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.

Refusing or Accepting an Event

There are three kinds of events as it comes to deciding whether to refuse or accept it's occurrence:

1. Only one consumer can make either accept or refuse

2. Both consumers can make either accept or refuse

3. Neither can make the decision, ie. the event simply happens

A Spiritual Event

A spiritual event means any event that has any direct spiritual or moral consequences. Any event that can happen has one of the following direct spiritual or moral consequences:

1. It makes the one better, but has no impact on the other

2. It makes the one worse, but has no impact on the other

3. It makes both better

4. It makes both worse

5. It makes the one better and the other worse

6. It has no impact on neither.

A Material Event

A material event means any event that has any direct material consequences. Any event that can happen has one of the following direct material consequences:

1. It increases the wealth of the one, but has no impact on the material wealth of the other

2. It decreases the wealth of the one, but has no impact on the material wealth of the other

3. It increases both consumers' wealth

4. It decreases both consumers' wealth

5. It increases the wealth of the one and decreases the wealth of the other

6. It has no impact on the material wealth of neither

An event can be both material and spiritual at the same time, both or neither.

Types of Choices

The consumers have four different kinds of choices they have to make:

1. To accept or reject the material event that has been offered them

2. To give or not to give to the other consumer

3. To act as one prefers or to act as one ought to

4. To accept or reject the spiritual event that has been offered them

Strict Monotonicity

Both of my imaginary friends prefer to consume more rather than less.

Transitivity

Both of the consumers have the capacity to make consistent choices according to their own preferences if they will.

Completeness

Both of my friends know, if given a choice between two options, which option they prefer, and can if they will to make a decision accordingly.

Cost of Giving Is Zero

Both of my consumers can either consume what they have or to give it or part of it away. If they decide to give to the other, then the cost of giving is zero.

No Production

The life of my imaginery friends is very simple in this that they don't produce anything. They simply receive what they have as a gift and then consume it or give it away.

One Good

My imaginery friends are alike in this that they both consume only one good. The name of this good is Materia.