Hi, hope all is well. I need some assistance with these couple of problems that will require an excel spreadsheet. Thank you!
Social Mobility Model
A study of social mobility across generations was conducted and three social levels were
identi?ed: 1= upper level (executive, managerial, high administrative, professional); 2=
middle level (high grade supervisor, non-manual, skilled manual); 3= lower level (semiskilled or unskilled). Transition probabilities from generation to generation were estimated
.45 .48 .07
P = .05 .70 .25 .
.01 .50 .49
Suppose that Adam is in level 1 and Cooper is in level 3, and that each person has one
o?spring in each generation. Consider T = 50 generations. Assume sample size N = 104
and initial distribution [0.5, 0.0, 0.5].
(a) What is the long-run percentage of each social level, i.e., steady-state distribution? What
if initial distributions is [1, 0, 0] or [0, 0, 1]? Does the initial distribution matter in the long
(b) Compute the probability A(t)( resp. C(t)) that the 1st, 2nd, . . . , 10th generation
o?spring of Adam (resp. Cooper) is in level 1, respectively. Graph A(t) and C(t) against
t = 1, 2, . . . , 10. What is A(10) and C(10)?
(c) On average, how many generations (mean and 95% CI) does it take for Adam?s family
to have the ?rst level 3 o?spring? On average, how many generations (mean and 95% CI)
does it take for Cooper?s family to have the ?rst level 1 o?spring?
(d) What are the social and policy implications of these results, in terms of eduction, taxation, welfare programs, etc.?
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