Consider the following FIRE-INSURANCE PROBLEM where fire partially destroys a $500 house. EVENT FIRE PROBABILITY 0.02 OUTCOME $100 NO FIRE 0.98 $500 INSURANCE PAYOUT PREMIUM $400 0 ?? ?? (a) What do we mean when we say an agent is Risk Averse? (b) Assume utility is U(x) = v(x). Why does this utility function imply the agent is risk-averse? Use a figure/diagram to explain. (c) What is the expected payoff and expected utility of having no insurance for this agent? (d) What do we mean by certainty equivalent? What is the certainty equivalent of no insurance? (e) What is the maximum the agent will pay for complete insurance that pays out $400 in the case of fire? Show your work. (f) Suppose insurance is incomplete and only pays out $300 in case of fire. What is the maximum the agent will pay for insurance now? Show your work and explain relative to (e). Note: I am interested in your solution technique more than the answer. So show your thought process.