Questions asked about cwk 9 and answers:


Q1: nx = CS(x)/λx does not give me the same values as nx(t) = 2tnx  ? for example n1=C/4 using first formula, and n1(t)=2n0=2c? using the second formula
 
 
A1: The Euler solution is one that has n_x(t)=(λ^t)n_x where n_x is the initial age distribution, i.e. n_x=n_x(t) at t=0.

For an Euler solution to exist, the birth rates and survival probs should stay constant over time. If this is the case then choosing λ to be the uniques positive solution of the equation sum_x b_xs(x)/λ^{x+1}=1 and choosing the initial age distribution in the form

n_x=(s(x)/λ^x)n_0   (The constant C in cwk 9 is just n_0)

one gets an Euler solution, i.e. n_x(t)=(λ^t)n_x satisfies eqs (1)-(2) in notes.

You seem to confuse the initial age distribution n_x (no dependence on time) and the Euler solution n_x(t)=(λ^t)n_x (where n_x is the initial age distribution).

Q2: Using the eigenvalues of the matrix, I was wondering if n0=24B is an arbitrary value assigned to n0, so that n1 and n2 will be integers?

A2: It is not necessary for n_0, n_1 and n_2 to be integers. These numbers can be rates or expected numbers in the age groups if the initial age distribution is uncertain and only probabilities are known.