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Mandos: Jim Rootham was advocating violence. That's what saying I "deserve a baseball bat between the eyes" means.

I have unpublished Jim Rootham's subsequent comments, which merely escalated the weapons.

Yes. That is thuggishness.

Okay, that's enough. Non-productive posts will get unpublished, and repeated attempts to post them will result in a banning. We're not paid enough to put up with this.

Jim, your next post better be an apology to Nick, or that last one will be your last on WCI. I'm not kidding. I mean a real apology; not "I didn't mean it" or "I'm sorry if you were offended."


"..This mean that wage inflexibility is bad, which is exactly the position that Nick is arguing the New Keynesian should not take. ...But wage flexibility is not something Keynes argued for, which is why New Keynesians are not very Keynesian at all, as I've argued. "

Again, Rowe does not AFAICT mention wage flexibility as a problem in this post: he only mentions monopoly power, which raises average wages. Some people argue that unions are bad because they increase wage rigidity, but perhaps this is wrong: most workers want to be insured from the risk of fluctuations in their income, which implies asking for (and receiving) reasonably rigid wages at least in occupations with low turnover. Also it is my understanding that most NK economists don't care much for increased price flexibility because the indivdual costs involved are very small (and hard to target), and the adverse effects can be countered with good monetary policy.

"..I don't believe in Say's law though in cases of deficient real demand- you can't and call yourself a follower of Keynes."

Perhaps you missed the reference, but I specifically mentioned Say's law as holding under perfect competition. This is just Econ 101: if you want to argue that PC with marginal cost pricing is not efficient, you really have to point to a specific market imperfection. And no, I don't see myself as a classicist because I don't think PC is a reasonable approximation, particularly in business cycle theory.

"An excess demand for money can also be called a shortfall in real demand."

Yes. But if prices were perfectly flexible, then the present price level and inflation rate would adjust to clear the excess demand. So your theory of demand shortfalls is now relying on what you called a monetarist assumption.

"..If firms slash prices, the marginal value product of labor for their goods would fall, and they would lay off workers."

Under PC, yes. In the real world? Not necessarily. Workers might be less productive, but their rigid wages are partly insurance against changing business conditions. In some sectors, they could be kept on reserve until business picks up again, and the extra expenses offset by lower profits.

"If you are arguing that prices, on the whole, are too high in recessions, then you are just arguing for deflation. That ... will hurt"

Money deflation can be offset by changes in monetary policy, though. When Keynes was writing his GT, monetary policy was very primitive and often harmful.

"... As a hint, cutting real wages will reduce aggregate demand as it decreases income."

Does it? Income is the sum of wages, profits and rents. If wages stay the same but profits decrease, that also cuts into aggregate demand, although the affected industries would change.

"We observe idle capital due to insufficient aggregate demand and the fact the installed capital is expensive to sell as uninstalled capital. It has nothing to do with the level of competitiveness."

Yes, indeed. An industry can be very competitive in a general sense, and prices might nevertheless be set above marginal cost in order to defray fixed expenses. And if economists want to model this mathematically, they have to use imperfect competition. In other words...

"Your argument implies that there could never be idle capital in a competitive industry, which is totally ridiculous. "

..a competitive industry is totally ridiculous. Well put. That's why we don't use them in modern models.

"If you think Keynes argued for imperfect competition being a major cause of recessions, show me the evidence."

Keynes could not be arguing for imperfect competition, because the distinction was not well understood at the time. Nowadays, we can tell that it is a crucial feature, and that increased market power can make things worse. This, I take to be the point of Nick Rowe's post.


Actually I thought I was being nice, I really thought you were just playing devil's advocate to stir up a lively debate. RSJ does too much in a mathematical example. You're wrong on this matter and just too stubborn to admit it.

Accounting is the mathematical basis to be considered, not economics, and accounting does not distinguish between equity paid as dividends and labor costs. They are both liabilities. And, an average of 61% of firm profits are paid out as dividends in the US... In the first three quarters of 2010, firms paid out $728.4 billion in dividends, roughly 61.0 percent of the after-tax corporate profits which can be read directly off the federal reserve flow of funds table F.4 line 12....

Unions in general would have a lot of wiggle room to negotiate a redistribution of that income without causing much of a stir... Especially because you cannot say how much of that dividend went to management owned shares given as bonuses to their salary.

The point is that wages are wages, no matter what the official title is (dividends or union benefits). Cut union wages, the balance sheet just credits a greater dividend payment to increase management salaries, the accounting bottom line doesn't change.

This is a poorly reasoned anti-union argument. There may be a well reasoned one out there but this isn't it.

RSJ: I really can't buy your assumption that workers and CEOs produce goods in fixed proportions; one CEO to every 100 workers, and the 101st worker adds nothing to output.

Nevertheless, lets run with it. If we assume both CEOs and workers are in perfectly inelastic supply, and if the number of workers born is exactly 100 times the number of CEOs born, and if all goods produced require exactly the same ratio of 100 workers per CEO, then yes, the relative wages of workers and CEOs is indeterminate.

Relax one of those assumptions slightly, and everything changes totally. For example, assume some goods are more labour intensive than others.

Again, the key point is this: will an increase in union power increase the marginal cost of the representative firm? In a monopolistically competitive model, if an increase in union power causes the individual firm's MC curve to shift up, then we get exactly the sort of aggregate demand externality that drives these NK models.

"I really can't buy your assumption that workers and CEOs produce goods in fixed proportions; one CEO to every 100 workers, and the 101st worker adds nothing to output."

OK, I don't buy it either. But I was playing in the neoclassical sandbox, trying to solve a specific optimization problem which I don't think is very realistic.

The problem is that if a manager is able to bargain down a worker, or obtain more output from that worker for the same cost, then according to your model, the firm is not willing to pay the manager more, as the MPP of the manager is unchanged.

Yet the manager is improving the profitability of the firm, and the firm should pay him more. He could threaten to leave and take his cost cutting skills elsewhere.

This is particularly acute in a model with a large variety of factors of production (e.g. you assume each person is selling a unique labor contribution, and each person has their own reservation price and bargaining power), so there are many possible configurations to choose from. But any such payments are going to result in the type of wage shift I outlined, and you don't need fixed ratio production for that.

I think we need a different model of the firm. Perhaps it's already out there -- but one in which firms have cost centers, and actively try to reduce their costs. Moreover, solving the optimization problem is costly, and firms hire people, as factors of production, to solve the problem. Those people would be managers, and according to this definition, the neoclassical model of the firm is one in which there is no management -- management is "free" -- and therefore no possibility of using your power to increase your own compensation at the expense of other factors of production.

"Again, the key point is this: will an increase in union power increase the marginal cost of the representative firm? "

Yes. Now in terms of which of these effects dominate -- e.g. a shift in the distribution of costs versus an overall increase in costs -- we can look at what happened to the U.S. The power of unions was effectively destroyed in this country, and yet where is the employment and productivity dividend?

And as we have exited the sandbox, then I think heterodox people would argue that the cost of capital is another degree of freedom, in that reduced costs giving rise to increased returns on capital could result in higher a cost of capital, rather than increased investment and output.

"The problem is that if a manager is able to bargain down a worker, or obtain more output from that worker for the same cost, then according to your model, the firm is not willing to pay the manager more, as the MPP of the manager is unchanged. Yet the manager is improving the profitability of the firm, and the firm should pay him more. He could threaten to leave and take his cost cutting skills elsewhere. "

Well, yes. A self-interested firm owner should contract so that the manager at least gets a share of the profits from better bargaining. But Nick's model is not about managers' haggling skill. When unions across the board are less able to extract rents, the gains are shared by owners, managers and consumers, including workers in other industries.

"I think we need a different model of the firm. Perhaps it's already out there ..."

Yes, in your model managers are probably in the best position to extract a surplus. But these managers compete with other firms' managers, so the surplus is dissipated through increased creation of firms. Generally speaking, the proceeds of improved resource allocation are not considered rents: they're wages of superintendence, or entrepreneurial profits.

" we can look at what happened to the U.S. The power of unions was effectively destroyed in this country, and yet where is the employment and productivity dividend?"

This is not a good argument, because there was no exogenous shift in the "power of unions". Unskilled workers found themselves at a disadvantage due to competition from low-cost foreign and immigrant labor. But the environment and milieu of increasingly stringent labor regulation which had been previously fostered by unions and 'pro-worker' policy-makers was left largely intact, and this made workers even worse off. Meanwhile, higher skill workers in most industries are largely protected from such competition by occupational licensing and similar restrictions. However, experience in a few relatively unrestricted sectors (notably IT) shows that workers in these sectors are quite well off, despite being exposed to foreign competition and low barriers to entry.

I'm not going to discuss the issue of compensation of CEO's and the like in large firms, because I think it is distracting. Yes, boards of directors have been largely captured by incumbent managers. But matters could be improved by getting rid of obstacles to hostile acquisition such as the "poison pill" and increasing shareholder activism.

RSJ and anon: that way of looking at it could be interesting though. But it might lead to rather surprising conclusions.

A sketch of a model: Assume labour is the only input. Start with a standard NK model, only with a competitive labour market. Now introduce unions, so the labour market goes monopolistic. So that's 2 models. Now introduce a third model that is halfway between the first and second. In the third model, individual firms can hire a CEO who is good at preventing unionisation. People with those skills are scarce. Assume that CEOs do absolutely nothing except prevent unions (or weaken the power of labour unions, or help resist union wage demands).

Given free entry, all firms earn zero profits in equilibrium. If, in equilibrium, some firms are unionised and some aren't, competition for CEOs between firms will ensure that CEOs are paid everything that unions could have captured. Firms will be willing to pay very high prices for protection from unions.

The paradox is that unions themselves, or rather the threat of unionisation, is what creates the demand for CEOs, and what creates very high CEO salaries, leaving less for workers.

If (non-CEO) labour is the only input in the first model, then wages will be 100% of GDP. In the second model, wages will still be 100% of GDP, but GDP will be lower, so wage income will be lower. In the third model, wages will be less than 100% of GDP, and GDP will be somewhere between the first and second model.

Nick "paine:
just sometimes,
you have a point
that is
both understandable
and good.
But not

Brilliant. Can I borrow this for my next referee's report ;-)

A bit of context: paine is the e e cummings in residence in the comments section over at Mark Thoma's blog.

I just did a quick scan - no mention of CONDITIONS. I've been reading Crooked Timber and their view is that conditions are a stronger reason for unions to exist than wages. And I'm inclined to agree. Single variable = money wages is too simple.

Nick, I was painting a different picture.

Imagine a labor supply supply function of workers that create physical output, viewed as a cumulative distribution function:

For a given wage, X, f(X) is the number of people willing to supply labor for one period for a wage less than or equal to X. Now suppose one unit of labor creates 10 goods, and that the output market is perfectly competitive, but the input market is not.

Where f(X) intersects the line P = 10 will be the "natural" labor force size if firms were price takers for labor input and did not bargain.

But now assume that the area between these two curves -- the labor surplus -- can be captured as a result of individually bargaining with each worker and paying each one only the wage that they are willing to take.

Search is the role of management, and doing this incurs costs.

If management supplies one unit of their labor, they get to draw from the pool and pick a random person, which they can either hire or toss back.

The firm will only hire someone if the wage demanded + the wage of the person hiring them is equal to 10. That's a simple model of cost minimization -- you are searching among different inputs that meet your production requirements in order to find the cheapest ones.

Management has its own labor supply curve, g(X).

Now its the war of all against all -- all firms will hire management in order to search for the lowest cost labor inputs, but by doing so, output and employment is lower than the neoclassical model predicts.

As workers begin to bargain collectively rather than individually, we get closer to the law of one price -- the labor supply curve becomes more flat so that the area between it and 10 gets smaller. That means that management wage shares fall, so we climb back down g(x) so that fewer workers are hired, and then we jump over to f(X) and obtain a lower set of wages at that level of employment.

There is some equilibrium determined by the shapes of the two labor supply curves.

But this equilibrium will have less than full employment, and all workers that produce physical output will be paid less than their MRP, due to the necessity of paying to solve the firm's cost minimization problem -- something that the neoclassical model assumes is free.

I assumed PC in the output market just to show that the this has nothing to do with the output market. The only assumptions I need are individual bargaining, non-flat labor supply curves, and a labor cost to cost minimization. Hope that make sense.

I apologize for making the remark about baseball bats. I should not have said that.

"The price of everything relative to everything must be one."

The buyer of everything has to offer superior utility to everything. This is why the price of everything is, quite ironically, exactly zero. It is also why everything is not a market commodity.

Also, the point of cartels is to make the prices sticky. This is the very powerful is/make diversion where something that is the result of very deliberate policy is transformed into a property that just happens to exist. Sort of like the animals asking the pigs "if the revolution is inevitable why do we have to do anything". The answer is STFU or you don't get tenure.

Jim: OK.

On building a macro model with monopoly power in the output market and monopsony power in the labour market. Yes, in that model, unions could/would increase employment (would, unless they overdid it). Check my earlier comments where I discuss this. I did build and publish a model like that once. It seemed a good idea at the time. Afterwards I saw that the model just didn't work. It predicted strongly pro-cyclical real wages (assuming sticky prices). It also predicted that there would almost always be an excess demand for labour at going wages. Firms would always be wanting to hire more workers. Just the opposite of the involuntary unemployment we normally see.


I think I understand the model you have sketched. It's interesting, but: I don't think it predicts what you think it predicts; I'm not sure it works empirically.

It's a model of a perfectly price (wage) discriminating monopsonist. Normally, under perfect price discrimination, you get the efficient level of output (employment in this case), but all the surplus is captured by one side. Your model is a little different, because it takes real resources to discover the reservation price. But suppose a manager has interrogated a potential hire, and discover that his reservation wage is $9.99. He will still hire that worker. Ex post, he regrets wasting his time interviewing the worker, but it's too late now. He can still capture the $0.01 surplus.

The managers' effort is a wasted resource, socially, because it only produces a transfer of rents, rather than useful output. But otherwise you get to the same competitive level of output and employment.

Empirically, it also says that firms are always on the lookout for potential hires. You would never get involuntary unemployment, where there's an unemployed worker able and willing to work at the same wage as employed workers.


"But suppose a manager has interrogated a potential hire, and discover that his reservation wage is $9.99. He will still hire that worker. Ex post, he regrets wasting his time interviewing the worker, but it's too late now. He can still capture the $0.01 surplus."

People do not consistently engage in activities that, ex-post, they regret. Or at least you need a reason for why they would.

Managers know the shapes of the curves. They know the average payout from spending a unit of labor searching, and if the expected payout is less than their own wage then they do not expend the labor unless they are willing to take the smaller wage.

Now whether they throw the person back or not is a game theory question, and the full answer should take into account diminishing MPL and MPK as well. But that's complex and I was just trying to make a simple argument about the tug of war between unions and management.

Suppose no one is thrown back that earns less than $10, and to keep the math simple, suppose everyone is willing to work for $10 or less.

The worker's supply curve is

1 + .01x, where 0 < X <= 900.

Full employment is 900 workers.

The labor surplus wedge is 1/2*(900)*9 = 4050.

The width of the wedge is 900, so the average gain from hiring one worker is 1/2*9 = 4.5. Yes, some workers will be hired for 9.99 and others will be hired for 1.01, but management understands this.

Suppose it takes .1 units of management labor to search for 1 worker. To hire all the workers would require 90 units of management labor. If management's labor supply curve is such that it is willing to supply 90 units of labor for a wage rate of 45, then there is no problem.

OK, suppose management's labor supply curve is

5 + .4x

The firm is humming alone just fine, as managers are willing to expend 90 units of labor for a wage of 45.

Then, the workers get together and decide on collective bargaining -- they do not wish to be haggled down individually. The effect of this is to flatten the worker's labor supply curve.

The new curve is:

1.9 + .009*x

But now, the gain from hiring one worker is just 4.05, not 4.5. And the gain from expending 1 unit of management labor is now 40.5, not 45.

According to management's labor supply curve, they are only willing to supply 88.75 units of labor, not 90. That means unemployment of 12.5 workers (and 1.25 managers). Yes it is voluntary unemployment, but so what? -- all workers are willing to work for less than or equal to their MRP, and no worker is rejected after being interviewed. The only crime committed by the workers is reducing the size of the search space and letting the economy operate in a more efficient way, nevertheless employment is reduced, as management is not working for free in this model.

OK, with fewer workers hired their MRP would rise, etc, and this would moderate the effect. Also, you should take into account strategic behavior -- e.g. throwing some fish back into the sea. Also, management may not be able to hire the factor for that wage -- perhaps it can only obtain a percent of the gain, and this would be a function of how talented management is, etc. Finally you would have a motivation for firms to keep some labor -- e.g. to engage in longer term contracts rather than hiring during each production period. All of that complicates the story, but at least you see the point, right?

"Empirically, it also says that firms are always on the lookout for potential hires."

No they are not. Firms are not looking for anyone -- management is. And management is only willing to search if it is worth its time to search. It has to be paid to search. Given a certain wage, it will only look if the expected gains from searching justify the wage.

Do you have any empirical evidence that shows damaging effects of unions? I don't see the point in playing around with models that show certain effects if those effects don't show up in the real world (unless what you are doing is looking for why the models fail).

Consider the following pieces of evidence:

Business publication
Scientific American
Inter American Development Bank

Do you have any that find the opposite?

Jim, the purpose of the model is not to directly describe the world, but to describe a trade-off. The "world" is the result of many of these trade-offs.

Now in the world, there seems to be several effects: people do get paid less than their marginal revenue product. There is unemployment.

How do you reconcile that to the neoclassical model?

One way is to recognize that the neo-classical model is really a partial equilibrium model in which the act of arbitrage is costless.

All the members of the walrassian auction who are evaluating bundles, putting in bids, retracting bids -- that all happens for free. It happens outside the model. None of those people need to eat or sleep as they haggle over prices.

Similarly, all the activities of firms -- deciding whether to open the plant in the low cost labor area, and how big the plant should be, that is also free.

Even though this is valuable work, and we know that people who perform this work are sought after and are highly paid, yet in the model it is apparently volunteer work. Only because it is costless can you argue that the arbitrage process drives wages and employment to the efficient level.

If you abandon that assumption, and assume that optimization itself requires resources and incurs costs -- at a minimum labor costs, but there would also be other adjustment costs -- then you end up with a different model.

In that model the marginal payment to the arbitrageur is equal to the inefficiency that remains, and as you try to remove inefficiency via optimization, then more and more resources are required to do that while the benefits of optimization decrease.

So at some point, the optimization process stops being cost-effective, and you are left with just enough inefficiency to justify the current level of optimization but no more optimization takes place.

So in a simple labor model, that means no more investment and hiring takes place.

I don't really think of this as a monopsony model per se.

Imagine that you start with many different towns, and each town has a prevailing wage rate, but they are not equal. Now firms can decide in which town to open a new plant. As long as the firm incurs costs in opening the new plant -- e.g. at a minimum, paying someone to make the decision, but also the costs of organizing and setting up the plant, as well as the time value of money lost when the plant is being built -- then the market process will not fully equalize the wages in all the towns.

That's not really monopsony, right? It just means that whatever costs are incurred in opening the new plant, these costs need to paid for by the expected wage arbitrage, and because these costs are not zero, then you cannot argue that firms will drive wages up to MRP in all towns. They will not always be looking to open new plants, once the difference in wages becomes too small.

But now you can see a tug of war between the share of revenues a firm allocates to solving the optimization problem and the share of revenues the firm allocates towards creation of physical product. This is the trade off that I am trying to describe.

If there is high variation in wages, then the gains from optimization are high, and the share of revenues devoted to optimization is higher than the share of revenues devoted to production. The firms will be spending more money investing and hiring more workers.

But similarly, if management has market power and demands high wages for optimization, then this requires, as a matter of necessity, that there be high variation in wages without a lot of investing and hiring.

If unions are able to remove the variation in wages via collective bargaining, then the gains from optimization decrease, and this must result in either management accepting a lower wage for optimization, or management reducing the amount of optimization it performs.

RSJ: I've read your 12.50AM post a couple of times. You say that unionisation would result in 12.5 workers out of 900 being unemployed. I don't think that's right. Rather, the managers would interview (900-12.5) workers, and offer the remaining 12.5 random workers a job without an interview.

Jim: The evidence you link to doesn't show that unions are good. Suppose unions were exactly like a minimum wage law. In any standard model, an increase in minimum wages would increase labour productivity precisely because it reduced employment, and because it reduced employment most of the least productive workers, and because it would be most likely to cause the closure of the least productive firms.

To give an analogy, suppose we passed a law imposing minimum rents on farmland. We would expect to see an increase in the the productivity of the farmland that remained in production. Only the best land would be farmed, farmers would use more labour intensive and capital intensive methods of farming, and only the best farmers would stay in business.

I wish I could think of some conclusive model-free test that could say whether unions were good or bad by some measure at the macroeconomic level. But even if I could show that countries with higher rates of unionisation systematically did worse, it couldn't prove anything. It might just be that countries that performed worse tended to become unionised.

Instead, the best I can do is think of what sort of macroeconomic model seems to work best at explaining the world, and ask how unions would affect things in that model. And the one piece of empirical evidence I keep coming back to is signs of involuntary unemployment. Generally, there seems to be an excess supply of most types of labour most of the time, especially for union jobs. By itself, that doesn't prove that unions are bad. But it is something I want to build into my model.

OK, but you are changing the model, and in an inconsistent way.

In my model, someone needs to be paid to decide to hire the workers. No worker can be hired without an interview.

Alternately, think of the costs of opening a new plant -- to increase hiring requires the opening of a new plant.

Your model has no adjustment costs, and therefore investment is undefined in your model -- the process of optimization is free. I am trying to internalize the costs of optimization, so that in my model, someone is paid to optimize.

RSJ: OK. But if the assumption is that no worker can be hired without an interview (so the interview is not just an attempt to discover the worker's reservation wage), then you need managers doing those interviews even in the competitive equilibrium. And if managers are scarce, the MRP of labour net of interviewing costs will be lower, so competitive equilibrium full employment would be lower too.

"then you need managers doing those interviews even in the competitive equilibrium."


"And if managers are scarce, the MRP of labour net of interviewing costs will be lower, so competitive equilibrium full employment would be lower too."

Bingo. Conflicting claims on output between management and labor, that could result in unemployment, with the average worker always paid less than their MRP according to whatever the production function happens to be, as that function is leaving out the costs of optimization.

But the way I prefer to think about it is that competitive equilibrium (in the real world) is not reached by solving an equation, but by a process of incremental arbitrage. You hire a few more workers in the low cost area, slowly driving their wages up and bringing us closer to full employment and the law of one of price.

But as long as the arbitrage process itself is costly, then the competitive equilibrium will never be reached, as the arbitrage will only continue up until the cost of performing the arbitrage is equal to the gains from the arbitrage. Some augmented equilibrium will be reached instead.

If we accept that this process of arbitrage is what drives hiring and investment, then the economy requires a certain amount of productive inefficiency -- a certain amount of rents are required. How much is determined in part by the labor power of the arbitrageurs -- which is why things like high CEO compensation or high levels of walls street compensation are so corrosive to an economy, as they require more productive inefficiency.

If we are going to be looking at knocking down barriers to entry or reducing the market power of a single group, then we need start with the arbitrageurs and those who organize production, rather than those who make physical product.

From the post:

If we aggregate up over ... downward-sloping ... curves, we get an Aggregate ... curve ... that is horizontal at one.

I know I am late to this post but how is that possible? Could anybody please explain this to me? I do not mean big economics words but in plain simple mathematical terms. Or modern economics is not relying on Euclidean geometry?!

Sergei: assume n firms. Each individual firm has a demand function y=(1/n).Y.(p/P)^B where y is individual firm's output, Y is aggregate output, p is individual firm price, P is an average of their prices, and the parameter B is the elasticity of demand (B must be less than minus one).

The individual firm's demand curve holds Y constant (n is large), and it slopes down as a function of the relative price (p/P). If an individual firm wants to sell more output, it must lower its relative price (p/P).

In aggregate, if all firms expand output together, and all firms set the same price and sell the same output, Y=ny and p/P=1, so (p/P) stays the same. It's horizontal.

Nick, that is what I was afraid of. But sorry, "if all firms expand output together, and all firms set the same price and sell the same output" then individual firm demand curve is horizontal!

But skipping all economic words, you simply can not have it both ways. Or you should be using some non-Euclidean geometry. In the Euclidean world if you aggregate downward-sloping curves on one axis then you will get an aggregate curve that is downward-sloping on the same axis. This is an axiomatic fact. How can you claim anything else?

my wrong. I should rather say that depending on the second axis you can get all types of aggerate curves where a horizontal one is a super special case.


You seemed to admit that (within the model at hand) unions might be beneficial if their members are relatively poor. What do you think the real-world implications would be of a policy allowing unions to operate only when their members earn relatively low wages?

Sergei: I don't understand non-Euclidean geometry. But let me try one last time:

If my firm expands output, holding all other firms' outputs constant, my relative price will fall.

If my firm expands output, and all other firms expand output by the same amount as me, at the same time, my relative price will stay the same.

(Yes, that is a special case; I'm assuming symmetry).

Analogy: If I stand up at the theatre, and everyone else stays where they are, I can see the stage better. If I stand up, and everyone else stands up too, I cannot see the stage better.

Blikk: if we care about both efficiency and equality, you could make a case for allowing lower paid to unionise. There *could* be gains to equality at the expense of efficiency. (It depends on how many get unemployed as a result).

But a minimum wage law could do the same thing more simply. And a progressive income tax, or wage subsidy for low-wage workers, could do the same thing better, without creating unemployment.

Nick, the way I see it, or the way I read from it the quote from the text above, is that once you make your assumption of "all other firms expand output by the same amount as me" than individual firms face horizontal demand curves. You can not aggregate individual demand curves subject to a special assumption. You should start with your assumptions in the first place, draw individual demand curves and then aggregate them. Otherwise it does not work. Or you have to be using non-Euclidean geometry which has its internal logic incorporating your assumptions. If you do, then downward sloping demand curves can produce a horizontal one. If you don not but instead assume standard geometry, then downward sloping demand curves will NEVER produce a horizontal one. That is impossible in Euclidean geometry. And if it is impossible than your model is mathematically inconsistent. I.e. before we get to any economic terms you model fails. It is like you are trying to prove that 2+2=5 but somewhere around operation "=" you assume that every operation of addition means add both numbers and then add 1 on top.

Sergei, the aggregate demand curve is in absolutely *no* sense an aggregation of individual demand curves.

The demand curve faced by an individual firm is akin to a partial derivative, we allow the firm's price to change and solve for the resulting demand while holding everything else in the entire economy constant. All the other firm's prices and quantities enter as a parameter into this function (whose only argument is the firm's price). If you change the value of any other firm's price then you shift the current firm's demand curve, the whole curve shifts.

Likewise, as the firm in question changes its price the demand curves faced by all other firms shift.

Now, the aggregate demand curve is derived by allowing all the other firms to react to the shift in their own demand curves. The result will in no sense be an aggregation of the individual demand curves, it is an entirely different thing. The Rational expectations equilibrium of the resuting system is exactly the Nash equilibrium, everyone is assumed to react optimally given the other players reactions.

What Adam said. When you move along firm 2's demand curve, you are changing something that is held constant when you draw firms 1's demand curve, and vice versa.

It's only legitimate to add up individual demand curves when each demand curve holds constant only things that aren't on the axes of the other individual demand curves.

Adam P and Nick, I wrote a full comment but honestly I do not know how to respond to this statement: "the aggregate demand curve is in absolutely *no* sense an aggregation of individual demand curves"

What exactly are we doing here?! Are we doing apples to apples or we are just making the stuff up?!

Anyway here is the comment that I wrote.

Lets work it backwards. We start with the aggregate demand curve. It is flat. And it obviously depends on individual demand curves. There is no way to avoid this statement if we want to compare apples to apples. Now we want to get to individual demand curves. So we do a partial derivative of aggregate demand curve with respect to the individual firm price. We arrive at some demand function for this particular firm. We repeate this n times and get n partial derivatives, i.e. n individual demand functions. Next, the aggregate curve was assumed to be flat, i.e. it does not depend on price. So the full derivative of the aggregate curve with respect to price is zero. This means that n partial derivatives have to sum up to zero. Can they? In general, yes, they can. But the only sure state where they do NOT sum up to zero is when all of them are downward sloping. Under this assumption the aggregate demand curve has to be downward sloping.

The only way you can reconcile this contradiction is to admit that individual demands do not sum up to the aggregate demand curve the way you want them to. And this is what Adam P has stated. And the reason it does not is because you add a special constraint to integration, i.e. "all other firms expand output by the same amount as me". But if this contraint is introduced on the macro level, then on the micro level all firms face horizontal demand curves. Because if "all other firms expand output by the same amount as me" then surely each firm gets a horizontal demand curve. Again, like I said before if you want to do 2+2= but around "=" you change the logic of "+" then you can not assume that this is what other people understand.

I am sticking to the rules of pure geometry or algebra here. Please do not try to scare me off with rational expectations or Nash equilibriums.

Sergei: Here's another example. It's not macro, and it's not quite the same, but it illustrates the point we are making.

The apple market is a duopoly. There are only 2 firms producing apples, but one produces Granny Smiths and the other produces MacIntosh.

They have the demand functions;

Q1=A - P1 + 0.5P2 and Q2=A - P2 + 0.5P1

Firm 1's demand curve (varying P1 holding P2 constant) has a slope of -1.

When we add the two together, to get the total demand for apples, we get:

(Q1+Q2) = 2A - 0.5(P1+P2)

Assuming that P1=P2=P in equilibrium, so that Q1=Q2=Q, we get the relation between average quantity demanded Q and average price P as:


Instead of the partial derivative -1, we get a sort of total derivative -0.5.

"Please do not try to scare me off with rational expectations or Nash equilibriums."

Trouble is, unless you understand the concept of a Nash Equilibrium, none of this will make any sense at all.

Sergei, you're not sticking to the rules of geometry or algebra, you're simply failing to correctly understand.

You *almost* have it right here: " the reason it does not is because you add a special constraint to integration". You then get the constraint all wrong!

The correct constraint is an aggregat resource constraint. Suppose, to take an easy example, that aggregate output was constrained not to exceed 100. Suppose all individual demand curves, the partial derivatives, slope down.

Suppose that initially each firm is producing 10 units of output.

Now suppose firm 1 lowers their price, they can now sell more ouput, say they now sell 20 units. The aggregate resource constraint means someone else must sell less output, the other 9 firms find that though they've not changed their prices they now collectively supply 80 units instead of the 90 they used to supply. (Homework assignment: figure out the mechanism that enforces this).

Now suppose that the other firms respond by also lowering their prices by whatever amount will get them back to their initial output. The end result of all this is that prices have fallen but nobody has changed their supply, the aggregate curve is horizental even though none of the individual ones are.

You're mistake is in not imposing the resource constraint, there is some set of feasible allocations. Individual demand curves take partial derivatives as you said but the "total derivative", whatever that means, is *not* the sum of the partial derivatives. It's the gradient projected on the trangent plane of the (usually) differentiable manifold that defines the set of feasible allocaitons.

Aggregate demand curves respect all aggregate constraints, individual demand curves don't.

Correction: My 5th paragraph should *not* have started with "suppose that the other firms respond by..."

The whole point Nick is making is that in the symmetric equilibrim all firms find it optimal to respond by lowering their prices by whatever amount will get them back to their initial output. The Nash equilibrium part is that they will find this optimal.

So paragraph 5 should read: In the symmetric equilibrium all firms will respond by lowering their prices by whatever amount will get them back to their initial output...

Sergei, I know you haven't had a chance to respond yet but in any event I'll give one more explanation. I stress that the following is meant to be an analogy and *not* an actual example of an economic model.

Consider a mapping from R3 (3 dimensional Euclidian space, I can't do the superscript) into R, call it F.

Consider also three mappings from R into R, x(t), y(t) and z(t). The set of points in R3 {(x(t), y(t), z(t)), t real} is a subspace of R3, call this supspace A.

The idea in passing from micro economics, where we study individual demand curves, to macro economics is essentially the difference between looking at F and looking at F restricted to A.

F has three partial derivatives, the analogy is that the three partial derivatives of F are the 3 slopes of the individual demand curves that face the 3 firms. So if x, y, z represent the respective prices of the three firms and F(x,y,z) is the total ouptut of the three firms (so F is already aggregate demand) then the partials of F with respect to any of its 3 arguments is negative.

However, suppose the set A is the set of possible outputs given resource constraints. Remember this is an analogy not an example so you can't take it too literally. On the other hand, perhaps t is something like the money supply that might be expected to govern aggregate demand.

So, what happens when say x is reduced? (t stays fixed.)

For fixed t we have that famous implicit function theorem that says that on A we can write y and z as y(x) and z(x). The partial of F with respect to x is negative, as is the partial of F with respect to y and z.

But the "total derivative" is not just the sum of dF/dx with dF/dy and dF/dz (read as partial derivs). By the chain rule the "total derivative" is the dot product of the vector (dF/dx,dF/dy,dF/dz) with the vector (1, y'(x), z'(x)).

Now, in the example Nick has in mind it happens that this dot product is zero even though all three partials of F are negative.

Now you can complain that the words "individual demand curve faced by the firm" should mean something different but that is no different than claiming the words "partial derivative of F with respect to x" should mean something different. The words mean what they mean, you're being silly accusing Nick of being wrong for using the economics phrasing correctly.

Finally, in a more realistic set up the aggregate constraint set is probably high dimensional so there may be no way to pin down the reaciton functions y(x) etc. from that alone. You then pin these functions down by using notions like Nash equilibrium, so you can't really avoid these concepts.

Wow! Yep. That's what I must have been saying. :-)

Hope that works. Thanks Adam.

My dad always says that the implicit function theorem, and the inverse function theorem, are the theorems that make math work.

Perhaps he's right.

Nick, your numeric example just proves my point, i.e. that downward sloping demand curves produce downward sloping aggregate curve. If you want to show your point you need to come up with an example where two downward sloping demand curves produce an aggregate horizontal one with 1-to-1 mapping without extra assumptions in between.

Adam P, it is simple. Your individual demand curves are not independent as you say it yourself:

"Now suppose that the other firms respond by also lowering their prices by whatever amount will get them back to their initial output"

If you want to build a model you first fully state your assumptions and only then proceed with logic. You can not change the rules half way through and claim that your initial steps still hold under new assumptions.

Overall you can either have:
a) independent individual downward sloping demand curves which produce aggregate demand curve which is downward sloping
b) inter-dependent individual demand curves but then you can not say that they are downward sloping with respect to the individual firms price dPn because dPn (in the dQn/dPn) is not the final term in the derivative. The full derivative can be upward sloping or anything else depending on the function of individual prices and output and actual values. The mapping is not from R3 {(x(t), y(t), z(t)), t real} into R but from R3 {(x(t, y, z), y(t, x, z), z(t, x, y)), t real} into R.

So whether it is Nash equilibrium or not that you try to squeeze in between, your modelling approach in internally inconsistent. And if you try to make it consistent you either get a downward sloping aggregate demand curve or horizontal individual demand curves.

I am shocked that we still discuss it because this is what you effectively try to prove, i.e. that individual firms can not gain which means they face horizontal demand curves which contradict your initial assumptions of downward sloping individual demand curves. This is the essence of your model after stripping all scary words from it.


where q is individual firm quantity, Q is average of all firms' quantities, p is individual firm's price, P is average of all firms' prices, B is a parameter like minus 2. There are n firms all with the same demand function, and n is large (take the limit).

:) Nick, you can not be serious with this one, can you?

However large but finite N is the aggregate demand curve will be downward sloping.

And if you say that N is infinite, as you want me to accept, then I will tell you a big fat NO.

and btw you can only calculate average values of quantities (P, Q) of infinite sets under quite special conditions. So generally to calculate such average values you need to know average values. So sorry, you do not know neither Q nor P when you take the limit.

Sergei: Adam and I have done our best to explain this to you, in a number of different ways.

If one firm wants to expand its sales, relative to other firms, it must cut its price, relative to other firms.

If all firms expand their sales in the same proportion, and all cut their prices by the same proportion, their relative prices can stay the same.

If you are unable to translate that simple idea into math, or geometry, that's unfortunate.

Nick, you are not listening to what I am saying. You simply ignore it.

You say that ...

"If all firms expand their sales in the same proportion, and all cut their prices by the same proportion, their relative prices can stay the same."

Then I say that under this assumptions individual firms are *not* independent. Therefore you can NOT start with assumption of independent individual demand curves. But if you start with inter-dependent firms then *under*your*assumption* you effectively have just ONE FIRM and its demand curve equals aggregate demand curve.

Your model is inconsistent and you are making the stuff up. It is not about my understanding but about your academic rigour.

We can agree to disagree of course.


Start in equilibrium, where each firm is choosing its price or output to maximise its profit, given the prices or outputs set by all other firms.

Start with a pair of purely hypothetical questions:

1. What would happen to one firm's relative price if it alone increased output? It would fall, and that firm would lose profits.

2. What would happen to one firm's relative price if all firms increased output? It would stay the same, and that firm might gain profits.

What could be bad for one firm might be good for all firms. Like Prisoners' dilemma.

Now think of a pair of policy experiments, so the firm's and firms' actions are not purely hypothetical.

1. Suppose there were some change (say, a reduction in Marginal Cost, or an output subsidy) for just one firm that caused that one firm to want to increase its output. What would happen to that firm's relative price? It would fall.

2. Suppose there were some change (say, a reduction in Marginal Cost, or an output subsidy) for all firms that caused all firms to want to increase their output. What would happen to each firm's relative price? It would stay the same.

You are obviously smart enough to have learned way more math than me. Now spend the 10 minutes it will take you to understand something that a brilliant mathematician came up with in his spare time:


Reading the first third of that short Wiki, up to and including the Prisoners' Dilemma, will be sufficient.

The individual firm's demand curve shows what happens as we move vertically (or horizontally) down the payoff matrix.

What I am calling the "aggregate demand" curve shows what happens as we move along the main diagonal.

Just to add: the downward-sloping individual firm's demand curve is the one that firms look at when deciding what price and output to set. They would only look at the horizontal, aggregate demand curve, if they all joined together into one big cartel. That observation may tie it back in with why you think this analysis is wrong. "Nash Equilibrium" is just a shorthand way of saying just that.

Another way of modelling non-walras, as nash equilibria rather than the agent based stuff I linked to earlier.

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