Setting the alarm: setting the alarm in the evening and pressing the snooze button when it goes off in the morning.

Smoking: 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).

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.

For utility function u(.), outcome stream x yields utility stream
u = (u0, u1, …, un), with ui = u(xi) for every i.

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!

Notation:
(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).