1. Many people fully intend to start exercising some day. Suppose there are thre
ID: 1113007 • Letter: 1
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1. Many people fully intend to start exercising some day. Suppose there are three dates: t-0,1 and 2. At time 0, two people, Hip and Hop, have the choice between the following two options, A and B: (A) exercising at time (utility received at time 1 is u(eercise)-0 i.e., it gives 0 utiles) and being healthy and happy at time 2 (utility received at time 2 is ulhealthy and happy)-12, i.e., 12 utiles); (B) watching television at time 1 (utility received at time 1 is uTV)-6,. 6 utiles being unhealthy and unhappy at time 2 (utility received at tirne 2 is u(unhealthy nd unhoppy)=0, i.e., 0 utiles) (a) Hip discounts her future utility exponentially (the model), with =2/3. From the point of view of time 0: What is her utility of A? What is her utility of B? (b) From the point of view of time 1: What is Hip's utility of A ? What is her utility of B? (c) Hop discounts his future utility hyperbolically (the -5 model), with =1/3 and =1 From the point of view of time 0: What is his utility of A ? What is his utlity of B? (d) From the point of view of time 1: What is Hop's utility of A? What is his utility of B? (e) Suppose that at time t=0. Hip and Hop cannot make any connnit ments. That is, their time 0 choices are reversible at time 1. Who will end up healthy an happy? Explain (f) Suppose that at time t=0. Hip and Hop can make firm commitments. That is, if they want, they can make sure that their choices at time 0 will be irreversible at time 1. Who will end up healthy and happy? Does your answer depend on whether Hop is a naive or sophisticated? ExplainExplanation / Answer
a)at point of view of time 0...Hop utilty of A is 12 and her utilty of B is 0
b)at point of view of time 1...Hips utility of A is 0 and her utilty of B is 6
c)at point of view of time 0...Hop utilty of A is 0 and her utilty of B is 6
d)at point of view of time 1...Hop utility of A is 0 and her utilty of B is 0
e)Hip will end up happy and healthy
f)If reversible, Hip will end up healthy and happy
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