Problem Set on Abstract Choice and Choice under Uncertainty

EC 323

    INSTRUCTIONS: You will be graded not just on the correctness of your responses, but also on how efficient and precise your reasoning is. Superfluous sentences will be penalized, and no answer should be more than a couple of sentences long. The onus is on you to demonstrate that your understanding of the material is clear.

    DUE DATE: 04/02/2021

    Q1. (Behavioral Distinctions) One would hope that two agents with different psychology can always be distinguished through their behavior. While they sometimes can, it is not always the case. This question explores this.

    (a) Suppose that an agent is offered money: she can choose any dollar amount upto $M. We see that she chooses

C({0, 1, ..., M}) = {M}.

    Show by example that this choice can be explain equally well by (i) utility maximization with diminishing marginal utility for money, and (ii) utility max-imization with increasing marginal utility for money.

    (b) Consider an agent who has to choose how many donuts to eat. He exhibits the choices

C({1, 2}) = {1, 2}andC({1, 2, 3}) = {2, 3}.

    Can these choices be explained by (i) maximization of a complete and transitive preference? (ii) satisficing? (iii) regret aversion?

    (c) Suppose now that the donut-eating agent exhibits the following choices:

C({1, 2}) = {1}andC({1, 2, 3}) = {2}.

    Can these choices be explained by (i) maximization of a complete and transitive preference? (ii) satisficing? (iii) motivated reasoning?

    Q2. (Motivated Reasoning and Intelligence) In the context of the motivated reasoning model, consider two agents who have the same true dark desires given by u(c) > u(b) > u(a). Show by a simple example that if agent A is more adept at coming up with rationales than agent B, then she can satisfy her true desires while agent B may not.

    Q3. (Reference-Dependence and Satisficing) Economic theory pre-dicts 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.1 In this problem you are asked to show that the cab drivers’ behavior can also be accommodated within a version of the Satisficing 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 − 5q2 (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 $20/hr and $50/hr respectively.2

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

    Q4. (Loss Aversion and Trade) A popular idea in economics (based on the so-called Coase Theorem) is that regardless of goods are allocated in an economy, people will trade their way to an efficient equilibrium. For instance, if there is one good and two agents, then no matter who starts by owning the good, the good will eventually be owned by the person who values it the most. In this problem we revisit this idea in the context of loss-aversion.

    Suppose there is a free concert that takes place every year, and agent A (resp. agent B) gets $50 (resp. $60) worth of utility from attending that concert in any year. The tickets to the concert are in excess demand every year. In 2018, agent A managed to get the ticket from the ticket office while agent B did not, and in 2019, B managed to get the ticket from the ticket office and A did not.

    (a) From the perspective of standard theory (where the utility of an alter-native is measured in dollar terms and any dollar payments are subtracted from it), what is the range of prices (if there exists any) in 2018 at which A would be willing to sell the ticket and B will be willing to buy it? What is the range in 2019 at which B would be willing to sell the ticket and A would be willing to buy it? For each of these years, say whether trade will take place and say who will end up with the ticket.

    (b) Suppose instead that the agents are reference-dependent and loss averse, in that the ticket-holder looks forward to attending the concert and incurs a $20 disutility if he does not end up going, while the agent who does not have the ticket expects not to go and experiences no loss if he does not end up going. Redo the analysis in part (a).