If a patient has a probability of being sick of 0.1 and a probability of being healthy of 0.9. If the person has a good health her wealth will be $100, if she has bad health her wealth will be $64. Suppose that the utility of wealth come from the following utility function: U(W)=W^0.5.
The reduction in wealth if the patient has bad health is
If person has a good health then income will be 100 and wealth=(100)0.5=10
If person had bad health, her wealth will be 64.
Thus reduction in wealth due to bad health=100-64=36
If a patient has a probability of being sick of 0.1 and a probability of being...
If a patient has a probability of being sick of 0.1 and a probability of being healthy of 0.9. If the person has a good health her wealth will be $100, if she has bad health her wealth will be $64. Suppose that the utility of wealth come from the following utility function: U(W)=W^0.5. The expected utility of the patient if she has no insurance is
If a patient has a probability of being sick of 0.1 and a probability of being healthy of 0.9. If the person has a good health her wealth will be $100, if she has bad health her wealth will be $64. Suppose that the utility of wealth come from the following utility function: U(W)=W^0.5. The fair premium if she is full insured is?
A lab test produces a positive result with 90% probability when the patient is actually sick and with 10% if the patient is healthy. It is known that 15% of the population is sick. (a) What is the joint probability function of patients’ health and test results? (b) If the test is positive, what is the probability that the patient is actually sick? (c) The probability you just calculated in part 1b is the _____ probability of ____ given _____.
Lisa just inherited a vineyard from a distant relative. In good years (no rain or frost), she earns $10,000 from the vineyard. In bad years, she earns only $2,500. She estimates that the probability of a good year is 60%. a) Calculate the expected value of her earnings from the vineyard. b) Suppose Lisa has a utility function U(w)= pw, where w is her wealth. Assume that she has 0 initial wealth. Ethan, a grape buyer, offers to lease the...
An investor's utility function for money (Bernoulli utility function) is the square root of money: u(x)=√x. Her decision making can be modeled by assuming that she maximizes her expected utility. Her current wealth is 100. (All quantities are in hundreds of dollars.) She has the opportunity to buy a security that either pays 8 (the "good outcome") or loses 1 (the "bad outcome"). She can buy as many units as she wishes. For example, if she buys 5 units, she...
i) Suppose that Mary’s utility function is where W is wealth. Is she risk averse? Suppose that Mary has initial wealth of $125,000. How much of a risk premium would she require to participate in a gamble that has a 50% probability of raising her wealth to $160,000 and a 50% probability of lowering her wealth to $90,000? ii) Suppose that Irma’s utility function with respect to wealth is U(W) = 100 + 80W − W2. Find her Arrow-Pratt risk...
1. Suppose that an individual has a wealth of $50,000 and the utility of U(W) = VW. This individual has the option of investing all wealth in risky stock, which is worth $100 per share, which will be worth $105 per share in a good state with probability 1/2 and $95 per share in a bad state with probability 1/2. Assume, the interest rate is zero. (a) Find the expected value and the expected utility of investing all wealth in...
Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the choice of investing in a safe asset or a risky asset. $1 invested in the safe asset returns $1 with certainty. $1 invested in the risky asset returns $1.25 when the market state is "good" and returns $0.8 when the market state is "bad". The good state occurs with probability 2/3 and the bad state occurs with probability 1/3. Let x be the amount...
A person with the following utility function, u(x) = ln(x) faces a world where with probability 0.1 will suffer of identity theft which will reduce their wealth from $250000 to $100000. This means that we can write: E{u(.)] = 0.91n(x) +0.1ln(y) where x would be the wealth under no identity theft and y the wealth under identity theft. This means that the marginal utilities are: MU 0.9, MUy = 0.1 Using this information answer the following questions 1) What is...
A person with the following utility function, u(x) In(x) faces a world where with probability 0.1 will suffer of identity theft which will reduce their wealth from $250000 to $100000. This means that we can write: Eu(.0.91n(x)+0.1n(y) where would be the wealth under no identity theft and y the wealth under identity theft This means that the marginal utilities are: MU0.9 MUy = 0.1 Using this information answer the following questions 1) What is this persons attitude towards risk? explain...