Economics 601 -Microeconomics: Theory and Applications
Final Exam
Please answer all questions below. Answers are due as a single document (pdf preferred) on Canvas. Feel free to scan / take photos of hand-drawn answers for math, figures, or diagrams, just make sure to embed them in your answers. Email me if you have any clarifying or similar questions, and good luck!
3. Social Preferences (20 points) A major theme of this class has been how social preferences influence behavior. Consider two students working on a joint project who care about both their own outcomes as well as the outcomes of students that they work with, such that for each individual i receiving payoffs πi while working with individual j receiving payoff πj :
Ui =πi +βπj
where:
β=(ai +λi aj)/(1+λi)
is the extent they care about the other student, ai ∈ [-1,1] is student i’s feelings of altruism or spite
towards student j (and vice versa), and λi ≥ 0 is student i’s preference for reciprocity.
3.1. Imagine a project where each contributor can expend continuous effort ei ∈ [0,1] with payoff
equal to the sum of all effort contributed divided by the number of participants (i.e., the average effort), and subjective cost of effort c(ei) = 3⁄4 e. If a single individual were choosing the amount of effort to contribute to such a project, how much effort would they put in? Explain.
3.2. Now imagine that the same project involves two students, such that the output of ei + ej is split equally between the two of them. The students are reasonably reciprocal, with λ = 1⁄2 , and reasonably altruistic, with a = 1⁄2 for each student, but that information is private, so each student i believes student j’s altruism aj corresponds to the effort ej they expect the other player to contribute to the project. Show that differing initial expectations of aj produce three distinct Nash Equilibria, indicate which ones are stable, and explain why a general norm of cooperating on student projects leads to a pareto-superior outcome.
