Expected Change in GNP: Calculation and Analysis

Expected Change in GNP

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Question

Suppose the probability that oil prices will rise any given quarter is 0.51, and the probability that oil prices will stay level or decline is 0.49. If oil prices rise, GNP will contract by 1% with 80% probability, and expand by 0.5% with 20% probability. If oil prices decline or stay level, GNP will expand 3% with a 75% probability and contract 0.5% with a 25% probability. What is the expected change in GNP in the next quarter?

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A

We need the total probability rule for expected value, for which the formula is E(X) = E(X | S_1) * P(S_1) + E(X |S_2) * P(S_2) + ... + E(X |S_n) * P(S_n). Here, E

(X) is the expected change in GNP. S_1 is the event that oil prices rise, and S_2 is the event that oil prices fall. Therefore, E(X) = 0.51 * (- 1%*80% + 0.5%*20%) +

0.49 * (3%*75% - 0.5%*25%) = 0.68%, an expansion.

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