6 Jan 2021

ABC plays football with the DEF Club in Mexico. If he does not suffer any injury by the end of the season, he will get a professional contract with GHI, which is worth 10,000 euros. If he is injured, he will get a contract as a fitness trainer in Ecuador, which is only worth 100 euros. The probability of suffering an injury is 10%. He is likely to get through the season unscathed with a 90%-probability.

Describe the gamble. How high is the expected value of this gamble? How high is the expected utility, if his Bernoulli utility function of the VNM-utility function is u(x)=x^0.5? Assuming he could buy insurance at the price P that would pay him 9,900 euro in the case of an accident, how high could the maximal value of P be for ABC to still afford the insurance? Interpret the certainty equivalent. How high is the certainty equivalent c of the above gamble? Calculate the coefficients of absolute risk aversion and interpret it. Is that a case of decreasing absolute risk aversion?

6 Jan 2021

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