3. Consider an agent who evaluates utility delayed by k periods with a discount factor of B8k. Time isdiscrete and indexed by t E {0,1,2, ...}. This individual has to complete a project (which only takes oneperiod to complete) before or during period T, where the (undiscounted) utility cost of completing thetproject in period t isa) Explain the difference between an exponential discounter, a naïve hyperbolic discounter and asophisticated hyperbolic discounter.b) Suppose the individual is an exponential discounter with Bcompleted?= 1 and 8 = 1. When will the project bec) Now suppose the individual is a naïve hyperbolic discounter with B = and 8 = 1. Calculate whenthis individual will plan on completing the project, and when it will actually be completed.d) Now consider the behaviour of a sophisticated hyperbolic discounter with B = and & = 1. Provethat if T is even, then the individual will finish the project in period 0, whereas if T is odd the project willbe completed in period 1. [Hint: start by considering how the individual will behave in period T-1, andthen work your way backwards.]

A desire for immediate gratification promotes seeking immediate enjoyment. As a result, the…

3. Consider an agent who evaluates utility delayed by k periods with a discount factor of 8k. Time is discrete and indexed by t € {0,1,2,...}. This individual has to complete a project (which only takes one period to complete) before or during period T, where the (undiscounted) utility cost of completing the is (²) ². project in period tis a) Explain the difference between an exponential discounter, a naïve hyperbolic discounter and a sophisticated hyperbolic discounter. b) Suppose the individual is an exponential discounter with = 1 and 8 = 1. When will the project be completed? c) Now suppose the individual is a naïve hyperbolic discounter with ß = 1 and 8 = 1. Calculate when this individual will plan on completing the project, and when it will actually be completed. d) Now consider the behaviour of a sophisticated hyperbolic discounter with ß = 1/2 and 8 = 1. Prove that if 'T' is even, then the individual will finish the project in period 0, whereas if 'T' is odd the project will

3. Consider an agent who evaluates utility delayed by k periods with a discount factor of 8k. Time is discrete and indexed by t € {0,1,2,...}. This individual has to complete a project (which only takes one period to complete) before or during period T, where the (undiscounted) utility cost of completing the is (²) ². project in period tis a) Explain the difference between an exponential discounter, a naïve hyperbolic discounter and a sophisticated hyperbolic discounter. b) Suppose the individual is an exponential discounter with = 1 and 8 = 1. When will the project be completed? c) Now suppose the individual is a naïve hyperbolic discounter with ß = 1 and 8 = 1. Calculate when this individual will plan on completing the project, and when it will actually be completed. d) Now consider the behaviour of a sophisticated hyperbolic discounter with ß = 1/2 and 8 = 1. Prove that if 'T' is even, then the individual will finish the project in period 0, whereas if 'T' is odd the project will

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

3. Consider an agent who evaluates utility delayed by k periods with a discount factor of B8k. Time is
discrete and indexed by t E {0,1,2, ...}. This individual has to complete a project (which only takes one
period to complete) before or during period T, where the (undiscounted) utility cost of completing the
t
project in period t is
a) Explain the difference between an exponential discounter, a naïve hyperbolic discounter and a
sophisticated hyperbolic discounter.
b) Suppose the individual is an exponential discounter with B
completed?
= 1 and 8 = 1. When will the project be
c) Now suppose the individual is a naïve hyperbolic discounter with B = and 8 = 1. Calculate when
this individual will plan on completing the project, and when it will actually be completed.
d) Now consider the behaviour of a sophisticated hyperbolic discounter with B = and & = 1. Prove
that if T is even, then the individual will finish the project in period 0, whereas if T is odd the project will
be completed in period 1. [Hint: start by considering how the individual will behave in period T-1, and
then work your way backwards.]

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