Question One Once upon a time, there was an isolated small village where the people loved their land and had no desire to move away. The adult villagers had five job options to become either a farmer, butcher, baker, teacher, or doctor. For convenience, let the above occupations be A, B, C, D, and E, respectively. It is also known that: • • • • Once a resident became a farmer, the probability for them to continue being a farmer or become a future butcher, baker, teacher, or doctor was 50%, 28%, 10%, 10%, and 2%. Once a resident became a butcher, the probability for them to continue being a butcher or become a future farmer, baker, teacher, or doctor was 50%, 20%, 10%, 19%, and 1%. Once a resident became a baker, the probability for them to continue being a baker or become a future farmer, butcher, teacher, or doctor was 50%, 20%, 20%, 8%, and 2%. Once a resident became a teacher, the probability for them to continue being a teacher or become a future farmer, butcher, baker, or doctor was 10%, 40%, 30%, 20%, and 0%. Once a resident became a doctor, the probability for them to continue being a doctor was 100%. Utilize the given information to complete the following: a) Present a model to describe the job situation in the village. b) Find the probabilities for grandparents and grandchildren to choose the same occupations. c) Suppose long-term research is conducted. When the number of generations goes to infinity, what predictions would you make about the population distribution among the occupations?
Question One Once upon a time, there was an isolated small village where the people loved their land and had no desire to move away. The adult villagers had five job options to become either a farmer, butcher, baker, teacher, or doctor. For convenience, let the above occupations be A, B, C, D, and E, respectively. It is also known that: • • • • Once a resident became a farmer, the probability for them to continue being a farmer or become a future butcher, baker, teacher, or doctor was 50%, 28%, 10%, 10%, and 2%. Once a resident became a butcher, the probability for them to continue being a butcher or become a future farmer, baker, teacher, or doctor was 50%, 20%, 10%, 19%, and 1%. Once a resident became a baker, the probability for them to continue being a baker or become a future farmer, butcher, teacher, or doctor was 50%, 20%, 20%, 8%, and 2%. Once a resident became a teacher, the probability for them to continue being a teacher or become a future farmer, butcher, baker, or doctor was 10%, 40%, 30%, 20%, and 0%. Once a resident became a doctor, the probability for them to continue being a doctor was 100%. Utilize the given information to complete the following: a) Present a model to describe the job situation in the village. b) Find the probabilities for grandparents and grandchildren to choose the same occupations. c) Suppose long-term research is conducted. When the number of generations goes to infinity, what predictions would you make about the population distribution among the occupations?
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.16P
Related questions
Question
Use Markov Chain to solve the questions.
Use probabilities like
PAB = workers leave A and move to B
and then create matrices.
Thank you
Transcribed Image Text:Question One Once upon a time, there was an isolated small village where the people loved
their land and had no desire to move away. The adult villagers had five job options to become
either a farmer, butcher, baker, teacher, or doctor. For convenience, let the above occupations
be A, B, C, D, and E, respectively.
It is also known that:
•
•
•
•
Once a resident became a farmer, the probability for them to continue being a
farmer or become a future butcher, baker, teacher, or doctor was 50%, 28%, 10%,
10%, and 2%.
Once a resident became a butcher, the probability for them to continue being
a butcher or become a future farmer, baker, teacher, or doctor was 50%, 20%,
10%, 19%, and 1%.
Once a resident became a baker, the probability for them to continue being a baker
or become a future farmer, butcher, teacher, or doctor was 50%, 20%, 20%, 8%,
and 2%.
Once a resident became a teacher, the probability for them to continue being a
teacher or become a future farmer, butcher, baker, or doctor was 10%, 40%, 30%,
20%, and 0%.
Once a resident became a doctor, the probability for them to continue being a
doctor was 100%.
Utilize the given information to complete the following:
a) Present a model to describe the job situation in the village.
b) Find the probabilities for grandparents and grandchildren to choose the same
occupations.
c) Suppose long-term research is conducted. When the number of generations goes to
infinity, what predictions would you make about the population distribution among
the occupations?
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