Question

Suppose Fred and Barney have different time discount rates. There are two periods of life: “young”, and “old”. Fred’s present value of receiving a dollar next period is given by $1/(1+r), r=0.25 whereas Barney’s value for r is 0.05. Fred and Barney are currently “young”, living in Colorado, and deciding whether to become marijuana smokers. Suppose all utility is viewed in dollars, and they both value the current (when “young”) utility of smoking to be $10,000 and they both understand that with probability 0.35, they would develop lung cancer when old (which would involve utility of -$40,000). [note: The scientific evidence on this is mixed, but let’s just suppose there is a 0.35 cancer risk].

Would Barney decide to become a smoker? Why or why not?

Would Fred decide to become a smoker? Why or why not?

How large would the loss of utility have to be to ensure neither Barney or Fred becomes a smoker?

Answer 1

STEP1 Lets understand The Basis of this question. To Understand It it is important to know the meaning of utility,negative utility and positive utility LETSthrow some light on it to solve the question.This terminologyy belongs to eceonomics and utility means Usefulness.Negative utility means when you consume an extra part or unit of something that causes harmful affect on you or is disadvantageous to you.Vice versa Positive utility with every additional unit consumed you get benefit or advantage.So in this question Negative utility of smoking has been taken into consideration by quantifying its value in $.

Step2:GIven Figures

Fred's Discount rate=0.25

Barney's Discount rate=0.05

NPV(net present value) =FV /1+R)^T

LET US ASSUME THAT BOTH FRED & BARNEY WILL BE OLD IN NEXT 50YEARS

NPV of Fred=-40000/(1+0.25)^50=-0.570

NPV of Barney=-40000/(1+0.05)^50=-3490

with above calculation After discounting

We conclude that NPV of Barney's negative utility is Higher than Fred..

Step3:Lets Answer The case scenerios

1.Barney's Negative utility is higher hence It is disadvantageous for barney to smoke as compared to fred hence Barney should not become a Smoker

2.Compared to Barney Fred's Negative utility is lower hence in his comparision he may choose to smoke.

3.Loss of Utility

probability of lung cancer 0.35 when old

hence probability of utility .65 when Current Value=$10000 (when they are young)

therefore 0.35(-40000) + 0.65*(10000)

=-14000+6500

= -7500.

=-7500

hence a situation where NOne of them should smoke would be when loss of utility is -7500.