Due to the COVID-19 pandemic, supply chain issues were made much worse. Assume that the level of supply chain disruptions (low, moderate, or high) experienced on a given month depends on the level of supply chain disruptions experienced the previous month. Such level is measured as the function of the supply delivery times and the manufacturing outputs. If the index of global supply chain disruptions is low in a given month, it will continue to be low in the next month with probability 0.7, and it will be moderate next month with probability 0.3. If the index is moderate in a given month, it will be low in the next month with probability 0.5; otherwise, it will be moderate or high with equal probability. If the index is high in a given month, then in the next month there is a 60% chance it will be high and a 40% chance it will be moderate.

(a) Define the states and transition probability matrix P.

(b) Assume that it is equally likely that the index will be moderate or low in July 2023 and it is four times more likely that the index will be high. Firms already worry about supply chain disruptions during the 2023 holiday season. What is the probability that the December 2023 index will be high?

(c) ( What proportion of months are expected to have a high index of global supply chain disruptions in the long run?

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