Task #2. (solve for various α, β, γ equal to 0,1,...,9)
There's not much time before a winter holiday. Tom got a plan for a gym training programme, encompassing 8 sessions with progressing difficulty. This difficulty (measured as loss of utility) is presented in the table below. Finishing the whole programme will allow Tom to have fun when skiing and will provide during winter vacation a utility equal to 130+3α+β=........
Missing even one session means the whole programme is ruined (no utility is gained when skiing).
Tom discounts future with a quasi-hyperbolic function, being indifferent between various moments in the future, but preferring the present moment to the future - the latter is discounted with a factor 1½.
Assume that Tom is just before the moment the first session should start. Assume that whenever he is indifferent between going to the gym and not, he will go.
Session
1
2
3
4
5
6
7
8
Disutility
1
1
2
2+α=........
2+2α+β=.........
30
40
50
A. How many times will Tom go if he is time consistent?
B. How many times will Tom go if he is naïve?
C. How many times will Tom go if he is sophisticated?
