# In the land of Longovia, everybody lives at most three periods

November 24, 2016

1. In the land of Longovia, everybody lives at most three periods. That is, everyone who enters period 3 alive dies. Some of the people in Longovia are from race A, and some from race B.

The probability that a race A person will survive period 1 is 1.00 (nobody dies), and the probability that a race B person will survive period 1 is 0.8. The probability that a race A person who enters period 2 will survive it is 0.2, and the probability for a race B person is 0.1.

At the beginning of 2013, race A had 1000 people starting each of three periods of their life. Race B had 2000 starting period 1, 1000 starting period 2, and 1000 starting period 3.

a. Find the crude death rate in 2013 for each race. Which race appears to be healthier?

b. Suppose that race B had the same distribution of ages as race A did. What would race B’s age-adjusted death rate be? Which race appears healthier?

c. Suppose that race A had the same distribution of ages as race B did? What would race A’s age-adjusted death rate be? Which race appears healthier?

d. Extra credit: Suppose that within each race the same number of people are born every year. In the long run, what is the age distribution within race A? Within race B? (HINT: in the long run, the number of people leaving each age will be the same as the number entering. Let the proportion in each age group be unknowns. The equality conditions between entering and leaving and the requirement that proportions sum to one give you the same number of equations as you have unknowns.) What are the crude death rates for each race in the long run.

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