12 A simple future elderly model. Our model will follow a cohort of 65-year-olds as they age, and each period of the model will represent one year. In the first version of our model, the elderly will have three states:h(healthy),s(sick with cancer), andr(deceased). In a given period, each elderly person assumes a certain state for the entire period. Between periods, the elderly transition with the following likelihoods:

1.Healthy to deceased:P(rt+1|ht)=

2.Healthy to sick:P(st+1|ht)=(1)

3.Sick to deceased:P(rt+1|st)=+(1)

where, for instance, condition 1 implies that a person has achance of becoming deceased in periodt+1, given that she is healthy in periodt.

cIn each period, the elderly incur certain health care costs. Assumech=$100 (that is, assume the healthy incur $100 each period). Also assumecs=$500 andcr=$0. How much will a cohort of 1,000 healthy 65-year-olds cost during the zeroth period of the model (when they are all still healthy)? How much would you expect they will cost altogether during the first period of the model (on average)? Express your answers in terms ofch,cs,cr,,, and.