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Behavioral eco lect 5: Intertemporal choice part 4 (Quasi-hyperbolic…
Behavioral eco lect 5: Intertemporal choice part 4
Quasi-hyperbolic discounting
The following graph gives the discounted utilities of these outcome computed at time t:
DU(x) = βδ^(6-t ) 3 and DU(y) = βδ^(10-t )x 4
Both lines useβ = 0.8 and δ = 0.95
NOTE
early on, for small t, you prefer y
later on, for larger t, you prefer x
Imagine receiving outcome y with utility u(y) = 4 at time t = 10 or outcome x with utility u(x) = 3 at time t = 6.
Self-commitment
People who are aware of their time-inconsistency, may have a preference for self-commitment: committing themselves now to a future choice.
EXAMPLE
Sign & magnitude effect
Magnitude effect
: large outcomes are discounted at a lower rate than small ones.
Sign effect:
losses are discounted at a lower rate than gains.
Two other deviations from exponential discounting that have been documented in the literature:
Violations of discounted utility**
Unpleasant events
According to impatience, you would prefer to go in one week.
But many people prefer to go today, even those people who prefer €100 today over €100 in one week.
Imagine you have to schedule a dentist appointment. What would you prefer : today or in a week?
Possible reason: we already derive utility from looking forward to events (= anticipation utility)
Increasing utility profiles
Impatience:
D(0) > D(1) > D(2) → DU(A) < DU(B)
Proof: DU(A) – DU(B) = [D(0)-D(2)]*[u(50) – u(150)] < 0
In practice many people prefer A, the improving profile
DU(B) = D(0)u(150) + D(1)u(100) + D(2)u(50)
DU(A) = D(0)u(50) + D(1)u(100) + D(2)u(150)
Which option do you prefer?
A: €50 today, €100 in one month, €150 in two months
B: €150 today, €100 in one month, €50 in two months
Possible reason: if we compare outcomes to previous ones, then in A we will not experience loss aversion, but in B we will.