On Any Particular Day,an Individual Can Take One of Two

question 21

Essay

On any particular day,an individual can take one of two routes to work.Route A has a 25% chance of being congested,whereas route B has a 40% chance of being congested.The probability of the individual taking a particular route depends on his previous day's experience.If one day he takes route A and it is not congested,he will take route A again the next day with probability 0.8.If it is congested,he will take route B the next day with probability 0.7.On the other hand,if he takes route B one day and it is not congested,he will take route B again the next day with probability 0.9.Similarly,if route B is congested,he will take route A the next day with probability 0.6.
a.Construct the transition matrix for this problem.(Hint: There are four states corresponding to the route taken and the congestion.The transition probabilities are products of the independent probabilities of congestion and next-day choice.)
b.What is the long-run proportion of time that route A is taken?

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Definitions:

Deadweight Loss

A decrease in economic efficiency occurring when a good or service does not reach its free market equilibrium.

Economic Profits

The difference between total revenue and total economic costs (including both explicit and implicit costs), representing the additional income above the opportunity cost.

Monopoly

A market structure characterized by a single seller who has exclusive control over the supply of a good or service, and where the entry of new firms is hindered.

Monopolist's Profit

The excess revenue a monopolist earns over its costs, attributable to its ability to set prices above competitive levels due to lack of competition.