# Enunciation/notation in utility maximisation model

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1. Jan 9, 2016

### vabm

Hi Everyone. I am working on a model that I think can be defined as a utility optimisation problem but I'm struggling with the enunciation and notation.

The model should describe how the utilities of a set of agents A={1,2,...,n} increase with the availability of a larger set of product types P={1,2,...n}, while the utilities of a supplier S decrease with the size of P. The ideal state for A is Pn and for S is P1 (one product type for each agent v/s a single product type for all). This assuming that each product type can potentially give a certain amount of utilities to each agent, so for A1 utilities might be u(P1) > u(P2), for A2 utilities might be u(P1) < u(P2), and for A3 utilities might be u(P1) = u(P2), etc. The utilities perceived are different for each agent and they are not indifferent to any product, so if P needs to be reduced to e.g. 5 types, the problem of choosing element types is not irrelevant.

Then, the (optimisation-like) problem is to maximise utilities for An finding the best combination of products among the whole 'virtual' set Pn if the 'actual' set P has to have no more than x number of elements.

Is this more or less ok or am I completely lost? How can I express it as a utility maximisation equation? Any help/directions refining this would be great help.

2. Jan 14, 2016

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?