A simple future elderly model. Which is a version of the FEM designed at RAND. 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), and r (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 a chance of becoming deceased in period t + 1, given that she is healthy in period t.

a. In this model, cancer patients never get cured; that is, they never return to state h once they enter state s. Express this idea in terms of a conditional probability statement like the ones listed above.

b. A diagram will be created, with circles representing each possible state and arrows between them with transition probabilities. Note that the sum of probability emanating from each state must equal one. [Hint: Some or all of the states may have self-directed arrows.]

c. In each period, the elderly incur certain health care costs. Assume ch = $100 (that is, assume the healthy incur $100 each period). Also assume cs = $500 and cr = $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 of ch, cs, cr, , , and .