tag:blogger.com,1999:blog-26706564.post9018078622276269099..comments2017-12-03T12:34:56.402-05:00Comments on Thoughts On Economics: Perfect Competition With An Uncountable Infinity Of FirmsRobert Vienneauhttp://www.blogger.com/profile/14748118392842775431noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-26706564.post-3448014380995981502017-06-17T13:24:03.324-04:002017-06-17T13:24:03.324-04:00«How can firms change hours worked (to optimise pr...«<i>How can firms change hours worked (to optimise profits) without dragging in the household optimisation problem? Both optimisation problems will interact with each other,</i>»<br /><br />Wave your hands and say "the auctioneer", "tatonnement", "rational expectations" at least three times. It usually works :-).<br />Blissexnoreply@blogger.comtag:blogger.com,1999:blog-26706564.post-67925127887079923012017-06-17T13:20:48.622-04:002017-06-17T13:20:48.622-04:00«For example, the probability density function for...«<i>For example, the probability density function for any continuous random variable is only defined up to a set of Lebesque measure zero.</i>»<br /><br />Ahem ahem, a number of sensible statisticians I suspect would have serious misgivings with any statement involving statistics and infinities or infinitesimals. It's a contentious issue.<br /><br />«<i>And probability theory is very useful empirically.</i>»<br /><br />Sure, but you are talking about a particular model/interpretation of probability theory, one that involves deep mathematical trickery that. A completely unrealistic model can still be an empirically useful model most of the time.<br />For example in signal processing it is often the case that a discrete signal is <em>approximated</em> with a continuous one, because the latter is more tractable symbolically, regardless of whether the continuous model is well-founded intellectually. "As long as it works". Physicists do a lot of the same misuse of cod-maths "because it works" "in most cases", without questioning the assumptions. As long as the bombs explode they get a lot of funding, very empirically :-).<br /><br />This is a problem that mathematicians themselves have had for a long time: much mathematics empirically worked most of the time even if its "foundations" were broken. Because actually "weak logics" tend to empirically work most of the time too. But even many logicians ignore that the study and use of "weak logics" is a fruitful and interesting topic...Blissexnoreply@blogger.comtag:blogger.com,1999:blog-26706564.post-56032378255607033292017-06-16T09:17:21.283-04:002017-06-16T09:17:21.283-04:00The thing that bothers me: how can firms change ho...The thing that bothers me: how can firms change hours worked (to optimise profits) without dragging in the household optimisation problem? Both optimisation problems will interact with each other, as well as government spending and the household budget constraint, which are specified as aggregate values.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.com