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]. 10. Cade Ward buys a new boat for $16,200. He puts 15% down and obtains a simple interest amortized loan for the rest of the amount at 6% for 5 years. (a) Find his monthly payment. (b) Find the total interest. (0) If Cade sells the boat 3 years after he bought it, nd the unpaid balance on his loan. (d) Estimate loan fees if the lender states that APR of the loan is 6.2 %. 12. Normative Economics is: A) An economic prediction based on an analysis of historical trends B) An analysis of actual economic results C) An economic model that predicts future economic results based upon assumed change to one or more economic factors, while holding other economic factors constant D) Both A and C 13. What can cause the Production Possibility Frontier (PPF) to contract, that is to say, move the PPF further to the left? A) Minimum Wage B) Price Ceiling C) An increase in raw materials needed in production D) Price Floor 14. When the market is in equilibrium: A) More profit is made B) Consumers benefit but producers do not C) The use of economic resources is maximized D) Both B and C 15. Minimum wage is a price floor that A) Might increase the cost of production if wages would have otherwise been lower B) May increase both consumer and producer value C) Might not increase the cost of production if wages are already higher D) Both A and C 16. Economic decisions are made "on the margin". What does this mean? A) Tradeoffs are based on marginal value B) Tradeoffs are based on average value C) Tradeoffs are based on total value D) None of the above 17. What does a Production Possibility Frontier represent? A) The line or curve that defines the comparative advantage between products B) The line or curve that defines the cost production tradeoffs between products C) The line or curve that defines the consumption tradeoffs between products D) Both A and B