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4. Do risk premiums vary with income? Let's consider a concrete case. You are an old person with some amount of wealth, W = X, which provides you utility U(W) = VW. Unfortunately, you are so old and frail there is 10% probability that you will be injured in a fall and your wealth will be reduced by $1000 to cover the medical expenses.' + i. Do you think the risk premium you are willing to pay for full insurance against the loss varies with X? If it does do you think it will be people with more wealth are more risk averse or less risk averse? Give some intuition. ii. Calculate the risk premium that you are willing to pay for full insurance at an actuarially fair price if your initial wealth is X = $2,000.- iii. Repeat the previous part for an initial wealth of X = $1,000,000. What did you learn? 4. Do risk premiums vary with income? Let's consider a concrete case. You are an old person with some amount of wealth, W = X, which provides you utility U(W) = VW. Unfortunately, you are so old and frail there is 10% probability that you will be injured in a fall and your wealth will be reduced by $1000 to cover the medical expenses.' + i. Do you think the risk premium you are willing to pay for full insurance against the loss varies with X? If it does do you think it will be people with more wealth are more risk averse or less risk averse? Give some intuition. ii. Calculate the risk premium that you are willing to pay for full insurance at an actuarially fair price if your initial wealth is X = $2,000.- iii. Repeat the previous part for an initial wealth of X = $1,000,000. What did you learn