5. [3] The U.S. economy is in trouble, and Congress is here to help. You have be

Question

5. [3] The U.S. economy is in trouble, and Congress is here to help. You have been hired to estimate the expected time until the economy recovers, given its current condition. Congress is about to enact special legislation to get the economy going again. You have estimated that after the legislation passes, there is ·a 20% chance the economy will recover in one year, ·a 75% chance the economy will sputter for 3 years and then return to its present condi- tion, and ·a 5% chance the economy will recover in 20 years. If the economy returns to its present condition (as in the second item above), you assume that another round of legislation will be passed, with identical probabilities above; that is, the process effectively "starts over." What is the expected time to economic recovery?

Explanation / Answer

Let's assume that the expected time to recovery is represented by E[T].

According to the given data we have:

E[T] = 0.20*1 + 0.75(3+E[T]) + 0.05*20

Solving the above equation we get:

x = 13.8 years

Hope this helps !

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