tag:blogger.com,1999:blog-1740670447258719504.post1427410961622653790..comments2024-03-27T03:00:27.024-04:00Comments on Facts & other stubborn things: Bob Murphy is too easy on KrugmanEvanhttp://www.blogger.com/profile/12259004160963531720noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-1740670447258719504.post-75020476883520952702012-07-20T05:42:37.662-04:002012-07-20T05:42:37.662-04:00The problem is: does everyone else's income fa...The problem is: does everyone else's income fall or just Wheelerdealers?<br /><br />Remember, the assumption is that Wheelerdealer is being paid his marginal product per hour. So if he withdraws his output he withdraws his income at the same time in equal measure.<br /><br />Now, what everyone is getting at is that this marginal proposition doesn't work on a larger scale. If say, 50% of the population worked 2/3rds of their old hours then it's pretty obvious that output would fall for others as well as for them.Currenthttps://www.blogger.com/profile/08645195276844244481noreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-80185873180277967942012-07-20T04:57:03.343-04:002012-07-20T04:57:03.343-04:00Isn't it easier than this? If Wheelerdealer wo...Isn't it easier than this? If Wheelerdealer works less, ouput falls; everyone's real wage falls. The only way that doesn't happen is if someone works more to compensate. Who? Why?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-24661496569486415202012-07-19T13:17:16.549-04:002012-07-19T13:17:16.549-04:00"But I don't think Krugman's right to..."But I don't think Krugman's right to be so sanguine about an accounting identity."<br /><br />Yah, I agree that is weak sauce. It's very irksome considering how often he harps on people misusing accounting identities.Dallas Woodhttps://www.blogger.com/profile/10007472086816707957noreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-41875153096469603802012-07-19T13:13:56.143-04:002012-07-19T13:13:56.143-04:00Yah, I think your edit works. Though, I think in p...Yah, I think your edit works. Though, I think in producer theory it is an "output effect" and not income effect (since firms do not have a fixed income). Though I like your idea of framing it in terms of something like the slutsky equation. :)<br /><br />I think if we wanted to state it formally, it would look like this. <br /><br />Let the production function be y=(x1^a)*(x2^(1-a)).<br />The optimal demand for the first factor is a function of wages and output: <br />x1(w1, w2, y*) <br />w1 = price of factor 1<br />w2 = price of factor 2<br />y* = profit maximizing level of output (which is itself a function of w1, w2)<br /><br />Take partial derivative of x1 with respect to w2. Using chain rule we get:<br />dx1/dw2 + ((dx1/dy)*(dy/dw2))<br /><br />The first term is always positive because x1 is a substitute for x2 (call it the "substitute effect"). <br /><br />The second term is always negative (call it the "output effect"). If x1 is a normal factor, then increasing produciton means increasing x1 (dx1/dy >0). Similarly, if x2 is a normal factor, then increasing its price should reduce output unless demand is totally inelastic (dy/dw2 <0).<br /><br />Whether demand for x1 increases or decreases will depend on which of the two effects is bigger. <br /><br />I am not sure exactly how to illustrate this graphically, but I would say your drawings are close enough.Dallas Woodhttps://www.blogger.com/profile/10007472086816707957noreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-89795016560280222772012-07-19T12:29:54.097-04:002012-07-19T12:29:54.097-04:00I did see it - I've been spending way too much...I did see it - I've been spending way too much time on these posts this morning already to really get into all of those points right now. Sorry :-/Daniel Kuehnhttp://www.factsandotherstubbornthings.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-60394225969265034592012-07-19T12:28:55.403-04:002012-07-19T12:28:55.403-04:00What really, really bugs me about the Krugman post...What really, really bugs me about the Krugman post is the <i>"income equals expenditure so it's all OK"</i> attitude. I'm happy to concede that substitution during reoptimization happens - it's in the graphic I drew in the next post to illustrate the differences. But I don't think Krugman's right to be so sanguine about an accounting identity. That's the sort of thing that they're supposed to get wrong, not us.Daniel Kuehnhttp://www.factsandotherstubbornthings.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-5744902364163075922012-07-19T12:27:03.680-04:002012-07-19T12:27:03.680-04:00Thanks - see what you think of the update. I think...Thanks - see what you think of the update. I think that works.Daniel Kuehnhttp://www.factsandotherstubbornthings.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-54354940847563158412012-07-19T12:06:47.707-04:002012-07-19T12:06:47.707-04:00You say that when the price of K increases, the de...You say that when the price of K increases, the demand for L will decrease. I don't think this is quite right. <br /><br />Intuitively, K and L are substitutes in the production process described by a Cobb-Douglas Production Function. So if the price of K increases, demand for its substitute (L) should increase for a given level of output.<br /><br />We can see mathematically that this is the case if we do the full cost-minimization problem--min wL + rK s.t. Y=(K^a)*(L^(1-a)).<br /><br />For simplicity, let a=1/2. Then solving the above optimization problem will yield the following conditional factor demand for L:<br />L=Y*((r/w)^(1/2))<br /><br />As we can see, an increase in r (the price of K) leads to an increase in L (demand for labor) for a given level of output Y. <br /><br />So we cannot jump from an increase in the price of K to a decrease in L or Y as you want to do in your post. Instead, if we want to know the profit-maximizing demand for L, we will need to more explicitly model the output market.<br /><br />If demand for output is totally inelastic, then Y would not to change at all, wages might increase, and Krugman's analysis might be closer to correct then you initially suspected. <br /><br />This remands me. I think Brad Delong has a law about what you should do when you think Paul Krugman is wrong. :)Dallas Woodhttps://www.blogger.com/profile/10007472086816707957noreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-11378581335771445552012-07-19T11:21:04.086-04:002012-07-19T11:21:04.086-04:00Thanks for the response, Daniel. BTW, did you get ...Thanks for the response, Daniel. BTW, did you get that long e-mail I sent to you? (I know you hate to see me put in a lot of energy into e-mails, but it's a habit of mine, I like putting a lot of effort into writing letters!)Blue Aurorahttps://www.blogger.com/profile/02044362251868221897noreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-64616548227877138732012-07-19T10:34:28.463-04:002012-07-19T10:34:28.463-04:00"However, Dr. Michael Emmett Brady did state ...<i>"However, Dr. Michael Emmett Brady did state somewhere that savings equates to investment at different levels of equilibria. It is only at a full employment equilibrium that savings, which equate to investment, become optimized (correct me if I'm wrong on this point)."</i><br /><br />Optimization implies some sort of value system.<br /><br />It's certainly true to say that it's only at full employment that savings, which is equal to investment, reflects investment at a full employment level!<br /><br />That sounds like I'm trivializing the question, but I'm actually trying to make a point: you can have non-full-employment levels of output in a situation where every single person in the economy is optimizing.<br /><br />So it really comes down to what we're calling "optimal".<br /><br />My knowledge of game theory is not particularly good. It's certainly not a panacea. But it is a better tool for some jobs than traditional marginal analysis.Daniel Kuehnhttp://www.factsandotherstubbornthings.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-1740670447258719504.post-6492480545981175512012-07-19T10:18:59.088-04:002012-07-19T10:18:59.088-04:00"Just because income equals expenditure does ..."<i>Just because income equals expenditure does not mean that national income remains unchanged when you rearrange production or demand! This is the whole point of Keynes's paradox of thrift. Just because income is still equaling investment doesn't mean that those quantities don't shift around. What it means is that if they shift around they're going to shift around together. That's all the accounting identity Krugman appeals to says.<br /><br />Accounting identities are funny like that.</i>"<br /><br />Keynes in the <i>General Theory</i> says that Investment = Savings in one chapter. I found that confusing. However, Dr. Michael Emmett Brady did state somewhere that savings equates to investment at different levels of equilibria. It is only at a full employment equilibrium that savings, which equate to investment, become optimized (correct me if I'm wrong on this point).<br /><br />But since you speak of game theory Daniel...how good is your knowledge of it? Game theory is not a panacea.Blue Aurorahttps://www.blogger.com/profile/02044362251868221897noreply@blogger.com