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As I explained in my last post, the cost curve in the Trea­sury’s mod­el of the RSPT is based on a fan­ta­sy. The sit­u­a­tion is even worse when we turn to the oth­er side of the mod­el, the demand curve: it is based not mere­ly on a fan­ta­sy, but an out­right fal­la­cy.

Legions of econ­o­mists believe that the demand curve for a com­pet­i­tive firm is hor­i­zon­tal, but their belief is based on the most fun­da­men­tal of math­e­mat­i­cal errors: con­fus­ing a very small amount (an infin­i­tes­i­mal) with zero. The Trea­sury repeats this fallacy—without know­ing it is one—in its expla­na­tion of why a roy­al­ty reduces out­put lev­els but the RSPT won’t.

Fig­ure 1: Trea­sury’s draw­ing of the demand and sup­ply curves fac­ing a min­ing ven­ture

In the absence of tax­es and roy­al­ties, the full?production rate of out­put would be deter­mined by the inter­sec­tion of the mar­gin­al rev­enue curve (line P) and the mar­gin­al cost curve… With the RSPT, how­ev­er, the select­ed out­put would remain at Q_A, since the price line P describes the rel­e­vant mar­gin­al rev­enues. (The Resource Super Prof­its Tax: a fair return to the nation, p. 39)

Trea­sury describes the line P as “the mar­gin­al rev­enue curve”, where mar­gin­al rev­enue means the increase in rev­enue that the firm gets for sell­ing an extra unit of out­put (say a ton). Trea­sury argues that this equals the mar­ket price, and is inde­pen­dent of the amount the firm pro­duces: if the mar­ket price is $100 a ton, then the firm gets $100 for every extra ton it pro­duces, from zero out to a mil­lion tons.

Here’s Trea­sury is sim­ply par­rot­ing First Year Micro­eco­nom­ics propo­si­tions that the mar­ket price falls as the quan­ti­ty sup­plied to the mar­ket increas­es, but that at the same time, any indi­vid­ual firm in a com­pet­i­tive indus­try has no impact on mar­ket price (see Fig­ure 2).

Fig­ure 2: Neo­clas­si­cal micro “mar­gin­al rev­enue equals price for com­pet­i­tive firms”

You won’t pass an exam in Micro­eco­nom­ics unless you accept that these two propo­si­tions are compatible—that an increased sup­ply to the mar­ket will cause the mar­ket price to fall, but indi­vid­ual firms have no impact on the market—and yet math­e­mat­i­cal­ly they are incom­pat­i­ble.

Amaz­ing­ly, this was first proven back in 1957 by one of the staunchest defend­ers of Neo­clas­si­cal eco­nom­ics ever, George Stigler (Stigler (1957)), using one of the sim­plest rules of math­e­mat­ics, the “Chain Rule”. Stigler decom­posed the alleged­ly hor­i­zon­tal indi­vid­ual firm demand curve faced into two com­po­nents: the mar­ket demand curve, and how much the indi­vid­ual fir­m’s change in out­put changes mar­ket out­put.

The first fac­tor is unam­bigu­ous­ly neg­a­tive: accord­ing to Neo­clas­si­cal the­o­ry, the mar­ket demand curve slopes down­wards, so if sup­ply increas­es, the mar­ket price must fall. So for the fir­m’s demand curve to be horizontal—in math­e­mat­i­cal terms, to have a slope of zero—the sec­ond fac­tor would have to be zero: an increase in sup­ply by an indi­vid­ual firm would have to make no change to mar­ket sup­ply.

This would only hap­pen if the rest of the indus­try reduced out­put as much as the sin­gle firm increased it; but that implies col­lu­sion when the the­o­ry assumes com­pe­ti­tion! Stigler instead gave this sec­ond fac­tor a val­ue of 1: if a sin­gle firm increas­es out­put by (say) 1000 tons, the amount sup­plied to the mar­ket ris­es by 1000 tons, so dQ/dq_i equals 1 (Fig­ure 3).

Fig­ure 3: Stigler uses the chain rule to show that dP/dq = dP/dQ

The log­ic behind Stigler’s propo­si­tion that sim­ply applies the “atom­ism” assump­tion that is part of the the­o­ry of com­pet­i­tive mar­kets: that firms in a com­pet­i­tive indus­try do not react strate­gi­cal­ly to the hypo­thet­i­cal actions of oth­er firms. Spelling this out in more detail, the result fol­lows as shown in equa­tion in the Appen­dix. Spelling that equa­tion out ver­bal­ly:

• The change in mar­ket price (dP) caused by a change in the out­put of a sin­gle firm (dq_i) equals
  • The change in mar­ket price (dP) caused by a change in mar­ket out­put (dQ)
• mul­ti­plied by
  • The change in mar­ket out­put (dQ) caused by a change in the out­put of a sin­gle firm (dq_i)
• The first com­po­nent is neg­a­tive since the mar­ket demand curve slopes down­wards
• The sec­ond com­po­nent is 1 because
  • Mar­ket out­put (Q) is the sum of the out­put of the n firms in the indus­try;
  • If a sin­gle firm (q_i) changes its out­put (by dq_i)
  • the oth­er firms in the indus­try don’t change theirs in response
  • so the increase in total mar­ket out­put equals the increase in out­put by the sin­gle firm
• So since the sec­ond com­po­nent is 1, the slope of the indi­vid­ual fir­m’s demand curve is the same as the slope of the mar­ket demand curve.

The upshot of Stigler’s very straight­for­ward math­e­mat­ics was that the demand curve fac­ing the indi­vid­ual firm can­not be hor­i­zon­tal, but has exact­ly the same neg­a­tive slope as the mar­ket demand curve: if the firm increas­es its sup­ply, mar­ket price (and the price the firm gets) will fall.

Stigler’s maths puts the lie to the stan­dard draw­ings via which econ­o­mists learn microeconomics—like the one in Fig­ure 4.

Fig­ure 4: A stan­dard text­book draw­ing of per­fect com­pe­ti­tion

Stigler’s math­e­mat­ics is both impec­ca­ble and sim­ple, and it’s eas­i­ly illus­trat­ed in dia­grams too. First­ly, if the mar­ket demand curve slopes down, then any small por­tion of it also slopes down—even the bit seen by a sin­gle com­pet­i­tive firm. Sec­ond­ly, for that firm to have no impact on mar­ket price, regard­less of the quan­ti­ty it sells, then the mar­ket price must be the same for the quan­ti­ty P(Q+q_i)—if the firm pro­duces some output—as it is for P(Q)—if the firm pro­duces noth­ing. But that con­tra­dicts the propo­si­tion that the mar­ket demand curve slopes down­wards (Fig­ure 5).

Fig­ure 5: A small seg­ment of a down­ward slop­ing line is still down­ward slop­ing

Equal­ly, firms are described as “ratio­nal prof­it max­i­miz­ers” in neo­clas­si­cal theory—but what’s ratio­nal about believ­ing that an increase in your out­put won’t affect mar­ket price, if you also believe that mar­ket price will fall if the quan­ti­ty sup­plied to mar­ket ris­es (Fig­ure 6)?

Fig­ure 6: Irra­tional ver­sus ratio­nal beliefs for a com­pet­i­tive firm

Why don’t econ­o­mists accept this math­e­mat­i­cal log­ic and devise a bet­ter the­o­ry of the firm? Because, if it is accept­ed, the whole the­o­ry of com­pet­i­tive mar­kets fails: mar­ket price is not set by the inter­sec­tion of sup­ply and demand curves, but by a markup on the cost of pro­duc­tion. The vision of per­fect com­pe­ti­tion, which frames how econ­o­mists think about the real world, is both a fan­ta­sy and a fal­la­cy.

This is so destruc­tive of the over­all Neo­clas­si­cal vision of how a mar­ket econ­o­my works that this very accu­rate math­e­mat­ics is suppressed—in the teach­ing of a dis­ci­pline that prides itself on being math­e­mat­i­cal. Instead, econ­o­mists con­tin­ue teaching—and 99% of them con­tin­ue believing—that the slope of the demand curve fac­ing the indi­vid­ual demand curve is hor­i­zon­tal (or “The price line is hor­i­zon­tal because the oper­a­tor is a price tak­er” as Trea­sury puts it, or some oth­er euphemism for a math­e­mat­i­cal fal­la­cy).

I redis­cov­ered this when writ­ing Debunk­ing Eco­nom­ics in 2000—and sub­se­quent­ly found that Stigler had beat­en me to it, before I’d even gone to school. So how did neo­clas­si­cal econ­o­mists jus­ti­fy sup­press­ing such a sim­ple demo­li­tion of a key plank of their sto­ry?

Because Stigler argued that he’d found a way out of the conun­drum in that same arti­cle: yes, indi­vid­ual firms face down­ward slop­ing demand curves, with exact­ly the same slope as for the mar­ket itself; but if they all set mar­gin­al cost equal to mar­gin­al rev­enue, then in the lim­it mar­gin­al rev­enue for the indi­vid­ual firm will con­verge to price, and the orig­i­nal unblem­ished sto­ry can be restored (See Fig­ure 7).

Fig­ure 7: Stigler’s way out

This is math­e­mat­i­cal­ly true: if firms equate mar­gin­al cost and mar­gin­al rev­enue, then mar­gin­al rev­enue will con­verge to mar­ket price for the indi­vid­ual firm. Giv­en this, and the belief that equat­ing mar­gin­al rev­enue and mar­gin­al cost will max­i­mize prof­its, econ­o­mists are con­tent to ignore Stigler’s analy­sis and just stick with the old but false propo­si­tion that the demand curve fac­ing the indi­vid­ual com­pet­i­tive firm is hor­i­zon­tal.

In itself this is men­da­cious: why teach a fal­la­cy, when there’s a more legit­i­mate way to reach the same result? But there’s a more impor­tant prob­lem that I dis­cov­ered after writ­ing Debunk­ing Eco­nom­ics: what neo­clas­si­cal econ­o­mists call “prof­it max­i­miz­ing behav­ior” does­n’t actu­al­ly max­i­mize profits—even if their mod­el of the firm was oth­er­wise cor­rect. Instead, a firm fol­low­ing their advice would pro­duce about twice the lev­el that actu­al­ly would max­i­mize prof­its, and lose mon­ey on the deal as well.

Equating marginal cost and marginal revenue doesn’t maximize profits

One of the basic mantras of neo­clas­si­cal eco­nom­ics is that all firms, from a monop­oly to a tiny com­pet­i­tive firm, max­i­mize prof­its by equat­ing mar­gin­al cost and mar­gin­al rev­enue. It’s the basis of Stigler’s “res­cue” of per­fect com­pe­ti­tion back in 1957: that even though the demand curve fac­ing the indi­vid­ual firm can’t be hor­i­zon­tal, as more firms enter an indus­try, mar­gin­al rev­enue con­verges to price if they all max­i­mize prof­its by equat­ing mar­gin­al rev­enue and mar­gin­al cost.

My per­son­al con­tri­bu­tion to this lit­er­a­ture was to show that this mantra isn’t true: equat­ing mar­gin­al rev­enue and mar­gin­al cost only max­i­mizes prof­its if there is just one firm in the industry—a monop­oly. With more than one firm, the cor­rect prof­it-max­i­miz­ing for­mu­la is to have mar­gin­al rev­enue exceed mar­gin­al cost.

Here n rep­re­sents the num­ber of firms in the indus­try, low­er­case let­ters rep­re­sent an indi­vid­ual firm, and upper­case let­ters rep­re­sent the mar­ket.

I’ve proven this is many dif­fer­ent ways, but the start­ing point of them all is that—ironically—the neo­clas­si­cal mantra ignores the mar­ket: even if an indi­vid­ual firm can’t affect what oth­er firms in the mar­ket do, what oth­er firms in the mar­ket do does affect the indi­vid­ual firm. There­fore to max­i­mize prof­its, the firm needs to behave as if it’s in a mar­ket where it is only one of the fac­tors affect­ing its prof­itabil­i­ty. The prof­it-max­i­miza­tion prob­lem is there­fore one of total dif­fer­en­tials, rather than the ordi­nary dif­fer­en­tial used by neo­clas­si­cal econ­o­mists.

The solu­tion, as explained in these papers, is the one shown in equa­tion lat­er on. And it does­n’t involve collusion—just the firm alter­ing its pro­duc­tion lev­els in response to changes in its prof­its.

Why does this matter?

To bring this back to prac­ti­cal issues, what neo­clas­si­cal econ­o­mists describe as prof­it-max­i­miz­ing behav­ior actu­al­ly involves sell­ing about 50% of out­put at a loss.

Nor­mal­ly this does­n’t have any prac­ti­cal impact—beyond mak­ing econ­o­mists sin­gu­lar­ly use­less in advis­ing a firm on out­put lev­els. But it has a real impact when com­pe­ti­tion reg­u­la­tors decide that a breakup of a monop­oly will result in low­er costs for the con­sumer because of com­pe­ti­tion, or that a util­i­ty should sell its out­put at its mar­gin­al cost—because accord­ing to neo­clas­si­cal the­o­ry, that is both social­ly opti­mal AND prof­it-max­i­miz­ing for the firm.

In fact, as con­sumers of pri­va­tized ser­vices often find, costs don’t fall, and com­pe­ti­tion frag­ments what was more effec­tive as a monop­oly-deliv­ered prod­uct; and as some util­i­ties find out to their great cost, mar­gin­al cost pric­ing involves cheap ser­vices to the pub­lic for a while (cheap elec­tric­i­ty, water, etc.) but a low or even neg­a­tive rate of prof­it that means the util­i­ty can’t be main­tained. Break­down of the system—as with elec­tric­i­ty sup­plies in Cal­i­for­nia ear­li­er this century—is often the out­come.

This the­o­ry is also the jus­ti­fi­ca­tion for the poli­cies of com­pe­ti­tion watch­dogs like the Aus­tralian Com­pe­ti­tion and Con­sumer Com­mis­sion (ACCC). While monop­o­lies can cer­tain­ly have dele­te­ri­ous con­se­quences in some con­texts, the auto­mat­ic bias that this the­o­ry leads to in favour of com­pe­ti­tion are not jus­ti­fied when the the­o­ry itself is erro­neous. Bad the­o­ry can lead to good pol­i­cy only by sheer acci­dent, and that’s an acci­dent that I would­n’t expect all that often.

Too low a rate of profit

The final flaw of the RSPT is prob­a­bly the most impor­tant of all: the rate of prof­it that it regards as indi­cat­ing super-prof­its is too low. The propo­si­tion that “super prof­its” occur when the rate of prof­it exceeds the long term bond rate is non­sense: any ven­ture that appeared to offer a rate of return that low would­n’t be under­tak­en by any sen­si­ble cap­i­tal­ist.

If the best esti­mate of a project is that it would return the long run bond rate, then why not buy long term bonds? At least they will exist in ten or so years time (well, maybe before the GFC any­way…) where­as your project may be brought undone by some­thing you can’t foresee—like a BP dis­as­ter in the Gulf of Mex­i­co bring­ing your plans for off­shore drilling in East Tim­or unstuck.

The bril­liant Aus­tralian Pro­fes­sor of Applied Math­e­mat­ics John Blatt showed decades ago that the best esti­mate of whether a project should be under­tak­en was a con­cept that neo­clas­si­cal econ­o­mists deride: the “pay­back peri­od” (Blatt (1980)). Blatt showed that the pay­back peri­od con­sid­ers both the dis­count rate that should be applied to expect­ed future cash streams—where the long term bond rate is a rea­son­able guide—and what Don­ald Rums­feld lat­ter famous­ly called “known unknowns” and “unknown unknowns”. The upshot is that the long term bond rate seri­ous­ly under­es­ti­mates the min­i­mum expect­ed rate of return that any pru­dent investor should con­sid­er. A rate that low isn’t super at all—and nor is the log­ic behind the RSPT, even though the con­cept itself is a valid one.

Appendix: Some mathematics

Preliminaries—why bother?

As I detail in Debunk­ing Eco­nom­ics, the neo­clas­si­cal the­o­ry of the firm is almost total­ly irrel­e­vant to how actu­al firms and mar­kets behave. Worse, it dis­tracts atten­tion from the real-world process­es that actu­al­ly mat­ter, in par­tic­u­lar the tech­no­log­i­cal and oth­er forms of prod­uct com­pe­ti­tion that firms under­take that both intro­duce new prod­ucts over time and reduce the costs of exist­ing ones.

It also encour­ages econ­o­mists to be “rev­o­lu­tion­ar­ies”: restruc­tur­ing indus­tries from the pat­tern they have evolved into, to the one that the text­book says is the best.

We’d be far bet­ter off aban­don­ing the the­o­ry com­plete­ly, and build­ing an entire­ly dif­fer­ent mod­el that suits real-world data—which shows that most indus­tries have a range of firm sizes rather than the eco­nom­ic fan­ta­sy of monop­oly at one end and per­fect com­pe­ti­tion at the other—and for which Schum­peter’s mod­el of com­pe­ti­tion is far more suit­able (Schum­peter (1934)).

So why waste time pulling it apart math­e­mat­i­cal­ly? Because the last time eco­nom­ics attempt­ed to break out of the neo­clas­si­cal straight­jack­et, the escape was sub­vert­ed by econ­o­mists rework­ing macro­eco­nom­ics until it was con­sis­tent with neo­clas­si­cal micro­eco­nom­ics. The so-called “micro­foun­da­tions debate” under­mined macro­eco­nom­ics because econ­o­mists believed that micro had sound foun­da­tions while macro did not.

The real­i­ty is that micro itself is unsound—but even now when I present to an audi­ence that includes neo­clas­si­cal econ­o­mists, I often hear them argu­ing that macro might be a mess (some­thing they are forced to con­cede because of the total fail­ure of neo­clas­si­cal macro­eco­nom­ics to antic­i­pate the GFC, and the suc­cess of poli­cies to counter the GFC that neo­clas­si­cal the­o­ry said could nev­er work), but micro is OK.

No it’s not. Every aspect of neo­clas­si­cal micro­eco­nom­ics is a pseu­do-sci­ence, includ­ing the the­o­ry of the firm. But giv­en the seduc­tive­ness of the vision it offers of a per­fect, com­pet­i­tive world in har­mo­nious equi­lib­ri­um, a prop­er expo­sure of its flaws is nec­es­sary.

With that caveat, I’ll turn to the proof of why “per­fect” com­pe­ti­tion can’t exist. This proof that equat­ing mar­gin­al cost and mar­gin­al rev­enue does­n’t max­i­mize prof­its inevitably involves math­e­mat­ics, but I know that for most read­ers that leads to what is known as the “MEGO” effect: “My Eyes Glaze Over”. For those who can cope with math­e­mat­ics, here’s the proof. For every­one else, it’s time to read a dif­fer­ent blog!

MEGO

First­ly, the proof that the slope of the indi­vid­ual fir­m’s demand curve is the same as that of the mar­ket demand curve. Apply­ing the chain rule, the slope of the indi­vid­ual fir­m’s demand curve can be bro­ken into the mar­ket demand curve, times how much mar­ket out­put changes if a sin­gle firm alters its out­put. Since mar­ket out­put is the sum of the out­put of all indi­vid­ual firms, and in the Mar­shal­lian mod­el firms don’t react strate­gi­cal­ly to each oth­er (in con­trast to the Cournot-Nash ver­sion), this last term is 1, as shown by a sim­ple expan­sion of mar­ket out­put:

There are many ways to prove that the actu­al prof­it-max­i­miz­ing out­put lev­el is giv­en by equa­tion rather than by equat­ing mar­gin­al cost and mar­gin­al rev­enue:

The tech­ni­cal­ly most cor­rect proof starts from the cor­rect ini­tial def­i­n­i­tion that the max­i­mum of the prof­it func­tion for a sin­gle firm isn’t sim­ply a func­tion of its own behav­ior, but also of what all oth­er firms do. So the true prof­it-max­i­miz­ing prob­lem is to solve the fol­low­ing equa­tion:

That’s do-able (and it’s done below), but it’s nor­mal­ly a stretch for econ­o­mists to fol­low, so a sim­pler proof can start from work­ing from the start­ing point of assum­ing that firms do what econ­o­mists advise them to do, and see what the out­come of that is when we cor­rect for the mis­take of putting rather than the cor­rect expan­sion that . If you can han­dle the more com­pli­cat­ed maths, skip the rel­a­tive­ly messy expla­na­tion in equa­tions to , and jump straight to equa­tion .

We start from assum­ing that the con­di­tion in equa­tion applies:

Then we expand what mr and mc are for the i^th firm:

And

The first term in the expan­sion for mar­gin­al rev­enue gives us n copies of P; in the sec­ond term can be replaced by , and the expres­sion can be rearranged to . So the expan­sion of mar­gin­al rev­enue is now com­plete:

The expan­sion of mar­gin­al cost sim­ply gives us n copies of indus­try lev­el mar­gin­al cost:

So the total expres­sion in equa­tion is as shown in equa­tion :

So if all firms fol­low neo­clas­si­cal prof­it-max­i­miz­ing advice, the aggre­gate sit­u­a­tion for the indus­try will be shown by the right hand side of equa­tion :

What does that apply for the indus­try lev­el of out­put? A bit of rear­rang­ing explains it: split off one term for P and one for MC and we get equa­tion :

Rear­rang­ing this (and omit­ting the depen­dence on Q to sim­pli­fy the nota­tion) gives us:

Only for a monopoly—where n=1—will equa­tion equal zero. For all oth­er indus­try struc­tures, what neo­clas­si­cal the­o­ry calls prof­it max­i­miz­ing behav­ior actu­al­ly results in part of mar­ket out­put being pro­duced at a loss—since then mar­gin­al rev­enue will be less than mar­gin­al cost. But the indus­try is just the sum of the firms in it; there­fore if each firm equates its mar­gin­al rev­enue and mar­gin­al cost, each firm must pro­duc­ing more than the prof­it-max­i­miz­ing lev­el.

So if fol­low­ing neo­clas­si­cal advice caus­es firms to pro­duce more than the prof­it-max­i­miz­ing lev­el, can the advice be mod­i­fied to work out the true prof­it-max­i­miz­ing lev­el? If each firm actu­al­ly does pro­duce the prof­it max­i­miz­ing lev­el for itself and no more, then indus­try lev­el mar­gin­al rev­enue will also equal indus­try lev­el mar­gin­al cost. Using the expres­sion for this in equa­tion , the real prof­it-max­i­miz­ing lev­el can be worked out using equa­tion :

Tak­ing P and MC inside the sum­ma­tion sign yields:

The prof­it-max­i­miz­ing lev­el for the sin­gle firm is thus to set equa­tion to zero:

That’s the messy way to derive the result. A clean­er method is to start from the total dif­fer­en­tial that actu­al­ly does max­i­mize prof­its:

We can drop since this is 1. Expand­ing out yields:

Expand­ing the first expres­sion gives us one copy of P (since if and on the one occa­sion that )

The sec­ond expres­sion in is how much the j^th fir­m’s costs change for a change in out­put by the i^th firm. This is zero n‑1 times and mar­gin­al cost for the i^th firm once. So the com­plete expres­sion is that the j^th firm will max­i­mize its prof­its if it pro­duces at the lev­el at which its mar­gin­al cost equals indus­try-lev­el mar­gin­al rev­enue:

This is oper­a­tional­ly equiv­a­lent to the expres­sion in .

There’s much more to the cri­tique than this, but that’s all I have time for here. Oth­er aspects include that the con­di­tions for the aggre­ga­tion of mar­gin­al cost curves from com­pet­i­tive firms to equal that for a monop­oly require either a fluke or con­stant mar­gin­al costs (see Appen­dix A.1 to Keen (2004)), that Cournot-Nash behav­ior is irra­tional (Keen and Stan­dish (2006, pp. 82–83)), and that a pop­u­la­tion of instru­men­tal­ly ratio­nal prof­it max­i­miz­ers will con­verge to the Keen solu­tion, not the Cournot-Nash solu­tion (Keen and Stan­dish (2006, pp. 83–85)).

Experimental Economics

Again I’m doing this too quick­ly because I want to get back to the impor­tant stuff of devel­op­ing an alter­na­tive cred­it-based macro­eco­nom­ics from Min­sky’s foun­da­tions, but one use­ful addi­tion­al way that I under­cut the con­ven­tion­al mod­el was to use com­put­er sim­u­la­tion.

The the­o­ry tells us that a mar­ket pop­u­lat­ed by prof­it max­i­miz­ing com­pet­i­tive firms would pro­duce where mar­gin­al rev­enue equals mar­gin­al cost. I instead pre­dict­ed that such an indus­try would pro­duce the amount pre­dict­ed by equa­tion . I test­ed this by build­ing a mod­el of a hypo­thet­i­cal mar­ket with a down­ward-slop­ing demand curve:

Fig­ure 8: Price, mar­gin­al cost, mar­gin­al rev­enue and neo­clas­si­cal pre­dic­tions

Iden­ti­cal firms were defined in such a way that the mar­gin­al cost curve for a monop­oly (with a sin­gle fac­to­ry) was iden­ti­cal to the sum of the mar­gin­al cost curves of a 100 firm com­pet­i­tive indus­try (with one fac­to­ry per firm):

Fig­ure 9: Firm costs defined to ensure that dif­fer­ent scales of out­put have the same aggre­gate mar­gin­al cost curve

Neo­clas­si­cal the­o­ry pre­dicts that the amount pro­duced will be a func­tion of the num­ber of firms in the indus­try: the more firms, the high­er the out­put and the low­er the mar­ket price:

Fig­ure 10: Neo­clas­si­cal pre­dic­tions

The pro­gram then runs through sim­u­la­tions of the behav­ior of “instru­men­tal prof­it max­i­miz­ers”, who sim­ply choose an out­put lev­el, choose an amount to vary out­put by, and vary out­put in search of high­er prof­it. It starts with a sim­u­la­tion of a monop­oly, and ends with a sim­u­la­tion of a 100 firm indus­try:

Fig­ure 11: The pro­gram in Math­cad

The aggre­gate out­come of the mod­el was very dif­fer­ent to the neo­clas­si­cal pre­dic­tions: rather than a com­pet­i­tive 100-firm indus­try pro­duc­ing much more than a monop­oly, they both pro­duced much the same amount.

Fig­ure 12: Out­come of the mod­el for monop­oly and 100 firm indus­try

A neo­clas­si­cal ref­er­ee who reject­ed this paper for a main­stream jour­nal claimed that this was because all the firms were doing the same thing and hence effec­tive­ly col­lud­ing. A close look at the behav­ior of three firms cho­sen at ran­dom from the 100-firm sim­u­la­tion shows that this was not the case:

Fig­ure 13: Out­put of 3 firms cho­sen at ran­dom and indus­try aver­age out­put over 1000 iter­a­tions

What’s more, the instru­men­tal­ly ratio­nal prof­it max­i­miz­ers made high­er prof­its than neo­clas­si­cal the­o­ry pre­dict­ed:

In gen­er­al, the num­ber of firms in the indus­try had no impact on the amount pro­duced by the indus­try:

And mar­ket price was also unaf­fect­ed by the num­ber of firms:

In sum­ma­ry, the neo­clas­si­cal the­o­ry of the firm and com­pe­ti­tion is “much ado about noth­ing”.

Blatt, J. M. 1980, ‘The Util­i­ty of Being Hanged on the Gal­lows’, Jour­nal of Post Key­ne­sian Eco­nom­ics, vol. 2, no. 2, pp 231–239.

Keen, S. 2004, ‘Dereg­u­la­tor: Judg­ment Day for Micro­eco­nom­ics’, Util­i­ties Pol­i­cy, vol. 12, pp 109–125.

Keen, S. and Stan­dish, R. 2006, ‘Prof­it max­i­miza­tion, indus­try struc­ture, and com­pe­ti­tion: A cri­tique of neo­clas­si­cal the­o­ry’, Phys­i­ca A: Sta­tis­ti­cal Mechan­ics and its Appli­ca­tions, vol. 370, no. 1, pp 81–85.

Schum­peter, J. A. 1934, The the­o­ry of eco­nom­ic devel­op­ment : an inquiry into prof­its, cap­i­tal, cred­it, inter­est and the busi­ness cycle, Har­vard Uni­ver­si­ty Press, Cam­bridge, Mass­a­chu­setts.

Stigler, G. J. 1957, ‘Per­fect Com­pe­ti­tion, His­tor­i­cal­ly Con­tem­plat­ed’, The Jour­nal of Polit­i­cal Econ­o­my, vol. 65, no. 1, pp 1–17.