1. Imagine you are a government minister faces with the decision to invest a long term infrastructure project. The choice is between a notional immediate investment & a long term reward, or an immediate gain without notional spend and no long term reward (and potential loss).
2. Would you prefer $500 now or $1000 in ten years?
--Most people would prefer the option with immediate reward, which has a lower value but has a higher utility because the utility of the other option is discounted by its delay.
Discounted Utility Model:
～Exponential Discounting
->Normative assumption of discount function-discount at an exponential constant rate.
->Where v=subjective discounted value, k=discount rate and d=the delay.
->3 properties that fit empirical behaviour:
=>If there is no delay there is no discounting.
=>As delay increases the present value decreases.
=>As delay approaches infinity the present value approaches 0.
->The normative model falls when the delay changes.
- Would you prefer $500 now or $1000 in 10 years?
- Would you prefer $500 in 10 years or $1000 in 20 years?
=>The 4th property-two discount functions with the same discount rates cannot cross.
*This dynamic inconsistency can be explained with the hyperbolic form of discount function.
~Hyperbolic Discounting
->Where v=subjective discounted value, k=the discount rate and D=the delay.
->Has the same 3 properties but does accommodate dynamic inconsistencies.
Why do people discount the future?
=>Interest rates
-If I take $500 now I could take control and invest it for a higher rate of return than the delayed alternative.
=>Uncertainty
-The future is both risky & uncertain. (What if the bank hold my investment? The currency collapse? Or the probability itself could discount in a similar way?)
=>Emotion based theories
- Loewenstein, 1996: Temporal & physical proximity of options that can reduce aversive states leads to a disproportionate increase in the attractiveness of those option.
- People with low discount rates (rather than exhibiting self control) are savouring the delayed gratification. They enjoy the wait in the knowledge that the result will be greater than if we impatiently take the immediate option.
- The discount rates differ between individuals. When we make decisions on behalf of others we do not directly experience the gratification itself.
- Ziegler & Tunney, 2012: estimate the discount rate for the decisions made when we are the recipient compared to when other people who differ in social distance to ourselves are the recipient.
- The discount rate varied as a function the coefficient of relatedness (as a measure of social distance) with decisions made for ourselves being more impulsive than decisions made for other people.
- Except for our close relative/best friends, the decisions made for strangers are the least impulsive.
The Sunk-cost fallacy:
=>Cost that has been incurred and could not be recovered once spent.
=>The tendency to continue an endeavour once an investment in money/effort/time has been made.
=>The fallacy occurs when we are committed to a current investment even when a switch has higher returns.
=>A rational agent is interested only in the future of current investments not previous ones.
=>Imagine you were a president of an airline company, of the following situations would you invest the last million dollars of your research funds.?
- $10 million has already been spent on building a radar-blank plane. When the project is 90% completed, another firm begins marketing a radar-blank plane, also their plane is much faster and more economical than the plane your company is building.
- Over 80% chose to continue building the radar-blank plane.
- You have received a suggestion to build a radar-blank plane. However, another film has just begun marketing their radar-blank plane which is much faster and economical than the plane your company could build.
- More than 80% chose to not invest on the radar-blank plane.
=>Thaler(1980) explained sunk-consts with prospect theory. Previous investment are treated as losses and the losses are meant to be avoided/recouped.
=>Arkes & Ayton (1999) argue that sunk-cost occur because of a simple heuristic to avoid waste. Money invested is wasted unless a dividend is returned is returned, even if that is on average less than an alternative.
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