Initial Utility Maximizing Amounts of Consumption

Initial utility maximizing amounts of consumption for both consumers are:

x* = w, where

again wealth is expressed in units of the one good in existence.

Initial Utility Functions

Because the only thing that the utility functions needs to capture initially is that both consumers want to consume rather more than less, caring nothing about the consumption of the other, so the utility function can be any increasing function of the amount of consumption, x. The simplest such function will be x itself and will thus be used. So, the utility functions of both consumers are initially:

u(x) = x.

Initial Budget Constraints

Because both consumers consume all the wealth they have, giving none away and liking more more than less, both consumers budget constraints will be of the form:

x = w,

where x is amount of consumption of the one good and w is wealth measured in units of the one good.

Both Consumers Are Initially Egoists

In the beginning both consumers only think of themselves in the sense that neither gives any part of their wealth to the other.

Goodness and Badness

In my imaginary world a perfect consumer would love the other consumer just as he loves himself. Preferences of both can be represented with a utility function.

Acting as One Prefers or as One Ought to

Both consumer know both what they prefer and what they ought to prefer, although they do not know what they ought to prefer perfectly. Every time they make a decision they have these options, to do what one prefers or to do as one ought.

Giving or Not Giving

Every consumer has to make the choice of how much of material wealth they are going to give to the other, if any.