Answer appropriately

Figure 1.2 4.0 Grades in Economics (G.P.A) 4.0 Grades in English (G.P.A) The PPC in Figure 1.2 indicates a student who: a. is equally proficient in Economics and English. O b. is more proficient at Economics than English O c. prefers Economics over English. d. is more proficient at English than Economics. e. prefers English over Economics.The fact that the F'F'F usually bows away from the origin implies that ii? getting more of one good means getting more of another good. as the production of any good increases. there is an increase in the opportunity cost of producing it. getting more of one good means getting less of another good- as the production of any good increases. there is a decrease in the opportunity cost of producing it. 1. (a) Explain what is meant by the transition probability matrix of a homogeneous Markov chain. [5 marks] (b) Explain what is meant by the stationary distribution of a Markov chain? [5 marks] (c) A Markov chain has transition probability matrix, A, with entries Ouj; and stationary distribution . Write down an expression for the entries of the reverse Markov chain. [5 marks (d) Consider the following transition probability matrix of a homogo- neous Markov chain, with three states i,j and k (the TPM is in that order). If the stationary vector of the chain is (1/9, 2/9, 2/3), determine whether the Markov chain is reversible. 1 /0.2 0.2 0.6 0.1 0.6 0.3 4 \\0.1 0.1 0.8 [5 marks] (e) Let X1, X2, Xa be a sequence of random variables resulting from the above Markov chain. If X1 = i and Xs = j what is the probability that X2 = k? [5 marks]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 A decrease in the supply of coconut will increase the price of German O 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