Suppose Tony is deciding on buying an expensive road bike. There are three periods: Period 0 Tony decides to buy or not to buy the bike. The cost of the bike is equal to P utility units. (u0(buy) = -P)
Period 1 If Tony has bought the bike, then he has to decide if he is going out for a ride. If he goes for a ride, then his effort generates a utility cost of E units of utility. (u1(ride) = -E)
Period 2 If Tony has bought a bike and has ridden on it, then a health benefit equivalent to B utility units accrues. (u2(ride) = B)

Required:
Suppose Tony is naive and absolutely patient in the long term (δ = 1) but has a severe present bias (β = 1/3 ). Assume again P = 2, E = 4 and B = 8. Is he in period 0 expecting to ride in period 1 if he buys the bike? Is he actually going to ride if he has bought a bike and arrives at period 1? Is he going to buy the bike?