Question

Suppose you are considering quitting smoking. This will be hard.  

The first day of quitting smoking your utility will drop (and then it goes up in the future).  

	Utility Today	Utility Tomorrow
Quit	5	10
Don't Quit	10	4

Question 9.

What is your present discounted utility of quitting smoking if you're daily discount rate is 0.8.  

Question 10

Likewise, what is your present discounted utility of not quitting?  

Question 11

Now suppose you use the same table as above, but you are a quasi hyperbolic discounter. Your discount rate is now 1/1+t : , where t is the number of days in the future. Now what is your presented discounted utility of quitting smoking?  

Question 12

What is your discounted utility of quitting smoking 8 days from now (meaning on the 8th day from now you quit)?  

Question 13

What is your present discounted utility of not quitting 8 days from now?

Answer 1

We are considering quitting smoking. This will be hard. The first day of quitting smoking your utility will drop (and then it goes up in the future).

Please look at the following table.

	Utility Today	Utility Tomorrow
Quit	5	10
Don't Quit	10	4

Now, we will answer the following questions with the help of the table above.

Now, before answering questions, let us see what is meant by discount rate.

Suppose, the utility in period 1 is u1 and in period 2 is u2. If the discount rate between period 1 and period 2 is 't', then the present discounted utility is Ud = u1 + t.u2. We will use this concept to answer the following questions.

Question 9

The utility of quitting smoking today is 5 and quitting tomorrow is 10.

If the daily discount rate is 0.8, then the present discounted value utility of quitting smoking is

(5+0.8×10) = 13 (Answer)

Question 10

The utility of not quitting smoking today is 10 and quitting tomorrow is 4.

If the daily discount rate is 0.8, then the present discounted value of utility of not quitting smoking is

(10 + 0.8×4) = 13.2 (Answer)

Now, we are quasi hyperbolic discounter. Hence,the discount rate is 1/(1+t), where t isthe number of days in future.

Question 11

Now, if we quit smoking tomorrow, then there is only 1 day in future. Hence t=1.

We get the discount rate is 1/(1+1) i.e. 0.5.

Hence, utility of quitting smoking today is 5 and quitting tomorrow is 10.

If, discount rate is 0.5, then the present discounted value of utility of quitting smoking is

(5 + 10×0.5) = 10 (Answer)

Question 12

If we quit smoking 8 days from now, then there are 7 days in future. Hence, t=7.

We get the discount rate is 1/(1+7) = 0.125.

Hence, utility of quitting smoking today is 5 and quitting tomorrow is 10.

If, discount rate is 0.125, then the present discounted value of utility of quitting smoking is

(5 + 10×0.125) = 6.25 (Answer)

Question 13

The utility of not quitting smoking today is 10 and quitting tomorrow is 4.

If, discount rate is 0.125, then the present discounted value of utility of not quitting smoking is

(10 + 0.125×4) = 10.5 (Answer)

Hope the solutions are clear to you my friend.