Question

you are given the option of when you would like to wash your neighbors car. You may choose any time in the next three days (today, tomorrow or the day
after tomorrow). Your consumption utility for washing a car is u(c) = -50c. You have a daily discount rate of 0.25.

a. Using the standard economic model of exponential discounting, when
do you choose to wash your neighbors car?

b. If you derive utility from anticipation and consumption and your α = 1 when do you wash the car?

c. If you derive utility from anticipation and consumption and your α = 3
when do you wash the car?

d. When do you wash the car if α = 3, but your daily discount rate is now
0.99?

Answer 1

u(c) = -50c , c= time period (for 3 days)

daily discount rate of 0.25.

The given below is the formula of calculating exponential discounting for intertemporal choices.

a) Today : -50(1) = -50

Tomorrow : 0.25*-50(2) = -25

Day after : 0.25^2*-50(3) = -25 = -6.125 (so washing tha car day after gives the maximum utility/minimum negative utility

(b) When we have utility from anticipation with alpha = 1

Today : -50(1) = -50

Tomorrow : (1)0.25*-50(2) = -25

Day after : (1)0.25^2*-50(3) = -25 = -6.125 (so washing tha car day after gives the maximum utility/minimum negative utility

(c) When we have utility from anticipation with alpha = 3

Today : -50(3) = -150

Tomorrow : (3)0.25*-50(2) = -75

Day after : (1)0.25^2*-50(3) = -25 = -18.125 (so washing tha car day after gives the maximum utility/minimum negative utility

(c) When we have utility from anticipation with alpha = 3 and now the discount rate is 0.99

Today : -50(3) = -150

Tomorrow : (3)0.99*-50(2) = -297

Day after : (3)0.99^2*-50(3) = -437 (so washing tha car day1 gives the maximum utility/minimum negative utility)