6. 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) = 2W , 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.