Precise Mathematical Conditions for Perfectly Competitive Markets Inhabited by Perfectly Rational Agents

Some econ­o­mist blogger called Dani Rodrick neatly trans­lates my sus­pi­cions about eco­nomics and econ­o­mists into economist-​​talk. He also man­ages to explain why some eco­nomic theory seems rea­son­able and forth­right while other of it seems impos­sibly ridicu­lous, or at least plau­sible and inter­nally coherent to some alter­nate uni­verse into which grad­uate stu­dents of schools of eco­nomics are whisked during their ori­en­ta­tion weeks, and where they con­tinue to live their intel­lec­tual lives while their phys­ical shades wander still in our world, saying these things which con­se­quently seem so strange to us.

The gut instinct of the mem­bers of the first group is to apply a simple supply-​​demand frame­work to the ques­tion at hand. In this world, every tax has an eco­nomic dead­weight loss, every restric­tion on indi­vidual behavior reduces the size of the eco­nomic pie, dis­tri­b­u­tion and effi­ciency can be neatly sep­a­rated, market fail­ures are pre­sumed non-​​existent unless proved oth­er­wise (and to be addressed only by the appro­priate Pigovian tax or sub­sidy), people are rational and forward-​​looking to the first order of approx­i­ma­tion, demand curves always slope down (and supply curves up), and general-​​equilibrium inter­ac­tions do not over­turn partial-​​equilibrium logic.…Those in the second group are inclined to see all kinds of com­pli­ca­tions, which make the text­book answers inap­pro­priate. In their world, the economy is full of market imper­fec­tions (going well beyond envi­ron­mental spillovers), dis­tri­b­u­tion and effi­ciency cannot be neatly sep­a­rated, people do not always behave ratio­nally and they over-​​discount the future, some oth­er­wise unde­sir­able policy inter­ven­tions can gen­erate pos­i­tive out­comes, and general-​​equilibrium com­pli­ca­tions render partial-​​equilibrium rea­soning suspect.”

There’s a problem here, for me. The bud­dhists council against believing some­thing just because it fits with your existing points of view (or pretty much any other reason actu­ally), and so I’d better watch it with this stuff. The internet will always supply some­body who’s got your back on what you already believe.That expe­ri­ence of having your ‘common sense’ sus­pi­cions ele­gantly rei­fied is a guar­an­teed zinger, and I think it’s where long-​​lasting ide­olo­gies are born. I don’t need any more ide­olo­gies. I’m finding the ones I already carry heavy enough, thank you.

So I’ll thank this Rodrick for being less con­vincing in future, and keep my eye open for some Uncle Milty apol­o­gists who can blithely rebut him, prefer­ably quickly, as I am busy.

Cosma Shalizi, as quoted at Crooked Timber, is clearly not the man for that job:

Now, I am the last person to deny that the invis­ible hand is a very pow­erful and valu­able con­cept, and I’m cer­tainly not going to deny the fun­da­mental the­o­rems of wel­fare eco­nomics; Debreu’s Theory of Value is one of my favorite books. Under cer­tain pre­cisely spec­i­fied math­e­mat­ical con­di­tions, per­fectly com­pet­i­tive mar­kets inhab­ited by per­fectly rational agents will allo­cate scarce resources in ways which cannot be altered without making some people worse off. Whether those con­di­tions are sat­is­fied by any eco­nomic system in the real world is an empir­ical ques­tion, and the answer is of course No. Given that those the­o­rems do not apply, the effi­ciency of mar­kets is another empir­ical ques­tion, or rather a whole series of ques­tions, with answers depending on the market and the tasks they are being asked to per­form. There are many sit­u­a­tions where mar­kets are a very valu­able and pow­erful social tech­nology, a useful way of coör­di­nating actions, allo­cating resources, and elic­iting valu­able efforts. … There are other sit­u­a­tions where they pro­duce awful, even per­verse results, and still others where they’d never begin to get off the ground, like funding basic research or national defense. … ”

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