(a) Consider an economy of population size P . Suppose in a given time period each person in

this economy has

n* = (1/a) (x/P) ^

children (assume , x and are strictly positive), and the population evolves according

to P' = nP , where P' denotes tomorrows population size. What is the steady state population size, P^ss?

(b) Consider an economy as described in d) that is in steady state. Now, suppose that a

catastrophic event kills half the population. Compute the values that P and n take in the short run and in the long run.

(c) Consider an economy as described in d) that is in steady state. Suppose the government

implements a policy that induces people to double their number of children. How do we need to change to reflect such a policy change. Compute the values that P and n take in the short run and in the long run if such a policy is implemented.