The notion that people might be “shortsighted” was formalized by David Laibson in “Golden Eggs
The notion that people might be “shortsighted” was formalized by David Laibson in “Golden Eggs and Hyperbolic Discounting” . In this paper the author hypothesizes that individuals maximize an intertemporal utility function of the form
where 0 <β <1 and 0 <δ <1. The particular time pattern of these discount factors leads to thepossibility of shortsightedness.
a. Laibson suggests hypothetical values of β =0.6 and δ =0.99. Show that, for these values, thefactors by which future consumption is discounted follow a general hyperbolic pattern. That is,show that the factors drop significantly for period t +1 and then follow a steady geometric rateof decline for subsequent periods.
b. Describe intuitively why this pattern of discount rates might lead to shortsighted behavior.
c. More formally, calculate the MRS between ct+1and ct+2at time t . Compare this to the MRSbetween ct+1and ct+2at time t +1. Explain why, with a constant real interest rate, this wouldimply “dynamically inconsistent” choices over time. Specifically, how would the relationshipbetween optimal ct+1and ct+2differ from these two perspectives?
d. Laibson explains that the pattern described in part (c) will lead “early selves” to find ways toconstrain “future selves” and so achieve full utility maximization. Explain why such constraintsare necessary.
e. Describe a few of the ways in which people seek to constrain their future choices in thereal world.
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Posted 18 Jun 2017 08:06 AM
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