David is planning to invest $100,000 for one year. There are two companies that interest David but he can only invest in one of them. David is a rational, risk-averse investor with utility equal to the square root of the net return on his investment. His choices are: 1. Action a: invest $100,000 in Electric Cars Inc. shares. 2. Action az: invest $100,000 in Cars Inc. shares. David's payoff from these investments depends on the future price of gasoline. If the price of gasoline is high, David will earn a net return of $1,500 on Electric Cars shares and only $400 on Cars shares. Alternatively, if the price of gasoline is low, he will earn $1,000 on Cars shares and only $500 on Electric Cars shares. David's prior probability on the price of gasoline being high is 0.3 and being low is 0.7. b. Instead of acting now, David decides to obtain more information. After undertaking extensive research, he determines that gasoline refiners are expecting good news. That is, gasoline refiners expect the price of gasoline to be high. He has determined that if future gasoline prices are going to be high, there is a 0.8 probability that gasoline refiners will expect good news. Alternatively, if future gasoline prices are going to be low there is a 0.3 probability that gasoline refiners will expect good news. Provide the information system in terms of the conditional probabilities, using a 2 x 2 matrix, that depicts this new information. c. Since gasoline refiners are expecting good news, determine whether David should invest in Electric Cars or Cars. Show your calculations