Question

Suppose the economy can be in one of the following two states: (i) Boom or "good" state and (ii) Recession or "bad" state. Both states can occur with a probability of 1/2. Consider a risky asset that would have a price of $30 in the good state and $10 in the bad state. Two investors are evaluating this asset. The asset is currently trading at $20. The utility function of the first investor (A) is u(W) = 2√W, where W is the wealth level. The utility function of the second investor (B) is u(W) = W + 10. a) What is the maximum price that investor A would be willing to pay for the risky asset? Show your calculations clearly. b) Draw the utility function of investor A and identify the maximum price the investor would be willing to pay for the risky asset. Please label the graph clearly. c) What is the maximum price that investor B would be willing to pay for the risky asset? Show your calculations clearly. d) Draw the utility function of investor B and identify the maximum price the investor would be willing to pay for the risky asset. Please label the graph clearly. e) Assume that the probabilities of good and bad states change due to some macroeconomic news announcement. The good state now is expected to occur with a probability of 2/3 while the bad state is expected to occur with a probability of 1/3. What is the maximum price investors A and B would be willing to pay for the risky asset now? Show your calculations clearly.

          Suppose the economy can be in one of the following two states: (i) Boom or "good" state and (ii) Recession or "bad" state. Both states can occur with a probability of 1/2. Consider a risky asset that would have a price of $30 in the good state and $10 in the bad state. Two investors are evaluating this asset. The asset is currently trading at $20. The utility function of the first investor (A) is u(W) = 2√W, where W is the wealth level. The utility function of the second investor (B) is u(W) = W + 10.

a) What is the maximum price that investor A would be willing to pay for the risky asset? Show your calculations clearly.
b) Draw the utility function of investor A and identify the maximum price the investor would be willing to pay for the risky asset. Please label the graph clearly.
c) What is the maximum price that investor B would be willing to pay for the risky asset? Show your calculations clearly.
d) Draw the utility function of investor B and identify the maximum price the investor would be willing to pay for the risky asset. Please label the graph clearly.
e) Assume that the probabilities of good and bad states change due to some macroeconomic news announcement. The good state now is expected to occur with a probability of 2/3 while the bad state is expected to occur with a probability of 1/3. What is the maximum price investors A and B would be willing to pay for the risky asset now? Show your calculations clearly.

Added by Frank K.

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