4. (20 points) Consider an economy where there are N individuals that either take occupations as fisherman or hunters. The fraction of fisherman and hunters at time are F; and H; respectively. Attime t = 0, F; = 0.10 and H; = 0.90. Each period, 90% of the fisherman become fisherman again in the next period, whereas the remaimning 10% become hunters. 70% of the hunters become hunters again the next period, whereas the remaining 30% become fisherman. a) (4 points) Let x; be the vector that denotes the fraction of the population 1n each occupation each period such that, F : = [Hi]a\"d = [n.gu : Find the Markov matnx, P, that solves x,.; = Px,. (Hint: The first column should be the transition fractions for people who are currently fisherman, and the second column should be the transition fractions for people who are currently hunters). b) (6 points) What fraction of the population will be fisherman at t = 37 ) (10 points) What 1s the steady state