Suppose the probability that electricity prices will rise any given quarter is 0.60, and the probability that oil prices will stay level or decline is 0.40. If electricity prices rise, corporate profits will decline by 2% with 90% probability, and increase by 0.5% with 10% probability. If electricity prices decline or stay level, corporate profits will increase 3% with a 65% probability and decline 0.5% with a 35% probability. What is the expected change in corporate profits in the next quarter?
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A. B. C. D.B
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 corporate profits. S_1 is the event that electricity prices rise, and S_2 is the event that electricity prices fall. Therefore, E(X) = 0.60 *
(-2%*90% + 0.5%*10%) + 0.40 * (3%*65% - 0.5%*35%)= -0.34%, a decline.