Jim and Dwight work for Dunder Mifflin Paper Company, Inc. Both of them are risk-averse in income and have the following utility function of wealth: U(W) = In (W) During any given year, the probability of becoming ill for Jim is Pjim= 0.3 and for Dwight is P Dwight = 0.1. Both Jim and Dwight have $5,000 in initial wealth. If a person falls ill, the cost of treatment (that is, damages) is $1000. Dunder Mifflin is deciding whether to offer insurance to Jim and Dwight. The firm is assumed to be risk-neutral. Each worker pays Dunder Mifflin a premium at the beginning of the year, and if the worker falls ill, the insurer will pay the worker some amount of coverage. Jim and Dwight know their respective probability of falling sick but neither Dunder Mifflin nor Dunder Mifflin's insurance company can observe their health status. Jim and Dwight will, of course, misrepresent their type if it is in their interest to do so. Dunder Mifflin decides what insurance plan (coverage and premium) to offer Jim and Dwight, and Jim and Dwight decide whether to purchase the plan or not by maximizing their expected utility.a) What is the expected utility of Jim if he does not purchase any insurance plans? (up to 4 decimal places) b) What is the expected utility of Dwight if he does not purchase any insurance plans? (up to 4 decimal places) c) Dunder Mifflin proposes a contract for Jim. The contract offers full coverage of the damages (i.e., Jim receives $1000 if he falls ill). What is the maximum premium that Dunder Mifflin can charge Jim so that Jim is indifferent between buying and not buying insurance? (up to 4 decimal places) (Hints for solving In(x) functions: If In(x) = 10, then x = e10 => .. x = 22026.4658 If In(x - 100) = 2, then x - 100 = e2 => x - 100 = 7.3891 => x = -92.6109 If In (225 - x) = 5, then 225 - x = e5 => 225 - x = 148.4132 => x = 76.5868d) If Dunder Mifflin offers Jim insurance at the premium that you found in (c), what is the expected payment that Dunder Mifflin could receive? (up to 4 decimal places) Would Dunder Mifflin be willing to offer Jim this contract? e) Dunder Mifflin proposes the same contract for Dwight which means that the contract offers full coverage of the damages (i.e., Dwight receives $1000 if he falls ill). What is the maximum premium that Dunder Mifflin can charge Dwight so that Dwight is indifferent between buying and not buying insurance? (up to 4 decimal places) f) If Dunder Mifflin offers Dwight insurance at this premium, what is the expected payment that Dunder Mifflin could receive? (up to 4 decimal places) Would Dunder Mifflin be willing to offer Dwight this contract? g) Say, only Jim bought the contract but Dwight did not. What should be the minimum premium that Dunder Mifflin could charge for a full insurance contract to just break even? Would Jim want to buy this contract? Might this contract seem attractive to Dwight?h) Dunder Mifin decides to launch two contracts \"Total Coverage\" and \"Minimal Coverage.\" The characteristics of both contracts are given in the following table. Total Coverage Minimal Coverage Payout it ill $1000 $250 Premium $310 330 (i) Calculate the following for Jim (up to 4 decimal places): E[U(T0tal)]= $ E[U(Minimal)]= $ E[U(No insurance)]= $ 0 Jim maximizes expected utility by buying (ii) Calculate the following for Dwight (up to 4 decimal places): E[U(Total)]= $ E[U(Minimal)]= $ E[U(No insurance)]= $ 0 Dwight maximizes expected utility by buying