Markov chain
2. A Markov chain with state space {1, 2, 3} has transition probability matrix 0.6 0.3 0.1 [Pa = 0.3 0.3 0.4 0.4 0.1 0.5 (a) Is this Markov chain irreducible? Is the Markov chain recurrent or transient? Explain your answers. (1)] What is the period of state 1? Hence deduce the period of the remaining states. Does this Markov chain have a limiting distribution? (0) Consider a general three-state Markov chain with transition matrix P11 P12 P13 1?: 1021 1022 p23 P31 P32 P33 Give an example of a specic set of probabilities pm; for which the Markov chain is not irreducible (there is no single right answer to this, of course l]. OPPORTUNITY COST WORKSHEET 2 Below, you are provided Gerardo's Production Possibilities Frontier between biology homework and economics homework before and after he attends economics tutoring sessions. You will use this information to identify how a technological innovation that affects production of only one good alters the opportunity cost associated with producing both goods. PPF1 depicts Gerardo's PPF between biology homework and economics homework before he attends economics tutoring sessions. PPF2 depicts Gerardo's PPF between biology homework and economics homework after he attends economics tutoring sessions. 14 Economic Homework (in pages] 10 12 14 Minlazy Homework [in pages) Part 1: Before Gerardo attends economics tutoring sessions, what is his opportunity cost of producing an additional page of economics homework? Part 2: Before Gerardo attends economics tutoring sessions, what is his opportunity cost of producing an additional page of biology homework? * Part 3: After Gerardo attends economics tutoring sessions, what is his opportunity cost of producing an additional page of economics homework?Part 1 (0.2 pt) X Feedback See Hint A consumer receives an endowment of $200.00 this period and $800.00 next period. Currently the interest rate is 11.00%. The present value of the endowment is $ X 222 . (Give your answer to two decimals.) Part 2 (0.4 pt) Feedback See Hint Suppose that instead, the endowment is $240.00 this period and $1040.00 next period. Suppose that the interest rate is still 11.00%. Now the present value of the endowment is $ x 1394.40 . (Give your answer to two decimals.) With the new endowments, the consumer is " wealthier Part 3 (0.4 pt) Feedback See Hint Now suppose that the endowment is $150.00 in the first period and $775.00 in the second period. The interest rate is still 11.00%. Now the present value of the endowment is $ x 1010.25 . (Give your answer to two decimals.) With the new endowments, the consumer is poorer
