Talk by Andrew Eberhard on 29 November
Next week, on Tue @ 11am (29/11/16), Prof. Andrew Eberhard will give a talk entitled "Revealed Preference Theory Revisited" here at RMIT. The details of the talk are below. As usual, we will have a light lunch after and a chance for networking.
Speaker: Prof. Andrew Eberhard, RMIT University
Title: Revealed Preference Theory Revisited
Date and time: Tuesday 29 November 2016, 11am-12pm
Location: 8.9.66 (RMIT Access grid room)
Abstract: When modelling consumer preference economist often model the demand relation as a solution to an optimisation problem which maximises some utility constrained to a given budget. In reality we are not a-priori given a utility but have only access to a finite selection of demand data that assigns a consumers choice of a commodity bundle at a given price. Most application simple statistically fit parameters of a given class of utility usually chosen according to some accepted economic dogma.
The problem of nonparametrically fitting a utility function to a finite data set was first solved by
Afriat in 1966. Mathematically this corresponds to the integration of a convex subdifferential (which also studied around the same time by Rockafellar). There have been other more recently proposed approaches, some of which we will briefly discuss.
In principle one might ask the philosophical question as to whether such methods approximate some "true" underlying utility in a limiting sense. This is known as the "Problem of revealed Preference" and has long history as well as being the subject of recent debates on the validity of certain axiomatic constructs. Accepting for now the status quo, this problem can be address via constructive variational approximations. This requires the use of some quite modern mathematical techniques relating to the convergence of sets and normal cones. We will make an attempt to disentangle several vexed issues in this context.
Based on joint work with Joint work with D. Ralph, JP Crouzeix, L Kocoska
Bio: Professor Eberhard obtained his PhD under the supervision of Charles Pearce at Adelaide. He has work most of his professional life at RMIT after short periods at Adelaide University and UniSA. He has served as a Discipline head of Mathematics at RMIT, been a deputy director of AMSI, served on a number AMSI committees including the AMSI board. His research interests include variational analysis, control and PDE theory, stochastic optimisation, algorithms in continuous and discrete optimisation and mathematical problems arising from economic theory.