tag:blogger.com,1999:blog-6837159629100463303.post6461156438794573724..comments2023-06-18T01:25:08.748-07:00Comments on Information Transfer Economics: Utility in an information equilibrium modelJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-6837159629100463303.post-38253435911622507152015-03-16T19:10:19.654-07:002015-03-16T19:10:19.654-07:00Yes, I think your argument still holds. You can ...Yes, I think your argument still holds. You can find a rational agent (although probably imaginary) that would have this utility function maximized for the max entropy for a large number of goods. As you point out there is no reason for this agent to have the same utility as an aggregate of the underlying agents or of the individual agents for exotic preferences or well behaved preferences over a small number of goods...<br /><br />However I think with this you could probably prove some pretty strong bounds about the maximum inefficiency (well-fare loss) in choosing the max entropy vs max utility for rational agents with continuous, monotonic, convex preferences.LALhttps://www.blogger.com/profile/08196675112184615614noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-27847854050753231342015-03-16T15:02:46.604-07:002015-03-16T15:02:46.604-07:00Another way, if the transformation was actually pr...Another way, if the transformation was actually preference preserving, then there would be no observable difference between MaxEnt equilibria and Max U(x) equilibria -- and I am saying there is an observable difference!Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-14022658124288668382015-03-16T14:55:59.869-07:002015-03-16T14:55:59.869-07:00I think you are right and I am wrong here -- the t...I think you are right and I am wrong here -- the transformation I show isn't actually preference preserving across baskets of goods. It actually changes the allocation.<br /><br />I will have to re-think that particular argument. However, I'm not sure the "preference preserving" aspect is necessary -- if prices are observable, but utility is not, then you can scale utility to conform with the observed equilibrium. The main question is still: do the observed equilibria correspond to maximum entropy or not (if not they can be described as the maximum utility solution for some utility function, and the maximum entropy equilibrium is not a good model).<br /><br />What I was attempting to say is that if all of the equilibria observed are maximum entropy equilbria, then there exists a utility function that makes them maximum utility solutions as well and both views are correct. If the equilibria aren't MaxEnt, then MaxEnt is not a good model.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-49017047814693887092015-03-16T13:35:46.504-07:002015-03-16T13:35:46.504-07:00my above comment is potentially ambiguous: any mon...my above comment is potentially ambiguous: any monotonic transformation preserves the ranking of bundles. you mean to be using the gauge theory to be talking about local transformations near the max entropy?LALhttps://www.blogger.com/profile/08196675112184615614noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-9840801772775589522015-03-16T13:29:40.419-07:002015-03-16T13:29:40.419-07:00I guess I am confused by your term "preferenc...I guess I am confused by your term "preference-preserving transformation".<br /><br />In economics that means a monotonic transformation of the utility curves that would change only the ordinal values of the utility function, but not the ranking of consumer bundles. Hence such a transformation wouldn't change the optimal choice.<br /><br />If I understand you correctly you are saying the transformation you have written down bends the curves to be tangent to the point on the budget constraint nearest the max entropy point?LALhttps://www.blogger.com/profile/08196675112184615614noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-88063414880067757792015-03-16T12:36:26.675-07:002015-03-16T12:36:26.675-07:00Cheers, LAL.
The realized value of utility evalua...Cheers, LAL.<br /><br />The realized value of utility evaluated at the entropy maximizing point can be changed by making utility transformations. Unlike utility maximizing point, the location of the entropy maximizing point is independent of the utility functions. <br /><br />The particular form of the transformation I wrote down scales the values of the exponents in the Cobb Douglas utility function at the top of the post. I can adjust those exponents so the utility level curves are tangent at the entropy maximizing point (in a large number of dimensions), making entropy maximization equivalent to utility maximization.<br /><br />Another way to put this is that the entropy maximizing and utility maximizing points only have to be distinguishable if you can actually measure prices and utility independently. Otherwise, you can re-scale utility to make the entropy maximizing point the utility maximizing point.<br /><br />Now this could of course be wrong -- entropy maximization says something specific and observable about where the equilibrium should be (near the middle of the budget constraint curve for a large number of items). I personally think that utility isn't really necessary (I use NGDP as the information source in the macro models) -- I'm mostly showing how one would approach it mathematically using information equilibrium.<br /><br />This is speculation at this point, but I think there may be a "gauge freedom" in <a href="http://en.wikipedia.org/wiki/Eric_Weinstein#Economic_theory" rel="nofollow">Weinstein's utility gauge theory</a> that explains why one is always able do that re-scaling. More to look into ...Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-9849701427339900832015-03-16T12:05:17.372-07:002015-03-16T12:05:17.372-07:00fascinating stuff...so the entropy maximizing poin...fascinating stuff...so the entropy maximizing point is dependent on utility transformations? and the transformation you suggested is there a particular reason to make it? or is it just one that works?LALhttps://www.blogger.com/profile/08196675112184615614noreply@blogger.com