Behavioral eco lect 5: Intertemporal choice part 1 (Agenda (Rational…
Behavioral eco lect 5: Intertemporal choice part 1
3 puzzling phenomena
Setting the alarm:
setting the alarm in the evening and pressing the snooze button when it goes off in the morning.
: planning to quit in the future but failing to do so.
Subscription to the gym
: buying a subscription to the gym rather than paying per visit, even when the latter would be cheaper (DellaVigna and Malmendier, 2006).
Sign and magnitude effect
Violations of discounted utility
Can we predict future utilities?
Time t = 1 is one period ahead (at one unit time distance from today)
We consider outcome streams x = (x0, x1, …, xn), which give outcomes xi at time i.
Time t = 0 represents today.
For utility function u(.), outcome stream x yields utility stream
u = (u0, u1, …, un), with ui = u(xi) for every i.
D(.) is the
We always assume that D(0) = 1 (today is not discounted)
The discounted utility (DU) of utility stream u = (u0, u1, …, un) is given by
DU(u) = u0 + D(1) u1 + … + D(n) un
The discounted utility (DU) of outcome stream x = (x0, x1, …, xn) is given by
DU(x) = u(x0) + D(1) u(x1) + … + D(n) u(xn)
NOTE: this definition of impatience is different from the one in the book. We will stick to the definition on this slide!
(s : x) stands for receiving outcome x at time s.
(s:x, t:y) stands for receiving outcome x at time s and outcome y at time t.
A person is impatient if he prefers an outcome with positive utility sooner rather than later:
A person is impatient if for all x ≻ 0 and s < t we have (s : x) ≻ (t : x).
Reasons for impatience
We can earn interest, so €100 now is worth more than €100 in the future.
The future is uncertain, and a risk averse person prefers a sure €100 (now) to an uncertain €100 (in the future):
one may not be sure whether one will receive the promised €100 in the future
one may not be sure what one can buy with €100 in the future.
We simply care more about the present than about the future, just like preferring a banana to an apple.