Determine the following

2. A Markov chain with state space {1, 2, 3} has transition probability matrix 00 0.3 0.1 a: 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. (b) What is the period of state 1? Hence deduce the period of the remaining states. Does this Markov chain have a limiting distribution? (c) Consider a general three-state Markov chain with transition matrix 3011 3012 1013 P = P21 P22 P23 1031 P32 P33 Give an example of a specic set of probabilities jag-'3; for which the Markov chain is not irreducible (there is no single right answer to this1 of course l]. 1. Consider the Markov chain with the following transition matrix. 0 0.5 0.5 0.5 0 0.5 0.5 0.5 0 (a) Draw the transition diagram of the Markov chain. (b) Is the Markov chain ergodic? Give a reason for your answer. (c) Compute the two step transition matrix of the Markov chain. (d) What is the state distribution *2 for t = 2 if the initial state distribution for t = 0 is no = (0.1, 0.5, 0.4) ?Determine if the following items represent an example of positive economics or normative economics. The richest 1% of Americans should pay more taxes than the rest of the 99%. O Positive Economics O Normative Economics O A decrease in the supply of coconut will increase the price of German Normative Economics chocolate cake, a good which requires coconut shavings as a key ingredient O Positive Economics The higher the minimum wage, the higher the price of goods and services Normative Economics is likely to bo. OO Positive Economics Social welfare spending in Sweden occupies too large a portion of the O Positive Economics national budget. O Normative Economics