(Reference-Dependence and Satisficing) Economic theory predicts that increases in wages normally lead to increases in the supply of labor. However, a popular study shows that cab drivers in New York City work longer hours on days when their per-hour wage is low, and it explains this in terms of cab drivers with a target revenue for the day that acts as their reference point.

In this problem you are asked to show that the cab drivers' behavior can also be accommodated within a version of the Satisfying model: the agent has a maximum of 12 hrs in a day that she can work, and her aspiration is not a utility level, but a target of making at least $500 in a work day. Her utility from working q hours at an hourly rate w is given by wq q2 (so she likes total income but dislikes working). If her target is not achievable, then she just maximizes her utility. If the target level of income is achievable, then she chooses any feasible number of hours that yield at least her target income.

Formulate the model by doing the following (warning: (i) and (ii) require care):

(i) Specify the choice domain.

(ii) Write the agent's menu when the hourly rate is w.

(iii) Determine the agent's choice from menus corresponding to wages $22/hr

and $50/hr respectively.2

(iv) Point out how the choices relate to the finding in the study.