Suppose Fred and Barney have different time discount rates T

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=0.5 whereas Barney’s value for r is 0.02. 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 0.3, 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 0.3 cancer risk].

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

Solution

Each and every person tries to maximize utility.

Fred’s present value of receiving a dollar next period is given by $1/(1+r), r=0.5 whereas Barney’s value for r is 0.02.

Here r is the discount rate used to derive present value of -$40000.

Let us assume that in next 40Years Fred and Barney would be \"Old\".

Now we find PV of -40000

For Fred= -40000/(1+0.5)^40

For Fred PV of -$40000 utility =-0.003618

For Barney,

=-40000/(1+0.02)^40

For Barney PV of -$40000 utility =-18115.62

NEGATIVE UTILITY exists when a phenomenon or action causes more harm than good. Whereas positive utility implies beneficence or increased hedonic pleasure, negative utility implies maleficence or decreased satisfaction. A good example of negative utility is the alcoholic who takes a drink. The drink may provide him with massive positive subjective utility but with net negative utility, because the alcohol is destroying his liver (as well as his kidneys and brain).

Here ,-18115.62 > -0.003618

i.e. For Barney it is causing more damage by being a smoker than for Fred.

Thus Fred would decide to become a smoker than Barney.

This happens because for Fred discount rate is higher than for Barney.