In a Certain City, the Democratic, Republican, and Consumer Parties

question 3

Multiple Choice

In a certain city, the Democratic, Republican, and Consumer parties always nominate candidates for mayor. The probability of winning in any election depends on the party in power and is given by the following transition matrix. ​ ​
Using the given transition matrix and assuming the initial-probability vector is , find the probability vector for the fourth stage of the Markov chain. (This initial-probability vector indicates that a Consumer is certain to win the initial election.)
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Definitions:

Phillips Curves

The economic theory suggesting an inverse relationship between inflation and unemployment rates over the short-term.

Expected Inflation

The rate of inflation that consumers, businesses, and investors anticipate will occur in the future, which can influence economic behavior in the present.

Phillips Curve

An economic theory that suggests an inverse relationship between the rate of unemployment and the rate of inflation in an economy.

Sacrifice Ratio

A measure of the economic costs of reducing inflation, often represented by the loss of output or employment.