when you're looking at er a simple 
Cournot product market story you know that in equilibrium in under symmetry er 
the the output choices of the two firms will be the same but you don't impose 
on the beginning you let that come out of an er of an equilibrium solution to 
the model and that's what we'll be doing here okay so we could have a a a 
general convectj-, conjectural variation approach and indeed in model one-one-
one that's that's what we're going to do okay so that's what's that's how the 
wages are being determined once the wage has been determined we then move into 
stage two in which with wages we could even say with the full vector of wages 
'cause of course this is generating a vector of wages W-I I going through one 
to N the vector of of wages er will be determined from stage one so it's been 
predetermined and firms then choose output and of course that's 
the same as choosing employment on this assumption of constant marginal product 
of labour especially with our numeraire assumption firms how do firms choose 
output well we're going to adopt again the conjectural variation approach which 
just generalizes the Cournot-Nash approach of of generating best reply 
functions and again if you don't like this idea just assume that the 
conjectural variation of it is zero er and look at the think about generating 
the Cournot-Nash equilibrium 
sm0793: do you mean firms will either choose to compete on price or 
nm0785: we're going to assume the competition is on quantity okay so we're not 
going to be thinking about Bertrand and in fact if we did we know that we'd 
just get to the competitive price and so there'd be no price mark up and 
there'd be no wage mark up unless we bring in some k-, other kinds of 
constraints to prevent that process unravelling in that way 
sm0793: mm 
nm0785: yeah er okay so that i think describes 
the the key assumptions and what i want us to do now is just to sketch er the 
method of of solving such a s-, simple model er and we've got this two stage 
game going on of course we know that backward in-, by back-, we solve it by 
backward induction we think first about stage one reason for doing that of 
course is that when unions er sorry let's think about stage two i've got i've 
written these in a strange way er we're going to think first about stage two 
because when unions and firms are choosing their wages they need to be doing 
that in the context of knowing what the implication will be for the stage two 
decision okay so we solve first stage two which essentially means we're 
generating labour demand functions and it's against those labour demand 
functions like these that firms and unions are then bargaining some subgame 
perfect wage so that we're getting subgame perfect Nash equilibria from this 
okay so we first er solve stage two by backward induction that gives 
us the er the labour demand curves against which the st-, the er we can analyse 
the stage one gain for wage determination okay so let's let's do that i'll 
adopt a primitive method for cleaning the board 
nm0785: so if we er then think first about stage two for employment 
determination i'm er i'll just go through this now in in the next four to five 
minutes and then we'll stop and have a break okay so stage two and you can 
follow this from from the handout if you if you prefer we're saying let's think 
about the decision bay-, being made by an individual firm I that firm is going 
to be er tr-, trying to maximize profits given by pi-I which of course is 
simply price minus wage costs of that firm I times its output level X-I which 
of course is also its employment level and price we know is being given by this 
linear demand function where market output is the sum of the outputs of the 
individual firms so we can substitute these two equations 
into the profit equation and from the point of view of the handout that's 
giving you equation four and when we then maximize profits with respect to the 
choice of output by firm I so when we look at D-pi-I by D-X-I we get equation 
five which is A minus W-I A of course is the reservation price from the product 
demand equation so okay so always be thinking about A as the reservation price 
intercept on the vertical axis in a price quantity diagram er minus the wage 
that the firm has to pay minus B which is the slope parameter from the market 
demand equation times the following thing X-I times D over the sum of X-Is and 
i'll explain this in a moment D-X-I plus the sigma X- I I going from one to N 
and that's the first order condition for product maximizing by the firm er in 
this way that's equation five from the handout okay you it's relatively 
straight forward to to to to demonstrate 
this for yourselves i'll leave that as an exercise if anyone wants any guidance 
on it by all means at any point come and see me i have a generally a an open 
door policy for people on this course so come by my office any time you like er 
then what what this is saying is that er if we if we rearrange it it's becomes 
easier to to see it er i guess well let's just think about it from this point 
of view W- I of course is the firm's marginal cost of an extra unit of output 
terms of having to employ an extra worker and and then the rest of the thing is 
giving us the the marginal er revenue to the firm from an extra unit of output 
and that's being made up not only of the price it's going to obtain from any 
increase in its own output but it has to bear in mind how a change in its 
output affects the output of other firms so this is where the conjectural 
variation parameter's going to come in and let's let's see that this thing here 
oops i've missed 
a bracket this thing here i'm saying is the er can be written as one plus 
lambda and let me just say why that is and it's because this change in the sum 
of all the Xs can be broken down into the change in firm I's output plus the 
change in the summed output of all the other firms so let's call that the sum 
of the X- Js where J goes from one to N but excludes firm I itself all over D-X-
I and it's clear that D-X-I over D-X-I is one that gives us that one here and 
lambda which we're defining as the conjectural variation parameter is telling 
us how the firm believes at least the out-, the sum of the output of all the 
other firms will respond to a change in firm I's output itself under the 
Cournot assumption lambda is zero of course because you take the output of the 
other firms as given okay so lambda is zero is is going to give us the 
special Cournot-Nash best reply function approach okay so that's the first 
order condition for this particular firm and of course there are N such first 
order conditions because there are N firms so we get N first order conditions 
when we solve those which is actually very very straightforward okay and the 
easiest way to solve it is is the following when you look at this in-, this 
firm I's first order condition you'll see that what we're wanting to do is to 
see how its output X depends upon the vector of wages okay its output X to 
maximize its profits we're just going to be two minutes finishing its its 
optimal choice of X is clearly going to depend upon its own wage as you'd 
expect in in a monopoly model of any model that would be true but what's 
happening here is that X is also going to depend X-I is going to depend er on 
all the X-Js and the X-Js of course will depend on the W-Js so 
what we want to do is to solve this 
sm0794: sorry 
nm0785: just be two more minutes what we're going to be doing is to to so-, to 
solve this for the X-I ex-, er getting rid of all the X-Js so that X-I can be 
expressed in terms of of stage one information the wages okay so what we want 
to do is to solve this first order condition to have the profit maximizing 
choice of X-I expressed not in any X-Js not in any stage two outputs but in 
terms purely of the vector of stage one information the wage information and 
it's easy to do that because er the sum of all the X-Is just comes by summing 
all of these first order conditions and then cancelling the sum of the X-Is or 
the at least the X-Js to leave us with X-I in terms of all the wages okay i'll 
leave that as an exercise for you to think about but it's actually once you've 
got it it's a nice little trick to do it again come and see me if you want a 
bit of guidance on that and that's where i'll resume af-, after a brief break