I hesitated a lot before writing this. How to write it? Should I write it at all? Then I thought: "What would Arnold do?".
I will probably fail, but I'm going to try anyway.
I was reading Steve Roth, who linked to your paper (pdf) with Russel Standish, so I started reading it.
First I'm going to try to put myself in your shoes. Suppose I figured out something I thought was wrong with economics. Something very basic, like MR=MC, that is taught to all first year students, and that would mean that a lot of the rest of economics was wrong too. And not just empirically wrong, but logically wrong. And so I wrote a paper on this, and sent it off to some top economics journals. And it got rejected. And I thought the referees were wrong. And I only managed to publish it in non-mainstream journals and books, and so my important point gets ignored by mainstream economists.
Yep. I would be peeved at the mainstream too.
But you also need to put yourself in my shoes. You need to understand why I hesitated to write this post. It's the same reason I don't start arguing with the smartly-dressed young people who knock on my door, even if I do sometimes skim the flyer they hand me. Or avoid the angry guy standing on a soapbox. I know I won't get anywhere. I don't need this. I don't need the aggro. Even if I "succeed", (which is unlikely) what's the upside?
My better judgment tells me to ignore the knock on the door, or keep on walking. Instead, I'm posting this.
I'm not going to critique your paper. Instead I'm going to tell you what I think. I've thought about what you think. I would like you to think about what I think.
Suppose there are a million small farmers, each growing wheat, and their wheat is all the same and all sells for the same price. There's a downward-sloping market demand curve where the price of wheat P depends on total output Q, which is the sum of a million little q's.
1. When we say that the individual farmer faces a "flat" demand curve for his wheat, while the market-demand curve is downward-sloping, what do we mean by "flat"? Or, better, what ought we mean by "flat"?
(Yep, I learned something from reading your paper, because I hadn't read Stigler 57 either.)
We mean, or we ought to mean, "nearly perfectly elastic". We do not mean, or we ought not mean, "nearly zero slope".
The slope of the individual farmer's (inverse) demand function, which tells us how P varies with the output of the first farmer, q1, holding all the other farmers' q's constant, is exactly the same as the slope of the market demand function. (We agree on that.)
But the elasticity of the individual farmer's demand function is much bigger than the elasticity of the market demand function. It will be one million times bigger, for the average individual farmer.
The elasticity of the market demand curve is E = (1/slope)(P/Q).
The elasticity of the individual farmer's demand curve is e = (1/slope)(P/q1).
Since the slope is the same, but Q is a million times bigger than q1 (if he is the average farmer), e will be a million times bigger than E.
When we draw the individual farmer's demand curve, we need a scale for the horizontal axis that is one million times bigger than when we draw the market demand curve. That's why it looks much flatter, even though the slopes are the same. Elasticity adjusts for scale. A 1 tonne increase in q1 will have the same effect on P as a 1 tonne increase in Q. A 1% increase in q1 will have one millionth the effect on P as a 1% increase in Q.
2. There's a relation between marginal revenue, elasticity, and price.
"Market" marginal revenue is MR = (1-(1/E))P.
"Individual" marginal revenue is mr = (1-(1/e))P.
3. An individual farmer's profit R1 is a function of {q1, q2, q3,…qm}.
When I model the individual farmer alone on his farm deciding how much wheat to grow, I take the derivative of R1 with respect to q1, dR1/dq1, assuming dq2 = dq3 =….= dqm = 0. This is equivalent to setting individual mr = marginal cost.
When I model the same individual farmer at a National Farmers Union meeting deciding whether all farmers' wheat quotas should be increased or decreased, I take the derivative of R1 with respect to q1, dR1/dq1, assuming dq1 = dq2 = dq3 = … = dqm. This is equivalent to setting market MR = marginal cost.
[Just as there is a distinction between individual marginal revenue mr and market marginal revenue MR, there is also a distinction between individual marginal cost mc and market marginal cost MC, because the supply curve of land and other inputs facing the individual farmer is much more elastic than the market supply curve facing all farmers. But I will ignore that distinction here.]
4. You say: "The error in the standard “Marshallian” formula is now obvious: it omits the number of firms in the industry from the expression for the individual firm’s marginal revenue. With this error corrected, the correct profit-maximizing rule for a competitive firm is very similar to that for a monopoly: set marginal cost equal to industry level marginal revenue." (emphasis original).
I agree that the "Marshallian" formula does indeed omit that term, but I do not think this is an "error".
I think that real world farmers likewise omit that same term, when they are alone on their farms deciding how much wheat to grow. They think about the cost of growing more wheat, and compare that to the price of wheat. This makes sense to me, because mr is very close to P, since e is very large, so they ignore the distinction between mr and P.
But those same real world farmers, speaking at an NFU meeting about wheat quotas, do not omit that same term. They know that MR is very different from P. They understand that they could maximise profits much better if they could persuade the government to set quotas where MR equals marginal cost.
The real world farmers I have spoken to do not do what you say profit-maximising firms do. They make the exact same Marshallian "error". Except at the NFU meeting, when they do something much closer to what you say profit-maximising firms will do.
And if real world farmers really did do what you say profit-maximising firms would do, they wouldn't need the government to impose quotas anyway.
5. Your simulations (I would call them "agent-based modelling") are interesting. If you had simply said "We do agent-based modelling to see whether firms will converge on the Cournot-Nash equilibrium or the cartel equilibrium" and then run the simulations, I think your paper might find a receptive audience from many economists. (I don't know this for sure, because I know little about this area and I don't know whether this has already been done.) I think I get the intuition behind your results. If we start somewhere between the Cournot-Nash and cartel equilibria, and if a slight majority of firms reduce output at random, and a minority increase output, profits will rise, and so they will all do the same again. And if a minority reduces output and a majority increases output, profits will fall, so next period they will all reverse direction. So either way we get a majority of firms reducing output towards the cartel equilibrium.
But my hunch is that your results would be very sensitive to your assumptions about "learning". I think the results would be very different in an evolutionary model, where firms with higher profits have a lower probability of exit. Or where firms with lower profits copy the strategy of firms with higher profits.
This agent-based modelling looks like interesting stuff to me. But I would guess that most economists would have stopped reading your paper long before they got to that part.
Worthwhile Canadian Initiative 
Nick: this has been pointed to Keen before.
link here pdf NR
I notice the version of the paper that eventually got published in the august “Real World Economic Review” omits Keen’s claim that mainstream economists never use dynamic models. (He proceeded to generously show us a dynamic model of a firm might be set up, and got it brutally wrong.)
Chris: did your paper ever get published/circulated in any form?
Nick, as always, an interesting post, which has actually made me curious to read Keen’s paper to see what sort of ABM he was actually using.
However, (and I realize this is a very personal pet peeve): could you please stop using the NFU as a place where people chat about wheat quotas? I think I’ve been to at least 18 national NFU meetings, and my family has held just about every position there is to hold in the organization, and I honestly can’t remember a time when people ever talked about wheat quotas. Milk quotas? yes. Actions to protect the Wheat Board as a marketing entity? Yes. But wheat quotas I don’t think ever came up. In fact, a quick search of their policy site for “quota” doesn’t term up a single hit. For that matter, given how international and homogeneous the wheat market is, I honestly can’t picture an Canadian wheat quota system doing anything besides hurting wheat farmers.
I know you might view it as a minor point, but when you’re you’re using real organizations as examples, perhaps you could see if they’ve ever supported the positions you talk about? Unless you would feel comfortable with someone talking about the U of Carlton Econ faculty sitting down to agree to unilaterally reject heterodox papers to raise the Marginal Citation Revenue from their own papers as a teaching example.
And why beholdest thou the mote that is in thy brother’s eye, but considerest not the beam that is in thine own eye?
It probably would be a different world if all markets were like the wheat market, but where so many firms won’t compete at all if they can’t be one of the top two firms in their market, knowing your competitors and anticipating their response to any action of yours and they to yours can be a powerful incentive to competitive avoidance.
Nick:
“When we draw the individual farmer’s demand curve, we need a scale for the horizontal axis that is one million times bigger than when we draw the market demand curve. That’s why it looks much flatter, even though the slopes are the same. Elasticity adjusts for scale. ”
That cannot be right on at least two counts:
1. If we assume that the farmer sees the whole market DC, the scale is immaterial. We can look at the tiny band around the market price wiggling along the market DC, while the farmer plays with quantities, that looks to the farmer as a horizontal/flat line — the standard model.
2. As we sort of agreed earlier, elasticity reflects a (p, q) position on the DC. Therefore assuming the same DC and the elasticity equal infinity, we get to the intercept price which is clearly absurd. Elasticity is not applicable to the entire curve only to a point on the curve except for some artificial cases.
Perhaps you meant something else, an individual farmer’s DC that can be summed up to the market DC ? Not sure if this point of view is very productive.
Nick: Nope, I never sent it anywhere for publication. These days it would’ve been a blog post or series thereof.
Also, on a more constructive note, a couple questions:
1. I find his agent-based model (ABM) interesting (currently trying to create a version to play around with), but I’m very curious to find out how sensitive its underlying assumptions. The one I’d be most interested to see the effect of would be even weak stochasticity in the demand function. Intuitively, it would seem that for a monopolist, a noisy price-demand function wouldn’t matter much, but it would make the MR curve look much flatter to an individual producer.
2. Wouldn’t Keen’s arguments equally apply to consumers? In that case, why do his simulations all just assume that the observed price follow a simple demand curve, rather than also simulating consumers making multiple price offers? I think this may relate to question 1, as well, in that dynamic consumers would introduce endogenous stochasticity into the demand function.
May I? A question.
Millions of farmers seems too theoretical to me. There are probably rather a couple of farmers in each region where trade between regions is costly. There is no MARKET curve for these farmers unless external MARKET price increases above additional costs they have to bear to transport their wheat. How do you build the MARKET curve under such conditions? And what form will it have?
Without having read Keen’s paper (I just can’t bring myself to do it), your characterisation of the simulations reminds me of these two papers:
Steffen Huck, Hans-Theo Normann, and Jorg Oechssler. Zero-knowledge coop-
eration in dilemma games. Journal of Theoretical Biology, 220:47{54, 2003.
Steffen Huck, Hans-Theo Normann, and Jorg Oechssler. Through trial and error
to conclusion. International Economic Review, 45(1):205{224, 2004.
The basic idea is that a reasonable learning model (win-continue lose-reverse, that is valid in situations where it is not possible to calculate best responses) can lead Cournot duopolists to the collusive, rather than Cournot-Nash, outcome. Similarly, it can lead to the cooperative outcome in a tragedy of the commons environment.
Worth pointing out mainstream econ got stuck in its own “is game theory a superior replacement to marginalist thinking? Are most economic interactions better characterized by strategic rather than static considerations?” debate back in the 1980s. The answer was, eventually, “no’.
Eric: my apologies to the Canadian NFU. “Milk” would have worked better than “wheat”, but we sold our (UK) milk quota long ago and went for cereals and beans. Yep, Canadian wheat farmers, even though large, are probably still too small a part of the world wheat market for Canadian wheat quotas to raise prices much.
Sandwich: that’s from the Bible, isn’t it?
Lord: Maybe, but that’s why we have Industrial Economics, and oligopoly theory, to try to figure out when firms will act like wheat farmers and when they will act like a cartel, and when they will do something in between. My view is that the assumption that their outputs are perfect substitutes is the assumption that needs relaxing. I normally prefer monopolistic competition.
bankster: If the individual farmer cuts his output 1%, all other farmers’ outputs staying the same, the effect on price will be one million times smaller than if all farmers cut output by 1%. That’s all I need to say that his demand curve is a million times more elastic than the market demand curve.
Nick,
“The elasticity of the market demand curve is E = (1/slope)(P/Q).
The elasticity of the individual farmer’s demand curve is e = (1/slope)(P/q1).
Since the slope is the same, but Q is a million times bigger than q1 (if he is the average farmer), e will be a million times bigger than E.”
The slope is only the same at all prices P if the market demand curve is linear. If instead the market demand curve has a constant elasticity then:
Qm = P^Em = Sum (Qi) = n * P^Ei for n firms
ln n = (Em – Ei) * ln P
Em – Ei = ln n / ln P
Em = Ei + ln n / ln P
For very large n’s and small P’s (a lot of farmers selling wheat) the elasticity of the market is overwhelmed by either the sheer volume of farmers or the very small margins irrespective of the elasticity of any one farmer. The opposite is true of a monopoly single farmer.
And so does the individual farmer know from going to the NFU meeting what the shape of the market demand curve is, and if so what is it?
Nick, Wasn’t yours, too?
Chris: that’s why blogs are good.
Eric: 1. My hunch is that stochastic market demand wouldn’t make much difference. But looking over the hedge to see what the richer/poorer farmer next door was doing would make a big difference. (My father would always look over hedges. Nowadays at universities we call it “benchmarking”.)
2. Hmmm. Probably.
Evan: that does sound very similar. Just skip down to page 65.
Sergei: if firms’ outputs are not perfect substitutes, it gets a little more complicated. You can still write an individual firm’s quantity demanded as a function of all firms’ prices, or an individual firm’s price as a function of all firms’ quantities (not just the sum).
“Since the slope is the same, but Q is a million times bigger than q1 (if he is the average farmer), e will be a million times bigger than E.”
The slope is only the same if we assume that all 999,999 other farmers hold their q’s constant. Any reasonable model or simulation that includes all 1,000,000 farmers is going to violate that assumption.
Nick:
” If the individual farmer cuts his output 1%, all other farmers’ outputs staying the same, the effect on price will be one million times smaller than if all farmers cut output by 1%. ”
That’s correct, but the sentence below does not follow:
“demand curve is a million times more elastic than the market demand curve.”
because the ‘standard’ elasticity does not express what you are trying to say. I do not even understand what “demand curve is more elastic” might mean since, as I’ve already said, the notion of elasticity is simply not applicable to the curve as a whole hence the above does not make mathematical sense.
Min: there’s a difference between “constant” and “independent”. Take a model where each farmer decides how much wheat to plant without observing other farmers’ decisions. That’s the Cournot-Nash model. A different model is the Stackelberg model, where 1 plants first, followed by 2, who observes 1, followed by 3, etc.
bankster: I’m talking about point elasticity.
Nick, do I understand you right? The outputs are perfect substitutes but trade involves costs which are like a step function. You say that such case is like firms not producing perfect substitutes?
But my question still is about the shape of the market demand curve. What is it?
Sergei: here are two cases:
1. All the buyers are in one location. Sellers are spread out, and have transportation costs of getting their product to market. That case is simple. Just add the transport costs to each seller’s MC curve.
2. The buyers are spread out over space, and the sellers are in fixed locations. The classic model is Hotelling’s
Actually, not Hotelling’s, because Hotelling’s ice cream sellers can move. But I’ve seen a variant somewhere with fixed locations for sellers. Differential transportation costs make the different firm’s wheat imperfect substitutes, even if the wheat is all the same.
Dear Nick,
Thanks for your post. You have actually engaged more with my analysis than any other Neoclassical economist to date, so I will happily write a response.
However I’m too busy with other issues to respond in detail for about a month. In the meantime, can I suggest another reading for you: Chapter 4 of Alan Blinder’s “Asking About Prices”:
Cheers, Steve Keen
Nice post (and Chris artikel was good to).
but what is this Cournot-Nash model you are talking about? In the regular Cournot model, each firm certainly do observe the other firms decisions and adjust its output in responce to it. (And if we assume that they carry through with the calculation, instead of just responding to the other firms behavior, they set their output to a level which is optimal with respect to their competitors likely responces)
Thanks Steve. Well, maybe, this post was worth writing.
I read an article by Blinder years ago, reporting the results of a survey he had done, asking firms why they had sticky prices. I think that’s the same thing. I thought it was an important article. I thought about the reasons the firms had given, and how to model them. Most of them are beyond my abilities to model usefully. I did once build a macro model explaining why firms had sticky prices. But in hindsight I’m not sure I like my model. But I think (most) prices are sticky, and price stickiness matters for short run macro, and maybe for some long run macro too. I assume prices are sticky. But I wish I understood better why prices are sticky, and exactly how and when they change, and what the short run Phillips Curve really looks like. Sometimes I try to have another go at that question. Mostly I feel old and hope the next generation will do better at solving it.
Nemi: Cournot-Nash is just another, more formal, name for Cournot.
Assume 2 firms in a one-period game, where each firm only has one move. If one firm moves first, and the second firm observes the first firm’s move before making its own move, we get a very different equilibrium. That’s Stackelberg. If both firms move at the same time, so neither gets to see the other’s move before deciding its move, that is Cournot-Nash.
In a repeated game, with multiple periods, things can get hairy. Especially if the players don’t know when the game will end. They might collude. I used to follow the game theory/IO literature on this, long ago. But now I don’t.
I wonder, if there are n players, moving in sequence, does Stackelberg equilibrium converge to Cournot equilibrium when n gets very large? I think it does. Does anybody know?
Chris: I read that paper, it was great!
Nick: Off topic, but could you pretty please do a response to this new David Glasner post? It was his contribution to MoA-MoE – he talks about how he disagrees with you and Bill on the endogeneity of inside money. Hoped that you could do a post straightening this out. Thanks in advance!
Nick Rowe: “there’s a difference between “constant” and “independent”.
That’s my line, Nick. 🙂
Suppose that Q = q1 + q2. Then
ΔQ = Δq1 + Δq2 , and
ΔQ/Δq1 = 1 + Δq2/Δq1 , and
∂Q/∂q1 = 1 , and
∂q2/∂q1 = -1
The last equation is true, even if q1 and q2 are causally independent.
The next to last equation is not what you get if you let the differences approach 0 in the limit. You have to treat q2 as constant, not as causally independent.
What you seem to be saying, and where you may differ with Keen, is that if the agents do not collude, they should use the next to last equation, and assume that everybody else makes no change. That is different from assuming independence.
Nick,
“I wonder, if there are n players, moving in sequence, does Stackelberg equilibrium converge to Cournot equilibrium when n gets very large? I think it does. Does anybody know?”
See http://en.wikipedia.org/wiki/Stackelberg_competition
Look under the heading credible and non-credible threats by the follower. The follower can punish the leader by choosing a non-optimal Stackelberg quantity that lowers the profitability of both the leader and the follower below the Cournot equilibrium.
Nick,
“But I think (most) prices are sticky, and price stickiness matters for short run macro, and maybe for some long run macro too. I assume prices are sticky. But I wish I understood better why prices are sticky.”
Prices are sticky because the cost of money (the interest rate) is limited to a 0% lower bound on a pre-tax basis. In credit based currencies, money begins as a legally binding obligation between borrower and lender. However there is no legal obligation to purchase goods and services. Hence you have a mismatched system, borrowers must repay lenders but holders of currency may shop at their leisure.
Duck Duck Go says King James Bible (Cambridge Ed.) Matthew 7:3
And why beholdest thou the mote that is in thy brother’s eye, but considerest not the beam that is in thine own eye?
walt: 1. You seem to have missed Sandwichman’s having made that exact same rather unproductive comment.
2. More importantly, you seem to have missed that what this post is doing is precisely what you say I should be doing. I am considering a very large beam that Steve Keen says is in my neoclassical eye.
Thanks for engaging with (and agreeing with?) Keen, and in such a civil manner. Helps us avoid the usual vitriol of heterodox versus mainstream.
Having said that, this post confuses me. Economists pride themselves on the logical consistency of their theories of profit maximisation – in fact, so much so that they seem to value it above the real world. Take a textbook I own:
“…[the student] rightly assumes that few firms can have any detailed knowledge of marginal revenue or marginal cost. However, it should be remembered that marginal analysis does not pretend to describe how firms maximise profits or revenue. It simply tells us what the output and price must be if they do succeed in maximising these items, whether by luck or judgement.”
So what about if we replaced appropriate words to include Keen’s qualifications? Surely the argument would still apply?
Now, you seem to imply this is a silly perspective in your post, and we should look at what farmers actually do. I agree. So why not just accept that they use cost plus pricing and do away with the whole marginalist theory of the firm?
Unlearning: very briefly, because I gotta go teach. I agree (I think) with Steve on the “flatness” of the individual firm’s demand curve and what we should mean by “flatness”. But we disagree on the bigger stuff.
“So what about if we replaced appropriate words to include Keen’s qualifications? Surely the argument would still apply?”
Sorry, you lost me there.
“Now, you seem to imply this is a silly perspective in your post,…”
I don’t think I meant to imply that, or maybe you lost me.
“So why not just accept that they use cost plus pricing and do away with the whole marginalist theory of the firm?”
1. Because the (wheat) farmers I know don’t do cost plus pricing. They don’t really do pricing at all. They choose q, not P. And they try to set q roughly where they think MC will equal P, as far as they can figure that out.
2. Because “cost plus pricing” can mean “marginal cost plus a-factor-that-depends-on-elasticity-of-demand pricing”, which is a marginalist theory of the firm, and very textbook.
With some trivial math (which I have probably screwed up), my “set q where mr=mc” can be rewritten as “set P equal to [1/(1-1/e))]mc”.
Nick, Perhaps the Sandwichman read too much into the “angry guy standing on a soapbox” framing of the post. At least there was nothing there about foaming at the mouth. But walt clearly didn’t ‘miss’ Sandwichman’s comment. He was playing straight man to your (presumably) ironic question about the passage being from the Bible. You need to put yourself in my shoes. I don’t have the deftness with the math that you do. I have to go through it step by step to make sure no one’s pulling a fast one on me. But meanwhile I pick up on the dismissive verbal cues and gestures. So by the time I get to “Suppose there are a million small farmers, each growing wheat, and their wheat is all the same and all sells for the same price” what I’m hearing is “assume we have a can opener.” What good is it going to do to “suppose there are a million small farmers…” when in the real world of Monsanto and Archer, Daniels, Midland, small farmers in India drink pesticide because, “the prospect of death is less of a threat to workers than going hungry and not being able to feed their families.”
To the Sandwichman, the beam is supposing there are a million farmers. The mote is knocking on one’s door, smartly dressed.
I apologize if I’m going into the weeds here … I’m probably missing something. I tried reading the Keen paper, but right off I get stumped. After the quote from the Stigler paper they say (I’ll use uppercase D for partial derivatives):
dQ/dq_i = dP/dQ * dQ/dq_i
= dP/dQ * (sum(j=1 to n) Dq_j/Dq_i)
= …
by dQ/dq_t does the author mean the total derivative (since presumably Q(q_0, q_1, … , q_n))? And if so, is it really just the sum of the partials w.r.t q_i?
Off topic, but of interest to Steve Keen foes and fans – U Western Sydney’s economics department is closing, and Professor Keen is in the firing line: http://www.abc.net.au/news/2012-11-06/uws-set-to-ditch-economics/4355272?section=nsw
Sandwichman: If you read Steve Keen’s paper you will see he is making the same assumption. Lots of small farmers. That is not what this argument is about.
“I don’t have the deftness with the math that you do.”
I am very undeft with math.
Patrick: remember, Q = sum of all the little q’s, and P is a function of that sum only. P(Q) = P(q0+q1+q2 etc.) I will have another look later. (The math formatting in that journal makes it a little trickier to read.)
Frances: yes. I think it has something to do with how the Australian government lets universities make conditional offers to students, affecting how many students apply in first and second rounds.
Interestingly, Nick, I think agriculture is one of the few areas that exhibits the kind of production function typically found in textbooks, so it’s quite feasible that farmers are more likely to follow that kind of rule.
Having said that, a lot of evidence suggests the majority of firms use a cost-plus rule (anecdotally, all of my friends who study/have studied business or some form of industry have learned cost-plus pricing and know nothing about marginalism, unless they happened to take an economics module).
“Sorry, you lost me there.”
Let me do the rewriting, then:
“I think that real world farmers likewise omit that same term, when they are alone on their farms deciding how much wheat to grow. They think about the cost of growing more wheat, and compare that to the price of wheat. This makes sense to me, because mr is very close to P, since e is very large, so they ignore the distinction between mr and P.”
can turn into:
“…[the student] rightly assumes that few firms can have any detailed knowledge of the minimal effect of an increase in quantity on the market price. However, it should be remembered that marginal analysis does not pretend to describe how firms maximise profits or revenue. It simply tells us what the output and price must be if they do succeed in maximising these items, whether by luck or judgement.”
“With some trivial math (which I have probably screwed up), my “set q where mr=mc” can be rewritten as “set P equal to [1/(1-1/e))]mc”.”
To me this isn’t the same as the usual cost-plus rule, which is AVC + x%. I know there are different versions but fundamentally there is no need to invoke marginal or even economic concepts.
I’ve read your post, Auld’s critique, Keen’s article and book.
The basic story is that if the firm doesn’t face a perfectly flat demand curve, and if there is any price change with their output, then the outcome of perfect competition is infeasible because all firms will simply reduce output (ever so slightly) to increase profits, until they all get back to the monopoly level of output.
While you say there are one million farmers, that means that each individual farmer only needs to reduce output by some fraction of one-millionth to get to the monopoly output.
If you take a look at it from a market-wide perspective, we have a bunch of producers essentially giving away surpluses to consumers because they can’t coordinate. Yet so many repeated games show that cooperative strategies evolve and work with large groups. They are stable in the long term.
Another point (that hasn’t really been addressed) is that firms don’t maximise profits, but returns. You know, the % profit per unit of cost. Where there is a flat demand curve, this is at the point of minimum average total cost. Why go past this point? Since the demand curve is flat, you could build two factories/farms producing at this point and make greater returns than expanding production to MR (demand) = MC.
Unlearning: One problem with the “set P = markup of x% over costs” rule is that it doesn’t tell us what x is. Marginal analysis tells us that x=1/(e-1) (unless I’ve screwed the math up again). The more elastic is demand, the smaller the markup over mc. Those goods which have a less elastic demand (at the level of the individual firm) will have a higher markup. That’s a (sort of) testable implication. And it looks right to me. The goods which do seem to have less elastic demands do seem to have higher markups. If you let x be anything you want, well, the theory doesn’t have much content. You can always find an x that fits the facts and makes the theory “true”.
Patrick: which page/equations are you looking at there?
On page 62, equation 0.4, Steve Keen is maximising firm i’s profit by taking the derivative of firm i’s profit wrt aggregate Q, not firm i’s qi. And he assumes just below equation 0.5 that dqj/dQ =1 for all j. That’s where he loses me.
“If you read Steve Keen’s paper you will see he is making the same assumption. Lots of small farmers.”
I don’t see “lots of small farmers,” “millions of small farmers” or even “farmers.” Page number?
Rumplestatskin: “The basic story is that if the firm doesn’t face a perfectly flat demand curve, and if there is any price change with their output, then the outcome of perfect competition is infeasible because all firms will simply reduce output (ever so slightly) to increase profits, until they all get back to the monopoly level of output.”
It’s that “…until they all get back to the monopoly level of output” I don’t buy.
If the number of farmers is finite, the individual farmer’s demand curve won’t be perfectly elastic, so mr will be a little bit below P, so each inddividual farmer will produce where individual mr=mc. How do you get to them reducing output from that point to where market MR=mc? At mr=mc, each farmer is maximising his profit given the output of every other farmer.
“If you take a look at it from a market-wide perspective, we have a bunch of producers essentially giving away surpluses to consumers because they can’t coordinate. Yet so many repeated games show that cooperative strategies evolve and work with large groups. They are stable in the long term.”
Then why do Canadian dairy farmers care whether the government abolishes milk quotas? If you were right, they would coordinate to get the monopoly output even if there were no government quotas.
And if the producers can always coordinate between themselves to maximise their joint producer surplus, why can’t they also coordinate with consumers to maximise the joint producer plus consumer surplus?
I long ago put up an applet at http://www.dreamscape.com/rvien/Economics/Applets/KeenSimulation/KeenSimulation.html. The Java source, using some long-deprecated methods, is downloadable there as a tar file. This code implements the Keen and Standish simulation at some stage of their work. I forget the details.
I thought it was well known that almost everything in intro neoclassical textbooks was wrong.
The limit case that Nick wants to consider, in which a countably infinite number of firms each produce a quantity of zero, is logically inconsistent with the existence of a U-shaped cost curve. It is also rejected by Aumann.
I note that Nick, in his story about wheat farmers, never brings up the existence of whatever is the Canadian equivalent of the Chicago commodity exchange. In actually existing capitalism, a market that acts if it is perfectly competitive, in some sense, must be carefully constructed. One does not have merely firms (= plants) and consumers, but also speculators who are willing to take either side of the market, as desired. One also has traders who must “make” the market and a set of rules who matching bids and asks.
Most industrially-produced commodities do not have such markets and do have prices that are administrated. They do not face U-shaped cost curves in their plants. They are not trading-off marginal costs for known technology. They introduce new technology, usually irreversibly, over time though. The principle of substitution is both empirically and logically false.
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Robert: The debate here is not about costs. It is about marginal revenue. Is the elasticity of demand for the individual wheat farmer equal to the elasticity of the market demand curve for wheat? I say it is much much greater. Do wheat farmer maximise joint profits of all wheat farmers? I say they don’t.
Nick,
Em(P) = ( P * dQm/dP ) / Qm
Em(P) * dP / P = dQm / Qm
Integral ( Em(P) * dP / P ) = Integral ( dQm / Qm )
Integral ( Em(P) * dP / P ) = ln ( Qm )
Ei(P) = ( P * dQi/dP ) / Qi
Ei(P) * dP / P = dQi / Qi
Integral ( Ei(P) * dP / P ) = Integral ( dQi / Qi )
Integral ( Ei(P) * dP / P ) = ln ( Qi )
Assuming Qm = n * Qi
Integral ( Em(P) * dP / P ) = ln ( Qi ) + ln ( n ) = Integral ( Ei(P) * dP / P ) + ln (n)
Integral [ ( Em(P) – Ei(P) ) * dP/P ] = ln (n)
Em(P) – Ei(P) = P * d ( ln(n) ) / dP = P/n * ( dn/dP )
Em(P) – Ei(P) is nonzero only if dn/dP is nonzero. If the elasticity of the number of farmers with respect to price is zero, then the elasticity of market demand will be equal to the elasticity of individual demand.
Think of it this way. If changing the number of farmers does not lead to more or less competition (reflected in higher prices for less competition, and lower prices for more competition), then the market demand elasticity is equal to the individual demand elasticity. This is true irrespective of the shape (linear or non-linear) of the market and individual demand curves.
Nick: You got much farther than I! Right off the bat in 0.1 where he applies the chain rule is where he looses me. Because I have a weak brain, I’m thinking of 2 producers producing q1 and q2. Q(q1,q2, …) is what? A curve confined to lie in the q1 + q2 plane? So I’m just thinking that maybe the application of the chain rule doesn’t all disappear quite like he claims. The Q curve could be ‘curvy’.
To use a physical analogy, one can be at position 0 with any number of velocities (or similarly one can have 0 velocity, but very large acceleration.
But I confess that it’s late and I’m probably missing something.
I may be missing something because I’ve only read quickly, but is he saying the standard model is wrong because it ignores the own-firm impact on market quantity/prices? If so that’s not an error but a simplifying assumption. I remember being told we assum the producer is relatively small enough to ignore that term. This is very common, for example the decentralised neoclassical model with aggregate capital externalities, we assume households are sufficiently small to ignore their own impact on the aggregate. This sort of thing happens all the time because models, particularly the model of perfect competition, are simple stories not super accurate simulcra of reality, as Keen should realise because he uses models that miss out a lot himself. He presents this stuff as some sort of take down of the mainstream, no wonder he is ignored.
On the idea that firms won’t necessarily compete but may learn to collude amongst themselves, we’ll that’s hardly a revolutionary idea, and of course true to some extent, in some cases. The predictions of perfect competition could be changed by any number of considerations
“fundamentally there is no need to invoke marginal or even economic concepts”
I’m going to assume you’ve expressed yourself poorly there, because otherwise you seem to be claiming that firms make costing and pricing decisions without thinking about what they’d expect revenues and profits to look like under different choices.
Obviously the quantity and price decisions of very few real world firms resemble those in (almost) perfectly competitive markets, and I’m sure there are lots of impeccably mainstream (industrial organization) economists who specialise in the details of firm pricing behaviour that could add a lot of detail here. Plus, I’m sure there’s always going to be a gap between theory and practise, and a lot of rule-of-thumb behaviour goes on. None of this suggests that concepts such as elasticity of demand or marginal cost are of no use.
one more thought … if I get the gist of Keen’s agent based simulations correctly, then it is a nice illustration of the point that ABM is no panacea, because it is not free of eminently questionable simplifying assumptions. The agents are following a simple decision rule, which is just as unrealistic as anything mainstream economics ever uses. Do these agents even consider the strategy of undercutting each other and winning market share? Does the model include frictions such as habit formation amongst consumers that might make winning market share more valuable than a simpler model might predict? etc.