Consider the time preference model of O'Donoghue and Rabin (1999), in which an agent has to complete ...

---

Consider the time preference model of O'Donoghue and Rabin (1999), in which an agent has to complete a task within T periods. (a) Assume that T = 4. Let time preferences be given by the (beta, delta)-model with delta = 1. The utility from completing the task is V, regardless of the completion date. While the utility occurs in the future, costs are immediate: C = 3 in t = 1, C = 5 in t = 2, C = 8 in t = 3, and C = 12 in t = 4. Time-inconsistent agents have beta = 1/3. Derive the perception-perfect strategies for the three types of agents (time-consistent, time-inconsistent sophisticates, and time-inconsistent naifs), and indicate for each type the period in which she effectively completes the task. Explain your answers. (b) Explain why sophisticates may behave in ways that seemingly contradict having present-biased preferences.