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

1. What is your present discounted utility of quitting smoking if you're daily discount rate is .8.  

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

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

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

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

Answer 1

Formula:
Present Discounted Utility = Utility today + Utility tomorrow/(1+r)

(1) Present Discounted Utility of quitting:
= 5 + 10/(1+0.8)
= 10.55 utils

(2) Present Discounted Utility of not quitting:
= 10 + 4/(1+0.8)
= 12.2 utils

(3) Discounted Rate = 1/(1+t)
Discounted Utility of quitting smoking:
= 5 + 10/(1.5)
= 11.67

Discounted utility of not quitting smoking:
= 10 + 5/(1.5)
= 13.33

(4) Here t = 8

Discount Rate:
= 1/(1+t)
= 1/(1+8)
= 1/9
= 0.11

Discounted utility of quitting smoking 8 days from now:
= 5+(10/1.11)
= 14

(5) Present discounted utility of not quitting from 8 days from now:
= 10 + (5/1.11)
= 14.5