# How to rationalize the following behaviors using preference relations?

1. The producer wishes to produce at least $$y^*$$ units. Once he has achieved that goal, he maximizes profit.

2. The producer maximizes profit, but already employs $$a^*_1$$ workers and will incur a cost c (whether in terms of money or the anguish it causes him) for each worker he fires. Thus, his utility function is given by π − c max{0,$$a^*_1 - a_1$$}.

3. The producer is a cooperative, which means that its profits are shared equally among its members who are both the owners and the workers. When choosing the number of members the cooperative seeks to maximize profit per member.

4. A“green producer” will have preferences over (π, pollution(z)) where pollution(z) is the amount of pollution, which is dependent on z.

More generally, what are the usual steps to rationalize a behavior?