tag:blogger.com,1999:blog-8291497071362959708.post2640492035940260799..comments2023-05-29T03:04:33.182-07:00Comments on The Analytical Economist: Math ArgumentsAnonymoushttp://www.blogger.com/profile/00238643861921736933noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8291497071362959708.post-39972377070757834622014-09-14T13:11:47.996-07:002014-09-14T13:11:47.996-07:00On functional analysis, copper miners aren't d...On functional analysis, copper miners aren't doing economics when they attempt to maximize or optimize output. Economists are interested in the fact that the miner will attempt to maximize profits, other things being equal, which is a more important caveat than you might think.<br /><br />Say I'm a copper miner. I keep close tabs on my mine, so I know that on average I can expect a ton of ore to yield a pound of pure copper, say. I've got some money in the bank and would like to increase my productive capacity, so on the back of a napkin I work out how much more I can produce in a month by hiring 5 more guys and buying $1M worth of gear. Maybe that would let me increase production by an even ton each month. Let's say we can simplify by holding all the variables constant - my mine's yield, the spot price of copper, factor prices, the weather, anything else that might affect my profit on a unit of product. Now I can math up a prediction that this project will pay for itself in one year, and increase my profits by 5% thereafter. None of this math has anything to do with economics - none of this has anything to do with human action. The economist is interested in whether, in the face of this prediction, made using assumptions which are unsafe in the real world, I will undertake the project. There are still other considerations - what is the market interest rate? Maybe I would be better off putting my money in savings than investing in this project. But in principle we can control for all those considerations, and still not predict what I will do, because we don't know my time preference - possibly I would rather buy some Lamborghinis to pick up chicks, than wait for the modest fruits of this investment.<br /><br />But even here, because we're looking at one guy and how I make my decisions in the face of a given set of circumstances, we're not doing economics - only praxeology. The economic question is, if I do make the investment and it does add a ton per month to the supply of copper, what will happen to the price of copper? All the economist can tell you is that it will be lower than it would otherwise have been. He can't say how much lower, and he certainly can't tell you what the price of copper will actually be, even if we stipulate that this is the only change worldwide to the supply of copper.<br /><br />Now back to the 30,000 foot view, everybody insists that you can legitimately use math in economics, and you're not the first to mention game theory as an alleged example of this, but nobody has ever actually offered up a valid economic mathematical proposition to be examined on its merits. Why is that?Anonymoushttps://www.blogger.com/profile/02033352780260681914noreply@blogger.comtag:blogger.com,1999:blog-8291497071362959708.post-74252288196465885372014-09-14T13:10:47.578-07:002014-09-14T13:10:47.578-07:00"Austrians should accept all mathematical pro..."Austrians should accept all mathematical propositions that are true, from 1 + 1 = 2 to the propositions in set theory or algebraic topology etc."<br /><br />And so we do.<br /><br />I consider game theory to be a branch of praxeology rather than of mathematics, though of course math is used to compute the optimal set of choices for each player. Which is not to say it uses math to predict the *actual* choices of each player, which is why it's of no use in economics. The (safe) assumption of game theorists is that each player will try to maximize his utility, his "payoff" in the face of imperfect information either about the details of the "game" or about the decisions other players would make that might ruin his strategy. Take the prisoners' dilemma, the classic example. Math is used to describe various possible strategies, to compute optimal outcomes etc., but it's of no use whatsoever in predicting the actual choices of each player - human action, the stuff economics is made of.<br /><br />"how do oligopolies decide on how much to produce given the production of the other firms? Game theory provides the answer to this question."<br /><br />So does economics, but only qualitatively. Neither branch of praxeology can predict the actual output of the firms - only that their owners will attempt to maximize their utility. Which is interesting because in this cartel scenario, the interests of individual producers are in conflict with those of the group, such that each producer has an incentive to overproduce to exploit the high prices established by cartelization and the other producers' underproduction. Not a single valid quantitative prediction emerges from this.Anonymoushttps://www.blogger.com/profile/02033352780260681914noreply@blogger.com