Steve Greene is considering purchasing fire insurance for his new home. The insurance policy would cost Steve $2,000 and would cover the full cost of all repairs to his house in the event of a fire. In Steve's area, the probability of not having a house fire P(none) = .90, the probability of having a fire that causes light damage P(light) = .05, and the probability of having a fire that causes heavy damage P(heavy) = .05. The costs associated with the two decision alternatives and the three states of nature are listed in the table below:

Steve is looking to select the decision with the lowest expected total cost. In the spaces provided below each question, please address the following:

(i) Prepare a fully labeled decision tree for this problem. Be sure to appropriately label all of the nodes and branches with decision alternatives, states of nature, prior probabilities, payoffs, and expected values. Show your calculations.

(ii) Should Steve buy fire insurance based upon the expected value approach to decision making? Justify your answer.

(iii) What would be Steve's expected cost if he could accurately predict the extent of fire damage to his home?

(iv) How much would it be worth to Steve if he could accurately predict the extent of fire damage to his home?

(v) Suppose that, for this question only, it has been an especially dry summer and the probabilities of light or heavy fire damage to Steve's home have doubled. Should Steve buy fire insurance based upon the expected value approach? Justify your answer.

(vi) Determine Steve's optimal decision strategy using the minimal expected regret criterion. Explain why it makes sense that the expected value of perfect information matches the minimum expected regret.